Ranges with a forecast regressor

match ← All flat growth benchmarks

80% ranges from 1,000 simulated paths on every past and future date, each future path using one of the temperature model's own simulated values.

Input

benchmark/inputs/v4/flat-correlated-regressors.json: 730 history rows and 180 forecast rows.

Output

Largest difference: 0.00026 (0.0020% of the input's range).

Every forecast row from both libraries.

Date	Effect Prophet	Python Prophet	Difference
2021-12-31	44.6640	44.6638	0.00024
2022-01-01	43.2809	43.2807	0.00024
2022-01-02	41.8068	41.8066	0.00026
2022-01-03	41.2981	41.2979	0.00026
2022-01-04	42.0470	42.0468	0.00026
2022-01-05	43.4620	43.4620	4.0e-5
2022-01-06	44.4592	44.4591	0.00011
2022-01-07	44.1913	44.1910	0.00023
2022-01-08	42.8044	42.8042	0.00024
2022-01-09	41.3266	41.3263	0.00025
2022-01-10	40.8143	40.8141	0.00026
2022-01-11	41.5597	41.5594	0.00025
2022-01-12	42.9712	42.9712	3.2e-5
2022-01-13	43.9649	43.9648	0.00010
2022-01-14	43.6937	43.6935	0.00022
2022-01-15	42.3035	42.3032	0.00023
2022-01-16	40.8224	40.8221	0.00024
2022-01-17	40.3068	40.3066	0.00025
2022-01-18	41.0489	41.0487	0.00024
2022-01-19	42.4571	42.4571	2.4e-5
2022-01-20	43.4476	43.4475	9.3e-5
2022-01-21	43.1730	43.1728	0.00021
2022-01-22	41.7794	41.7791	0.00022
2022-01-23	40.2948	40.2946	0.00023
2022-01-24	39.7757	39.7755	0.00024
2022-01-25	40.5142	40.5139	0.00023
2022-01-26	41.9187	41.9187	1.6e-5
2022-01-27	42.9053	42.9053	8.5e-5
2022-01-28	42.6268	42.6266	0.00021
2022-01-29	41.2293	41.2290	0.00021
2022-01-30	39.7406	39.7404	0.00023
2022-01-31	39.2174	39.2171	0.00023
2022-02-01	39.9516	39.9513	0.00023
2022-02-02	41.3518	41.3518	8.7e-6
2022-02-03	42.3340	42.3339	7.8e-5
2022-02-04	42.0511	42.0509	0.00020
2022-02-05	40.6490	40.6488	0.00021
2022-02-06	39.1558	39.1556	0.00022
2022-02-07	38.6280	38.6278	0.00022
2022-02-08	39.3576	39.3574	0.00022
2022-02-09	40.7533	40.7533	9.4e-7
2022-02-10	41.7310	41.7309	7.0e-5
2022-02-11	41.4436	41.4434	0.00019
2022-02-12	40.0370	40.0368	0.00020
2022-02-13	38.5395	38.5392	0.00021
2022-02-14	38.0073	38.0071	0.00022
2022-02-15	38.7327	38.7324	0.00021
2022-02-16	40.1241	40.1241	6.8e-6
2022-02-17	41.0977	41.0976	6.2e-5
2022-02-18	40.8062	40.8060	0.00018
2022-02-19	39.3956	39.3954	0.00019
2022-02-20	37.8941	37.8939	0.00020
2022-02-21	37.3581	37.3579	0.00021
2022-02-22	38.0797	38.0795	0.00020
2022-02-23	39.4674	39.4674	1.5e-5
2022-02-24	40.4373	40.4372	5.4e-5
2022-02-25	40.1421	40.1419	0.00017
2022-02-26	38.7279	38.7277	0.00018
2022-02-27	37.2228	37.2226	0.00020
2022-02-28	36.6832	36.6830	0.00020
2022-03-01	37.4012	37.4010	0.00019
2022-03-02	38.7854	38.7854	2.2e-5
2022-03-03	39.7516	39.7516	4.6e-5
2022-03-04	39.4529	39.4527	0.00017
2022-03-05	38.0351	38.0350	0.00017
