---
url: >-
  https://jer-k.github.io/effect-prophet/benchmarks/linear/evaluation-linear-long-history-parallel.md
---

# Twelve folds, three years, sequential and parallel

 [← All linear growth benchmarks](/benchmarks/linear)

Prophet's default model on three years of daily rows, with twelve monthly cutoffs forecasting 30 days each. Python Prophet is also timed with `parallel="threads"` and `parallel="processes"`, which must give the same forecasts as running sequentially.

## Input

[`benchmark/inputs/v3/linear-long-history.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v3/linear-long-history.json): 1095 history rows and 365 forecast rows.

## Output

Largest difference: **0.22** (0.052% of the input's range).

Each row is one forecast made during cross-validation, next to the value that actually happened.

| Date | Actual | Effect Prophet | Python Prophet | Difference |
| --- | ---: | ---: | ---: | ---: |
| 2022-01-02 | 247.4845 | 249.4687 | 249.4689 | 0.00017 |
| 2022-01-03 | 247.9985 | 249.1054 | 249.1071 | 0.0017 |
| 2022-01-04 | 250.9901 | 249.6220 | 249.6254 | 0.0034 |
| 2022-01-05 | 251.2120 | 250.9387 | 250.9439 | 0.0052 |
| 2022-01-06 | 251.1885 | 252.4220 | 252.4295 | 0.0074 |
| 2022-01-07 | 253.9641 | 253.0253 | 253.0352 | 0.0099 |
| 2022-01-08 | 254.6540 | 252.4625 | 252.4751 | 0.013 |
| 2022-01-09 | 251.3803 | 251.5582 | 251.5739 | 0.016 |
| 2022-01-10 | 250.4844 | 251.1908 | 251.2098 | 0.019 |
| 2022-01-11 | 253.2622 | 251.7039 | 251.7264 | 0.022 |
| 2022-01-12 | 253.9025 | 253.0179 | 253.0439 | 0.026 |
| 2022-01-13 | 252.7291 | 254.4993 | 254.5292 | 0.030 |
| 2022-01-14 | 254.2625 | 255.1016 | 255.1356 | 0.034 |
| 2022-01-15 | 255.5510 | 254.5389 | 254.5771 | 0.038 |
| 2022-01-16 | 252.7853 | 253.6358 | 253.6785 | 0.043 |
| 2022-01-17 | 251.0825 | 253.2707 | 253.3181 | 0.047 |
| 2022-01-18 | 254.0671 | 253.7873 | 253.8395 | 0.052 |
| 2022-01-19 | 256.3301 | 255.1059 | 255.1628 | 0.057 |
| 2022-01-20 | 255.5859 | 256.5930 | 256.6549 | 0.062 |
| 2022-01-21 | 256.5866 | 257.2020 | 257.2691 | 0.067 |
| 2022-01-22 | 258.7042 | 256.6469 | 256.7192 | 0.072 |
| 2022-01-23 | 256.9688 | 255.7522 | 255.8298 | 0.078 |
| 2022-01-24 | 254.4117 | 255.3961 | 255.4792 | 0.083 |
| 2022-01-25 | 256.4301 | 255.9221 | 256.0108 | 0.089 |
| 2022-01-26 | 259.1693 | 257.2503 | 257.3443 | 0.094 |
| 2022-01-27 | 258.1911 | 258.7470 | 258.8467 | 0.10 |
| 2022-01-28 | 257.5578 | 259.3655 | 259.4708 | 0.11 |
| 2022-01-29 | 259.2236 | 258.8193 | 258.9303 | 0.11 |
| 2022-01-30 | 258.2893 | 257.9328 | 258.0497 | 0.12 |
| 2022-01-31 | 255.3471 | 257.5840 | 257.7067 | 0.12 |
| 2022-02-01 | 256.5991 | 258.2684 | 258.3412 | 0.073 |
| 2022-02-02 | 260.3858 | 259.6215 | 259.7009 | 0.079 |
| 2022-02-03 | 260.6900 | 261.0567 | 261.1437 | 0.087 |
| 2022-02-04 | 259.7344 | 261.7153 | 261.8098 | 0.095 |
| 2022-02-05 | 261.4424 | 261.2615 | 261.3635 | 0.10 |
| 2022-02-06 | 262.2243 | 260.3283 | 260.4377 | 0.11 |
| 2022-02-07 | 259.8835 | 259.9449 | 260.0616 | 0.12 |
