---
url: >-
  https://jer-k.github.io/effect-prophet/benchmarks/linear/map-regressors-medium.md
---

# Four regressors

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

256 daily rows with a yes/no regressor and three numeric ones, each standardized differently.

## Input

[`benchmark/inputs/v1/map-regressors-medium.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v1/map-regressors-medium.json): 256 history rows and 64 forecast rows.

## Output

Largest difference: **0.0042** (0.0043% of the input's range).

Every forecast row from both libraries.

| Date | Effect Prophet | Python Prophet | Difference |
| --- | ---: | ---: | ---: |
| 2020-09-13 | 107.1325 | 107.1342 | 0.0017 |
| 2020-09-14 | 107.5505 | 107.5522 | 0.0017 |
| 2020-09-15 | 107.9540 | 107.9558 | 0.0018 |
| 2020-09-16 | 108.3428 | 108.3447 | 0.0019 |
| 2020-09-17 | 107.8253 | 107.8272 | 0.0019 |
| 2020-09-18 | 110.0095 | 110.0115 | 0.0020 |
| 2020-09-19 | 110.3598 | 110.3619 | 0.0021 |
| 2020-09-20 | 110.7007 | 110.7029 | 0.0022 |
| 2020-09-21 | 109.6759 | 109.6779 | 0.0021 |
| 2020-09-22 | 110.0064 | 110.0085 | 0.0021 |
| 2020-09-23 | 110.3365 | 110.3387 | 0.0022 |
| 2020-09-24 | 110.6695 | 110.6718 | 0.0022 |
| 2020-09-25 | 111.4725 | 111.4748 | 0.0023 |
| 2020-09-26 | 111.8221 | 111.8244 | 0.0023 |
| 2020-09-27 | 114.0074 | 114.0099 | 0.0025 |
| 2020-09-28 | 114.3866 | 114.3891 | 0.0025 |
| 2020-09-29 | 115.2481 | 115.2507 | 0.0025 |
| 2020-09-30 | 112.4892 | 112.4917 | 0.0025 |
| 2020-10-01 | 112.9312 | 112.9337 | 0.0025 |
| 2020-10-02 | 113.3969 | 113.3995 | 0.0026 |
| 2020-10-03 | 114.3501 | 114.3527 | 0.0026 |
| 2020-10-04 | 114.8637 | 114.8664 | 0.0027 |
| 2020-10-05 | 115.4003 | 115.4030 | 0.0027 |
| 2020-10-06 | 117.7807 | 117.7836 | 0.0029 |
| 2020-10-07 | 118.8214 | 118.8243 | 0.0029 |
| 2020-10-08 | 119.4154 | 119.4184 | 0.0029 |
| 2020-10-09 | 118.2009 | 118.2038 | 0.0029 |
| 2020-10-10 | 118.8196 | 118.8225 | 0.0029 |
| 2020-10-11 | 119.9091 | 119.9120 | 0.0029 |
| 2020-10-12 | 120.5392 | 120.5422 | 0.0030 |
| 2020-10-13 | 119.8145 | 119.8175 | 0.0030 |
| 2020-10-14 | 120.4431 | 120.4462 | 0.0031 |
| 2020-10-15 | 123.3525 | 123.3557 | 0.0032 |
| 2020-10-16 | 123.9685 | 123.9718 | 0.0032 |
| 2020-10-17 | 124.5751 | 124.5783 | 0.0033 |
| 2020-10-18 | 123.3482 | 123.3514 | 0.0032 |
| 2020-10-19 | 124.3954 | 124.3986 | 0.0032 |
| 2020-10-20 | 124.9670 | 124.9702 | 0.0032 |
| 2020-10-21 | 125.5265 | 125.5298 | 0.0033 |
| 2020-10-22 | 126.0748 | 126.0781 | 0.0033 |
| 2020-10-23 | 127.0762 | 127.0795 | 0.0033 |
| 2020-10-24 | 129.4280 | 129.4315 | 0.0035 |
| 2020-10-25 | 129.9503 | 129.9538 | 0.0035 |
| 2020-10-26 | 129.1120 | 129.1155 | 0.0035 |
| 2020-10-27 | 128.2673 | 128.2707 | 0.0034 |
| 2020-10-28 | 128.7807 | 128.7842 | 0.0035 |
| 2020-10-29 | 129.2951 | 129.2986 | 0.0035 |
| 2020-10-30 | 129.8121 | 129.8157 | 0.0036 |
| 2020-10-31 | 130.7965 | 130.8000 | 0.0036 |
| 2020-11-01 | 131.3223 | 131.3259 | 0.0036 |
| 2020-11-02 | 133.6761 | 133.6799 | 0.0038 |
| 2020-11-03 | 134.2128 | 134.2166 | 0.0038 |
| 2020-11-04 | 135.2179 | 135.2217 | 0.0038 |
| 2020-11-05 | 133.9410 | 133.9448 | 0.0038 |
| 2020-11-06 | 134.4892 | 134.4931 | 0.0038 |
| 2020-11-07 | 135.0382 | 135.0421 | 0.0039 |
| 2020-11-08 | 134.6934 | 134.6973 | 0.0039 |
| 2020-11-09 | 135.2371 | 135.2410 | 0.0039 |
| 2020-11-10 | 135.7742 | 135.7782 | 0.0040 |
| 2020-11-11 | 138.1248 | 138.1290 | 0.0042 |
| 2020-11-12 | 139.1046 | 139.1087 | 0.0042 |
| 2020-11-13 | 139.6068 | 139.6111 | 0.0042 |
| 2020-11-14 | 138.2703 | 138.2745 | 0.0042 |
| 2020-11-15 | 138.7384 | 138.7426 | 0.0042 |