2022-03-06	36.5265	36.5263	0.00019
2022-03-07	35.9833	35.9831	0.00019
2022-03-08	36.6976	36.6974	0.00019
2022-03-09	38.0781	38.0781	3.0e-5
2022-03-10	39.0407	39.0407	3.9e-5
2022-03-11	38.7384	38.7382	0.00016
2022-03-12	37.3170	37.3168	0.00017
2022-03-13	35.8046	35.8045	0.00018
2022-03-14	35.2578	35.2576	0.00019
2022-03-15	35.9686	35.9684	0.00018
2022-03-16	37.3455	37.3456	3.8e-5
2022-03-17	38.3047	38.3046	3.1e-5
2022-03-18	37.9988	37.9987	0.00015
2022-03-19	36.5740	36.5739	0.00016
2022-03-20	35.0584	35.0582	0.00017
2022-03-21	34.5083	34.5081	0.00018
2022-03-22	35.2159	35.2157	0.00017
2022-03-23	36.5898	36.5898	4.6e-5
2022-03-24	37.5459	37.5459	2.3e-5
2022-03-25	37.2371	37.2370	0.00014
2022-03-26	35.8095	35.8093	0.00015
2022-03-27	34.2911	34.2909	0.00016
2022-03-28	33.7384	33.7382	0.00017
2022-03-29	34.4434	34.4432	0.00016
2022-03-30	35.8147	35.8148	5.3e-5
2022-03-31	36.7685	36.7684	1.5e-5
2022-04-01	36.4574	36.4572	0.00014
2022-04-02	35.0275	35.0273	0.00014
2022-04-03	33.5069	33.5067	0.00016
2022-04-04	32.9520	32.9518	0.00016
2022-04-05	33.6549	33.6547	0.00016
2022-04-06	35.0242	35.0243	6.1e-5
2022-04-07	35.9759	35.9759	7.7e-6
2022-04-08	35.6628	35.6627	0.00013
2022-04-09	34.2310	34.2309	0.00014
2022-04-10	32.7085	32.7083	0.00015
2022-04-11	32.1517	32.1516	0.00016
2022-04-12	32.8528	32.8527	0.00015
2022-04-13	34.2203	34.2204	6.9e-5
2022-04-14	35.1702	35.1702	7.7e-8
2022-04-15	34.8554	34.8553	0.00012
2022-04-16	33.4219	33.4218	0.00013
2022-04-17	31.8977	31.8976	0.00014
2022-04-18	31.3394	31.3392	0.00015
2022-04-19	32.0389	32.0387	0.00014
2022-04-20	33.4049	33.4050	7.7e-5
2022-04-21	34.3534	34.3534	7.8e-6
2022-04-22	34.0372	34.0371	0.00011
2022-04-23	32.6024	32.6023	0.00012
2022-04-24	31.0770	31.0769	0.00013
2022-04-25	30.5175	30.5174	0.00014
2022-04-26	31.2160	31.2159	0.00013
2022-04-27	32.5811	32.5812	8.4e-5
2022-04-28	33.5287	33.5288	1.6e-5
2022-04-29	33.2118	33.2117	0.00010
2022-04-30	31.7764	31.7763	0.00011
2022-05-01	30.2505	30.2504	0.00013
2022-05-02	29.6906	29.6904	0.00013
2022-05-03	30.3887	30.3886	0.00012
2022-05-04	31.7535	31.7536	9.2e-5
2022-05-05	32.7011	32.7011	2.3e-5
2022-05-06	32.3841	32.3840	9.7e-5
2022-05-07	30.9486	30.9485	0.00010
2022-05-08	29.4228	29.4227	0.00012
2022-05-09	28.8631	28.8629	0.00012
2022-05-10	29.5614	29.5613	0.00012
2022-05-11	30.9266	30.9267	1.0e-4
2022-05-12	31.8744	31.8744	3.1e-5
2022-05-13	31.5578	31.5577	8.9e-5
2022-05-14	30.1228	30.1227	9.7e-5
2022-05-15	28.5975	28.5974	0.00011
2022-05-16	28.0383	28.0382	0.00012
2022-05-17	28.7373	28.7372	0.00011
2022-05-18	30.1030	30.1031	0.00011
2022-05-19	31.0515	31.0516	3.9e-5
2022-05-20	30.7357	30.7356	8.2e-5
2022-05-21	29.3014	29.3014	8.9e-5
2022-05-22	27.7769	27.7768	0.00010