| 2022-02-08 | 260.2769 | 260.5958 | 260.7203 | 0.12 |
| 2022-02-09 | 264.2745 | 261.9491 | 262.0794 | 0.13 |
| 2022-02-10 | 265.4254 | 263.3815 | 263.5183 | 0.14 |
| 2022-02-11 | 263.6723 | 264.0341 | 264.1769 | 0.14 |
| 2022-02-12 | 264.2739 | 263.5711 | 263.7194 | 0.15 |
| 2022-02-13 | 265.3932 | 262.6252 | 262.7787 | 0.15 |
| 2022-02-14 | 263.3564 | 262.2257 | 262.3839 | 0.16 |
| 2022-02-15 | 262.6971 | 262.8572 | 263.0202 | 0.16 |
| 2022-02-16 | 266.5974 | 264.1877 | 264.3534 | 0.17 |
| 2022-02-17 | 269.2112 | 265.5942 | 265.7629 | 0.17 |
| 2022-02-18 | 267.9074 | 266.2180 | 266.3890 | 0.17 |
| 2022-02-19 | 268.0179 | 265.7234 | 265.8962 | 0.17 |
| 2022-02-20 | 270.0612 | 264.7435 | 264.9175 | 0.17 |
| 2022-02-21 | 269.3271 | 264.3080 | 264.4827 | 0.17 |
| 2022-02-22 | 268.1310 | 264.9017 | 265.0771 | 0.18 |
| 2022-02-23 | 271.2582 | 266.1931 | 266.3673 | 0.17 |
| 2022-02-24 | 274.5037 | 267.5597 | 267.7329 | 0.17 |
| 2022-02-25 | 273.1327 | 268.1431 | 268.3148 | 0.17 |
| 2022-02-26 | 271.6122 | 267.6080 | 267.7778 | 0.17 |
| 2022-02-27 | 273.0118 | 266.5882 | 266.7557 | 0.17 |
| 2022-02-28 | 272.8794 | 266.1135 | 266.2786 | 0.17 |
| 2022-03-01 | 271.1045 | 266.6693 | 266.8322 | 0.16 |
| 2022-03-02 | 273.1610 | 267.9245 | 268.0834 | 0.16 |
| 2022-03-03 | 277.1583 | 273.2936 | 273.2856 | 0.0080 |
| 2022-03-04 | 276.9590 | 273.7956 | 273.7876 | 0.0081 |
| 2022-03-05 | 275.1011 | 273.2680 | 273.2599 | 0.0081 |
| 2022-03-06 | 276.5327 | 272.3073 | 272.2992 | 0.0081 |
| 2022-03-07 | 277.9394 | 271.7741 | 271.7660 | 0.0081 |
| 2022-03-08 | 276.7574 | 272.2363 | 272.2282 | 0.0081 |
| 2022-03-09 | 277.9098 | 273.5448 | 273.5366 | 0.0081 |
| 2022-03-10 | 281.9897 | 274.8497 | 274.8415 | 0.0082 |
| 2022-03-11 | 282.5472 | 275.3009 | 275.2928 | 0.0081 |
| 2022-03-12 | 279.7528 | 274.7318 | 274.7237 | 0.0081 |
| 2022-03-13 | 279.7227 | 273.7388 | 273.7308 | 0.0080 |
| 2022-03-14 | 281.3051 | 273.1825 | 273.1746 | 0.0079 |
| 2022-03-15 | 280.2837 | 273.6302 | 273.6224 | 0.0078 |
| 2022-03-16 | 280.1554 | 274.9324 | 274.9247 | 0.0077 |
| 2022-03-17 | 283.7964 | 276.2385 | 276.2309 | 0.0076 |
| 2022-03-18 | 285.5681 | 276.6974 | 276.6899 | 0.0074 |
| 2022-03-19 | 283.1294 | 276.1416 | 276.1343 | 0.0072 |
| 2022-03-20 | 282.5301 | 275.1665 | 275.1595 | 0.0070 |
| 2022-03-21 | 285.0162 | 274.6316 | 274.6248 | 0.0068 |
| 2022-03-22 | 285.4836 | 275.1030 | 275.0965 | 0.0065 |
| 2022-03-23 | 285.1026 | 276.4301 | 276.4238 | 0.0063 |
| 2022-03-24 | 288.1820 | 277.7611 | 277.7551 | 0.0060 |
| 2022-03-25 | 290.8026 | 278.2440 | 278.2383 | 0.0057 |
| 2022-03-26 | 288.5662 | 277.7102 | 277.7049 | 0.0054 |
| 2022-03-27 | 286.4696 | 276.7543 | 276.7493 | 0.0050 |
| 2022-03-28 | 288.2471 | 276.2349 | 276.2303 | 0.0047 |
| 2022-03-29 | 289.2176 | 276.7177 | 276.7134 | 0.0043 |
| 2022-03-30 | 288.1322 | 278.0513 | 278.0473 | 0.0040 |
| 2022-03-31 | 289.8585 | 279.3839 | 279.3801 | 0.0037 |
| 2022-04-01 | 292.8975 | 279.8630 | 279.8596 | 0.0034 |
| 2022-04-02 | 291.6381 | 290.9205 | 290.9291 | 0.0087 |