## Internal fit differences

The forecasts match, so this case passes. Both libraries search for the best-fitting parameters and stop when they are close enough. On this input they stopped at slightly different points, so these internal numbers differ by more than the threshold where we take a closer look.

| Check | Effect Prophet | Python Prophet | Threshold |
| --- | ---: | ---: | ---: |
| Stationarity residual (lower is closer to the best fit) | 83.9188 | 35.2434 | 0.01 |

## Timing

Median of all measured repetitions.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Convert input rows | 118 µs | 689 µs | 5.8× faster |
| Fit | 3.12 ms | 10.5 ms | 3.4× faster |
| Predict | 506 µs | 3.60 ms | 7.1× faster |
| Fit and predict | 2.65 ms | 14.1 ms | 5.3× faster |
| Convert, fit and predict | 3.64 ms | 14.8 ms | 4.1× faster |
| First forecast in a new process | 179 ms | 1.46 s | 8.2× faster |
| Save model to JSON | 23 µs | 737 µs | 32× faster |
| Load model from JSON | 111 µs | 3.08 ms | 28× faster |
| Load and predict in a new process | 169 ms | 1.46 s | 8.6× faster |

## Settings

The case declaration both libraries ran.

```json
{
  "kind": "linear-map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "linear-output-first-v4"
  },
  "configuration": {
    "effectMap": "explicit",
    "changepoints": {
      "mode": "explicit",
      "timestamps": [
        "2020-03-21T00:00:00.000Z",
        "2020-06-29T00:00:00.000Z"
      ]
    },
    "changepointPriorScale": 0.2,
    "seasonalities": [],
    "events": [],
    "regressors": [
      {
        "name": "binary-auto",
        "priorScale": 10,
        "standardization": "auto"
      },
      {
        "name": "numeric-auto",
        "priorScale": 10,
        "standardization": "auto"
      },
      {
        "name": "numeric-always",
        "priorScale": 7,
        "standardization": "always"
      },
      {
        "name": "numeric-never",
        "priorScale": 5,
        "standardization": "never"
      }
    ]
  },
  "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
  }
}
```