2022-05-23	27.2186	27.2185	0.00011
2022-05-24	27.9185	27.9184	0.00010
2022-05-25	29.2852	29.2853	0.00012
2022-05-26	30.2348	30.2348	4.7e-5
2022-05-27	29.9201	29.9200	7.4e-5
2022-05-28	28.4870	28.4869	8.1e-5
2022-05-29	26.9638	26.9637	9.5e-5
2022-05-30	26.4068	26.4067	0.00010
2022-05-31	27.1081	27.1080	9.4e-5
2022-06-01	28.4764	28.4765	0.00012
2022-06-02	29.4276	29.4276	5.4e-5
2022-06-03	29.1145	29.1145	6.6e-5
2022-06-04	27.6833	27.6832	7.4e-5
2022-06-05	26.1619	26.1619	8.7e-5
2022-06-06	25.6069	25.6068	9.3e-5
2022-06-07	26.3103	26.3102	8.6e-5
2022-06-08	27.6807	27.6808	0.00013
2022-06-09	28.6341	28.6342	6.2e-5
2022-06-10	28.3234	28.3233	5.8e-5
2022-06-11	26.8945	26.8944	6.6e-5
2022-06-12	25.3756	25.3755	7.9e-5
2022-06-13	24.8231	24.8230	8.5e-5
2022-06-14	25.5290	25.5289	7.8e-5
2022-06-15	26.9020	26.9021	0.00014
2022-06-16	27.8580	27.8581	7.0e-5
2022-06-17	27.5500	27.5499	5.0e-5
2022-06-18	26.1238	26.1238	5.8e-5
2022-06-19	24.6077	24.6076	7.2e-5
2022-06-20	24.0579	24.0578	7.8e-5
2022-06-21	24.7667	24.7666	7.0e-5
2022-06-22	26.1425	26.1426	0.00015
2022-06-23	27.1014	27.1015	7.8e-5
2022-06-24	26.7963	26.7962	4.3e-5
2022-06-25	25.3730	25.3730	5.0e-5
2022-06-26	23.8598	23.8597	6.4e-5
2022-06-27	23.3130	23.3130	7.0e-5
2022-06-28	24.0248	24.0247	6.3e-5

Timing

Median of all measured repetitions.

Step	Effect Prophet	Python Prophet	Effect Prophet is
Convert input rows	237 µs	924 µs	3.9× faster
Simulate uncertainty	18.1 ms	277 ms	Not compared: different work
First simulation in a new process	239 ms	1.80 s	Not compared: different work

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.

• Simulate uncertainty, First simulation in a new process: Python's predict(vectorized=False) also builds the point forecast and every component, while Effect Prophet's predictUncertainty returns only the ranges.

Settings

The case declaration both libraries ran.

{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "flat-map-additive-v1"
  },
  "configuration": {
    "growth": "flat",
    "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": 2,
        "priorScale": 10
      }
    ],
    "events": [],
    "regressors": [
      {
        "name": "temperature",
        "priorScale": 10,
        "standardization": "auto",
        "predictor": true
      },
      {
        "name": "baseline",
        "priorScale": 10,
        "standardization": "never"
      }
    ]
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  },
  "uncertainty": {
    "seed": 19,
    "samples": 1000,
    "intervalWidth": 0.8,
    "output": "intervals",
    "algorithm": "scalar-continuous-time",
    "evidence": "docs/validation/uncertainty.md#evidence-classes",
    "samplerMemoryLimitBytes": 67108864
  }
}