| 2022-04-03 | 289.0806 | 290.1965 | 290.2061 | 0.0096 |
| 2022-04-04 | 290.7580 | 289.9624 | 289.9730 | 0.011 |
| 2022-04-05 | 293.2819 | 290.6229 | 290.6344 | 0.012 |
| 2022-04-06 | 293.0056 | 292.1059 | 292.1177 | 0.012 |
| 2022-04-07 | 294.0576 | 293.7295 | 293.7424 | 0.013 |
| 2022-04-08 | 297.3727 | 294.4500 | 294.4640 | 0.014 |
| 2022-04-09 | 297.1483 | 294.0321 | 294.0472 | 0.015 |
| 2022-04-10 | 293.9302 | 293.2842 | 293.3004 | 0.016 |
| 2022-04-11 | 294.2305 | 293.0281 | 293.0453 | 0.017 |
| 2022-04-12 | 296.8925 | 293.6684 | 293.6865 | 0.018 |
| 2022-04-13 | 296.7386 | 295.1330 | 295.1513 | 0.018 |
| 2022-04-14 | 296.3564 | 296.7398 | 296.7591 | 0.019 |
| 2022-04-15 | 298.9138 | 297.4451 | 297.4653 | 0.020 |
| 2022-04-16 | 299.6192 | 297.0135 | 297.0345 | 0.021 |
| 2022-04-17 | 296.5856 | 296.2531 | 296.2749 | 0.022 |
| 2022-04-18 | 296.1329 | 295.9854 | 296.0079 | 0.023 |
| 2022-04-19 | 299.5533 | 296.6147 | 296.6379 | 0.023 |
| 2022-04-20 | 300.9548 | 298.0688 | 298.0919 | 0.023 |
| 2022-04-21 | 300.5203 | 299.6653 | 299.6891 | 0.024 |
| 2022-04-22 | 302.6884 | 300.3600 | 300.3845 | 0.024 |
| 2022-04-23 | 304.4650 | 299.9174 | 299.9425 | 0.025 |
| 2022-04-24 | 301.9610 | 299.1453 | 299.1710 | 0.026 |
| 2022-04-25 | 300.2501 | 298.8649 | 298.8912 | 0.026 |
| 2022-04-26 | 303.0226 | 299.4804 | 299.5072 | 0.027 |
| 2022-04-27 | 304.9521 | 300.9192 | 300.9460 | 0.027 |
| 2022-04-28 | 303.7988 | 302.4990 | 302.5265 | 0.027 |
| 2022-04-29 | 304.4095 | 303.1754 | 303.2036 | 0.028 |
| 2022-04-30 | 306.2936 | 302.7128 | 302.7418 | 0.029 |
| 2022-05-01 | 304.5405 | 301.9190 | 301.9489 | 0.030 |
| 2022-05-02 | 302.1741 | 304.0927 | 304.0737 | 0.019 |
| 2022-05-03 | 304.6087 | 304.8080 | 304.7886 | 0.019 |
| 2022-05-04 | 307.9782 | 306.2527 | 306.2325 | 0.020 |
| 2022-05-05 | 307.7325 | 307.7969 | 307.7762 | 0.021 |
| 2022-05-06 | 307.8145 | 308.5446 | 308.5235 | 0.021 |
| 2022-05-07 | 310.1221 | 308.1607 | 308.1392 | 0.022 |
| 2022-05-08 | 309.6832 | 307.3150 | 307.2931 | 0.022 |
| 2022-05-09 | 306.9906 | 307.0405 | 307.0181 | 0.022 |
| 2022-05-10 | 308.2351 | 307.7280 | 307.7052 | 0.023 |
| 2022-05-11 | 311.8262 | 309.1442 | 309.1208 | 0.023 |
| 2022-05-12 | 311.7904 | 310.6593 | 310.6357 | 0.024 |
| 2022-05-13 | 310.4008 | 311.3776 | 311.3537 | 0.024 |
| 2022-05-14 | 311.7102 | 310.9641 | 310.9399 | 0.024 |
| 2022-05-15 | 311.9404 | 310.0888 | 310.0644 | 0.024 |
| 2022-05-16 | 309.2367 | 309.7848 | 309.7601 | 0.025 |
| 2022-05-17 | 309.4774 | 310.4431 | 310.4183 | 0.025 |
| 2022-05-18 | 313.5734 | 311.8307 | 311.8054 | 0.025 |
| 2022-05-19 | 315.0322 | 313.3178 | 313.2925 | 0.025 |
| 2022-05-20 | 313.6756 | 314.0089 | 313.9835 | 0.025 |
| 2022-05-21 | 314.6800 | 313.5692 | 313.5437 | 0.025 |
| 2022-05-22 | 316.1507 | 312.6687 | 312.6432 | 0.025 |
| 2022-05-23 | 314.3035 | 312.3405 | 312.3149 | 0.026 |
| 2022-05-24 | 313.5828 | 312.9759 | 312.9503 | 0.026 |
| 2022-05-25 | 317.1887 | 314.3415 | 314.3158 | 0.026 |
| 2022-05-26 | 319.3184 | 315.8079 | 315.7823 | 0.026 |
| 2022-05-27 | 317.3580 | 316.4794 | 316.4539 | 0.025 |
| 2022-05-28 | 316.7188 | 316.0210 | 315.9957 | 0.025 |
| 2022-05-29 | 318.0634 | 315.1027 | 315.0776 | 0.025 |
| 2022-05-30 | 316.7687 | 314.7576 | 314.7326 | 0.025 |
| 2022-05-31 | 315.1805 | 315.3767 | 315.3519 | 0.025 |
| 2022-06-01 | 318.1442 | 318.5423 | 318.4948 | 0.047 |
| 2022-06-02 | 321.4909 | 320.0152 | 319.9627 | 0.052 |
| 2022-06-03 | 320.4123 | 320.6533 | 320.5956 | 0.058 |
| 2022-06-04 | 319.2757 | 320.2653 | 320.2022 | 0.063 |
| 2022-06-05 | 321.0970 | 319.4190 | 319.3504 | 0.069 |
| 2022-06-06 | 321.3380 | 319.0225 | 318.9482 | 0.074 |
| 2022-06-07 | 319.7577 | 319.6481 | 319.5681 | 0.080 |
| 2022-06-08 | 321.7722 | 321.1005 | 321.0151 | 0.085 |
| 2022-06-09 | 325.5143 | 322.5505 | 322.4591 | 0.091 |
| 2022-06-10 | 324.8509 | 323.1659 | 323.0684 | 0.097 |
| 2022-06-11 | 322.3382 | 322.7555 | 322.6519 | 0.10 |
| 2022-06-12 | 323.0377 | 321.8873 | 321.7776 | 0.11 |
| 2022-06-13 | 323.7641 | 321.4692 | 321.3533 | 0.12 |
| 2022-06-14 | 322.0110 | 322.0740 | 321.9518 | 0.12 |
| 2022-06-15 | 322.7581 | 323.5059 | 323.3782 | 0.13 |
| 2022-06-16 | 326.6841 | 324.9362 | 324.8023 | 0.13 |
| 2022-06-17 | 327.3461 | 325.5325 | 325.3925 | 0.14 |
| 2022-06-18 | 324.8311 | 325.1039 | 324.9578 | 0.15 |
| 2022-06-19 | 325.1933 | 324.2181 | 324.0659 | 0.15 |
| 2022-06-20 | 327.2292 | 323.7832 | 323.6250 | 0.16 |
| 2022-06-21 | 326.6002 | 324.3718 | 324.2077 | 0.16 |
| 2022-06-22 | 326.6812 | 325.7884 | 325.6190 | 0.17 |
| 2022-06-23 | 330.3217 | 327.2040 | 327.0287 | 0.18 |
| 2022-06-24 | 331.8829 | 327.7863 | 327.6051 | 0.18 |
| 2022-06-25 | 328.9989 | 327.3442 | 327.1571 | 0.19 |
| 2022-06-26 | 327.7645 | 326.4454 | 326.2526 | 0.19 |
| 2022-06-27 | 329.5546 | 325.9979 | 325.7993 | 0.20 |
| 2022-06-28 | 329.3595 | 326.5743 | 326.3699 | 0.20 |
| 2022-06-29 | 328.4014 | 327.9789 | 327.7693 | 0.21 |
| 2022-06-30 | 331.0840 | 329.3826 | 329.1672 | 0.22 |
| 2022-07-01 | 333.5709 | 332.3614 | 332.3370 | 0.024 |
| 2022-07-02 | 331.4386 | 331.9142 | 331.8853 | 0.029 |
| 2022-07-03 | 329.6199 | 331.1087 | 331.0752 | 0.033 |
| 2022-07-04 | 331.8183 | 330.7658 | 330.7277 | 0.038 |
| 2022-07-05 | 333.2760 | 331.3468 | 331.3039 | 0.043 |
| 2022-07-06 | 332.6007 | 332.7785 | 332.7288 | 0.050 |
| 2022-07-07 | 334.5693 | 334.3120 | 334.2577 | 0.054 |
| 2022-07-08 | 337.6645 | 334.9285 | 334.8693 | 0.059 |
| 2022-07-09 | 336.2361 | 334.4750 | 334.4106 | 0.064 |
| 2022-07-10 | 333.2577 | 333.6635 | 333.5943 | 0.069 |
| 2022-07-11 | 334.3411 | 333.3151 | 333.2408 | 0.074 |
| 2022-07-12 | 336.2128 | 333.8908 | 333.8113 | 0.079 |
| 2022-07-13 | 335.2879 | 335.3170 | 335.2306 | 0.086 |
| 2022-07-14 | 335.7703 | 336.8451 | 336.7538 | 0.091 |
| 2022-07-15 | 338.7160 | 337.4559 | 337.3594 | 0.096 |
| 2022-07-16 | 338.3773 | 336.9961 | 336.8944 | 0.10 |
| 2022-07-17 | 335.2625 | 336.1780 | 336.0712 | 0.11 |
| 2022-07-18 | 335.8574 | 335.8224 | 335.7104 | 0.11 |
| 2022-07-19 | 338.9806 | 336.3902 | 336.2729 | 0.12 |
| 2022-07-20 | 339.3421 | 337.8080 | 337.6835 | 0.12 |
| 2022-07-21 | 339.3938 | 339.3269 | 339.1974 | 0.13 |
| 2022-07-22 | 342.2458 | 339.9280 | 339.7931 | 0.13 |
| 2022-07-23 | 343.0675 | 339.4581 | 339.3177 | 0.14 |
| 2022-07-24 | 339.9018 | 338.6294 | 338.4836 | 0.15 |
| 2022-07-25 | 339.0669 | 338.2629 | 338.1114 | 0.15 |
| 2022-07-26 | 341.9505 | 338.8196 | 338.6624 | 0.16 |
| 2022-07-27 | 342.7403 | 340.2263 | 340.0615 | 0.16 |
| 2022-07-28 | 341.6719 | 341.7342 | 341.5638 | 0.17 |
| 2022-07-29 | 343.2964 | 342.3245 | 342.1483 | 0.18 |
| 2022-07-30 | 344.7394 | 341.8443 | 341.6619 | 0.18 |
| 2022-07-31 | 342.1337 | 342.9966 | 343.0009 | 0.0044 |
| 2022-08-01 | 340.5326 | 342.7334 | 342.7380 | 0.0046 |
| 2022-08-02 | 343.6341 | 343.4160 | 343.4209 | 0.0049 |
| 2022-08-03 | 346.0641 | 344.8585 | 344.8637 | 0.0051 |
| 2022-08-04 | 345.4489 | 346.4123 | 346.4177 | 0.0054 |
| 2022-08-05 | 346.5311 | 347.1559 | 347.1616 | 0.0057 |
| 2022-08-06 | 348.7743 | 346.7642 | 346.7703 | 0.0060 |
| 2022-08-07 | 347.1907 | 345.9451 | 345.9515 | 0.0064 |
| 2022-08-08 | 344.7301 | 345.6902 | 345.6969 | 0.0067 |
| 2022-08-09 | 346.8386 | 346.3814 | 346.3884 | 0.0070 |
| 2022-08-10 | 349.7330 | 347.8328 | 347.8402 | 0.0074 |
| 2022-08-11 | 348.9082 | 349.3958 | 349.4035 | 0.0077 |
| 2022-08-12 | 348.3797 | 350.1489 | 350.1570 | 0.0081 |
| 2022-08-13 | 350.1852 | 349.7667 | 349.7752 | 0.0084 |
| 2022-08-14 | 349.4445 | 348.9571 | 348.9659 | 0.0088 |
| 2022-08-15 | 346.6578 | 348.7117 | 348.7209 | 0.0092 |
| 2022-08-16 | 348.0326 | 349.4124 | 349.4219 | 0.0095 |
| 2022-08-17 | 351.9950 | 350.8732 | 350.8831 | 0.0099 |
| 2022-08-18 | 352.4895 | 352.4453 | 352.4556 | 0.010 |
| 2022-08-19 | 351.6617 | 353.2074 | 353.2180 | 0.011 |
| 2022-08-20 | 353.4954 | 352.8340 | 352.8449 | 0.011 |
| 2022-08-21 | 354.1486 | 352.0330 | 352.0443 | 0.011 |
| 2022-08-22 | 351.6580 | 351.7960 | 351.8076 | 0.012 |
| 2022-08-23 | 351.8511 | 352.5049 | 352.5168 | 0.012 |
| 2022-08-24 | 355.6892 | 353.9739 | 353.9860 | 0.012 |
| 2022-08-25 | 356.7271 | 355.5540 | 355.5664 | 0.012 |
| 2022-08-26 | 354.8193 | 356.3241 | 356.3367 | 0.013 |
| 2022-08-27 | 355.2506 | 355.9587 | 355.9716 | 0.013 |
| 2022-08-28 | 356.2652 | 355.1657 | 355.1789 | 0.013 |
| 2022-08-29 | 354.1369 | 354.9369 | 354.9503 | 0.013 |
| 2022-08-30 | 353.3316 | 355.7108 | 355.7123 | 0.0015 |
| 2022-08-31 | 357.1015 | 357.2352 | 357.2368 | 0.0016 |
| 2022-09-01 | 359.6401 | 358.7786 | 358.7802 | 0.0016 |
| 2022-09-02 | 358.2290 | 359.5176 | 359.5193 | 0.0017 |
| 2022-09-03 | 358.1837 | 359.2156 | 359.2174 | 0.0018 |
| 2022-09-04 | 360.1130 | 358.4444 | 358.4463 | 0.0019 |
| 2022-09-05 | 359.2938 | 358.1521 | 358.1541 | 0.0019 |
| 2022-09-06 | 357.9573 | 358.9167 | 358.9186 | 0.0020 |
| 2022-09-07 | 360.9322 | 360.4543 | 360.4565 | 0.0021 |
| 2022-09-08 | 364.0892 | 362.0121 | 362.0143 | 0.0022 |
| 2022-09-09 | 362.6310 | 362.7664 | 362.7687 | 0.0022 |
| 2022-09-10 | 360.9742 | 362.4805 | 362.4828 | 0.0023 |
| 2022-09-11 | 362.2704 | 361.7260 | 361.7284 | 0.0023 |
| 2022-09-12 | 362.0934 | 361.4509 | 361.4533 | 0.0024 |
| 2022-09-13 | 360.2420 | 362.2329 | 362.2353 | 0.0024 |
| 2022-09-14 | 362.1902 | 363.7880 | 363.7906 | 0.0025 |
| 2022-09-15 | 366.1339 | 365.3631 | 365.3656 | 0.0025 |
| 2022-09-16 | 365.9028 | 366.1345 | 366.1370 | 0.0025 |
| 2022-09-17 | 363.9537 | 365.8651 | 365.8676 | 0.0025 |
| 2022-09-18 | 365.2891 | 365.1264 | 365.1289 | 0.0025 |
| 2022-09-19 | 366.6559 | 364.8663 | 364.8687 | 0.0025 |
| 2022-09-20 | 365.4156 | 365.6623 | 365.6647 | 0.0024 |
| 2022-09-21 | 366.4559 | 367.2305 | 367.2330 | 0.0025 |
| 2022-09-22 | 370.4591 | 368.8176 | 368.8200 | 0.0024 |
| 2022-09-23 | 370.9876 | 369.5999 | 369.6023 | 0.0024 |
| 2022-09-24 | 368.1239 | 369.3404 | 369.3428 | 0.0024 |
| 2022-09-25 | 368.0052 | 368.6107 | 368.6130 | 0.0023 |
| 2022-09-26 | 369.5646 | 368.3587 | 368.3610 | 0.0023 |
| 2022-09-27 | 368.5395 | 369.1620 | 369.1643 | 0.0023 |
| 2022-09-28 | 368.3561 | 370.7369 | 370.7393 | 0.0024 |
| 2022-09-29 | 371.9570 | 372.1876 | 372.1832 | 0.0044 |
| 2022-09-30 | 373.7488 | 372.9358 | 372.9313 | 0.0045 |
| 2022-10-01 | 371.3045 | 372.6447 | 372.6401 | 0.0046 |
| 2022-10-02 | 370.6507 | 371.9761 | 371.9714 | 0.0047 |
| 2022-10-03 | 373.1223 | 371.7555 | 371.7506 | 0.0049 |
| 2022-10-04 | 373.6071 | 372.4903 | 372.4853 | 0.0050 |
| 2022-10-05 | 373.1885 | 374.0908 | 374.0856 | 0.0052 |
| 2022-10-06 | 376.2125 | 375.7636 | 375.7583 | 0.0053 |
| 2022-10-07 | 378.8387 | 376.5259 | 376.5205 | 0.0054 |
| 2022-10-08 | 376.6111 | 376.2490 | 376.2435 | 0.0055 |
| 2022-10-09 | 374.4718 | 375.5947 | 375.5890 | 0.0057 |
| 2022-10-10 | 376.2352 | 375.3883 | 375.3824 | 0.0059 |
| 2022-10-11 | 377.2531 | 376.1373 | 376.1313 | 0.0060 |
| 2022-10-12 | 376.1880 | 377.7519 | 377.7458 | 0.0062 |
| 2022-10-13 | 377.9024 | 379.4386 | 379.4324 | 0.0063 |
| 2022-10-14 | 380.9852 | 380.2148 | 380.2084 | 0.0064 |
| 2022-10-15 | 379.7980 | 379.9514 | 379.9450 | 0.0065 |
| 2022-10-16 | 377.2568 | 379.3105 | 379.3039 | 0.0066 |
| 2022-10-17 | 378.9434 | 379.1172 | 379.1105 | 0.0067 |
| 2022-10-18 | 381.5336 | 379.8789 | 379.8722 | 0.0068 |
| 2022-10-19 | 381.3085 | 381.5061 | 381.4992 | 0.0069 |
| 2022-10-20 | 382.3544 | 383.2049 | 383.1980 | 0.0069 |
| 2022-10-21 | 385.6931 | 383.9929 | 383.9860 | 0.0069 |
| 2022-10-22 | 385.5398 | 383.7411 | 383.7342 | 0.0069 |
| 2022-10-23 | 382.3524 | 383.1114 | 383.1045 | 0.0070 |
| 2022-10-24 | 382.6586 | 382.9291 | 382.9221 | 0.0070 |
| 2022-10-25 | 385.3897 | 383.7016 | 383.6947 | 0.0070 |
| 2022-10-26 | 385.3282 | 385.3393 | 385.3323 | 0.0070 |
| 2022-10-27 | 384.9885 | 387.0485 | 387.0415 | 0.0070 |
| 2022-10-28 | 387.6014 | 387.8466 | 387.8397 | 0.0069 |
| 2022-10-29 | 388.4262 | 387.6647 | 387.6543 | 0.010 |
| 2022-10-30 | 385.4924 | 387.0061 | 386.9954 | 0.011 |
| 2022-10-31 | 385.0906 | 386.8835 | 386.8723 | 0.011 |
| 2022-11-01 | 388.6003 | 387.6953 | 387.6837 | 0.012 |
| 2022-11-02 | 390.1265 | 389.2879 | 389.2759 | 0.012 |
| 2022-11-03 | 389.7624 | 390.9979 | 390.9853 | 0.013 |
| 2022-11-04 | 391.9774 | 391.8720 | 391.8588 | 0.013 |
| 2022-11-05 | 393.8582 | 391.6083 | 391.5945 | 0.014 |
| 2022-11-06 | 391.4623 | 390.9553 | 390.9411 | 0.014 |
| 2022-11-07 | 389.8043 | 390.8382 | 390.8234 | 0.015 |
| 2022-11-08 | 392.6521 | 391.6555 | 391.6402 | 0.015 |
| 2022-11-09 | 394.7188 | 393.2537 | 393.2379 | 0.016 |
| 2022-11-10 | 393.6781 | 394.9695 | 394.9531 | 0.016 |
| 2022-11-11 | 394.3672 | 395.8499 | 395.8329 | 0.017 |
| 2022-11-12 | 396.3847 | 395.5931 | 395.5756 | 0.018 |
| 2022-11-13 | 394.7992 | 394.9477 | 394.9297 | 0.018 |
| 2022-11-14 | 392.5476 | 394.8388 | 394.8203 | 0.018 |
| 2022-11-15 | 395.0878 | 395.6652 | 395.6463 | 0.019 |
| 2022-11-16 | 398.6212 | 397.2733 | 397.2541 | 0.019 |
| 2022-11-17 | 398.5279 | 398.9998 | 398.9801 | 0.020 |
| 2022-11-18 | 398.7023 | 399.8917 | 399.8716 | 0.020 |
| 2022-11-19 | 401.1262 | 399.6471 | 399.6266 | 0.020 |
| 2022-11-20 | 400.8501 | 399.0145 | 398.9937 | 0.021 |
| 2022-11-21 | 398.2790 | 398.9189 | 398.8979 | 0.021 |
| 2022-11-22 | 399.6134 | 399.7589 | 399.7377 | 0.021 |
| 2022-11-23 | 403.3529 | 401.3807 | 401.3596 | 0.021 |
| 2022-11-24 | 403.4907 | 403.1210 | 403.0997 | 0.021 |
| 2022-11-25 | 402.2241 | 404.0264 | 404.0050 | 0.021 |
| 2022-11-26 | 403.6660 | 403.7949 | 403.7735 | 0.021 |
| 2022-11-27 | 404.0945 | 403.1749 | 403.1535 | 0.021 |
| 2022-11-28 | 401.5749 | 403.1275 | 403.1196 | 0.0079 |
| 2022-11-29 | 401.9505 | 404.0278 | 404.0190 | 0.0088 |
| 2022-11-30 | 406.2184 | 405.6914 | 405.6815 | 0.0098 |
| 2022-12-01 | 407.8879 | 407.3893 | 407.3784 | 0.011 |
| 2022-12-02 | 406.6894 | 408.2941 | 408.2820 | 0.012 |
| 2022-12-03 | 407.8231 | 408.1353 | 408.1218 | 0.013 |
| 2022-12-04 | 409.4766 | 407.4984 | 407.4836 | 0.015 |
| 2022-12-05 | 407.8166 | 407.3692 | 407.3530 | 0.016 |
| 2022-12-06 | 407.2235 | 408.2666 | 408.2489 | 0.018 |
| 2022-12-07 | 410.9716 | 409.9258 | 409.9066 | 0.019 |
| 2022-12-08 | 413.3034 | 411.6182 | 411.5974 | 0.021 |
| 2022-12-09 | 411.5217 | 412.5165 | 412.4940 | 0.022 |
| 2022-12-10 | 411.0229 | 412.3505 | 412.3263 | 0.024 |
| 2022-12-11 | 412.5601 | 411.7062 | 411.6802 | 0.026 |
| 2022-12-12 | 411.4964 | 411.5698 | 411.5419 | 0.028 |
| 2022-12-13 | 410.0893 | 412.4602 | 412.4304 | 0.030 |
| 2022-12-14 | 413.2225 | 414.1131 | 414.0815 | 0.032 |
| 2022-12-15 | 416.7979 | 415.8003 | 415.7667 | 0.034 |
| 2022-12-16 | 415.9408 | 416.6946 | 416.6591 | 0.035 |
| 2022-12-17 | 414.9639 | 416.5262 | 416.4888 | 0.037 |
| 2022-12-18 | 416.9633 | 415.8813 | 415.8419 | 0.039 |
| 2022-12-19 | 417.4284 | 415.7460 | 415.7045 | 0.041 |
| 2022-12-20 | 416.0295 | 416.6396 | 416.5961 | 0.043 |
| 2022-12-21 | 418.1866 | 418.2977 | 418.2522 | 0.045 |
| 2022-12-22 | 422.1237 | 419.9919 | 419.9445 | 0.047 |
| 2022-12-23 | 421.6804 | 420.8951 | 420.8458 | 0.049 |
| 2022-12-24 | 419.3352 | 420.7373 | 420.6860 | 0.051 |
| 2022-12-25 | 420.2060 | 420.1043 | 420.0511 | 0.053 |
| 2022-12-26 | 421.1697 | 419.9820 | 419.9269 | 0.055 |
| 2022-12-27 | 419.6437 | 420.8894 | 420.8323 | 0.057 |

## Timing

Median of all measured repetitions.

Effect Prophet runs cross-validation folds one at a time, so only Python Prophet has parallel timings.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Cross-validate | 953 ms | 2.61 s | Not compared: different work |
| Cross-validate, Python `parallel="threads"` | — | 1.10 s | — |
| Cross-validate, Python `parallel="processes"` | — | 2.49 s | — |
| Cross-validate with ranges | 964 ms | 2.71 s | Not compared: different work |
| Cross-validate with ranges, Python `parallel="threads"` | — | 1.15 s | — |
| Cross-validate with ranges, Python `parallel="processes"` | — | 2.49 s | — |

Some steps aren't compared, because the two libraries' public calls produce different outputs. Their times show what each call costs, not which library is faster.

* **Cross-validate, Cross-validate with ranges:** Python Prophet's cross-validation returns different outputs, and baselines, search and holdout reports have no Python API, so the benchmark times equivalent application code. The two libraries also compute ranges and some metrics differently.

## Settings

The case declaration both libraries ran.

```json
{
  "kind": "evaluation",
  "comparison": {
    "kind": "different-public-work",
    "evidenceId": "rolling-origin-evaluation-v1"
  },
  "configuration": {
    "growth": "linear",
    "scaling": "absmax",
    "seasonalityMode": "additive",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "auto",
      "count": 25,
      "range": 0.8
    },
    "changepointPriorScale": 0.05,
    "seasonalities": [
      {
        "name": "yearly-custom",
        "periodDays": 365.25,
        "fourierOrder": 10,
        "priorScale": 10
      },
      {
        "name": "weekly-custom",
        "periodDays": 7,
        "fourierOrder": 3,
        "priorScale": 10
      }
    ],
    "events": [],
    "regressors": []
  },
  "effectOptimizer": {
    "algorithm": "auto",
    "maxIterations": 10000,
    "fallback": "newton",
    "lbfgs": {
      "historySize": 5,
      "initAlpha": 0.001,
      "tolObj": 1e-12,
      "tolRelObj": 10000,
      "tolGrad": 1e-8,
      "tolRelGrad": 10000000,
      "tolParam": 1e-8
    }
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  },
  "plan": {
    "horizonMs": 2592000000,
    "cutoffs": [
      "2022-01-01T00:00:00.000Z",
      "2022-01-31T00:00:00.000Z",
      "2022-03-02T00:00:00.000Z",
      "2022-04-01T00:00:00.000Z",
      "2022-05-01T00:00:00.000Z",
      "2022-05-31T00:00:00.000Z",
      "2022-06-30T00:00:00.000Z",
      "2022-07-30T00:00:00.000Z",
      "2022-08-29T00:00:00.000Z",
      "2022-09-28T00:00:00.000Z",
      "2022-10-28T00:00:00.000Z",
      "2022-11-27T00:00:00.000Z"
    ]
  },
  "metricAggregation": "horizons",
  "interval": {
    "seed": 19,
    "samples": 256,
    "intervalWidth": 0.8
  }
}
```