---
url: >-
  https://jer-k.github.io/effect-prophet/benchmarks/linear/uncertainty-linear-offset-scaling-absmax-historical-intervals-128.md
---

# Ranges over past dates

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

80% ranges from 128 simulated paths on 8 dates inside the history.

## Input

[`benchmark/inputs/v1/linear-offset-scaling.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v1/linear-offset-scaling.json): 96 history rows and 24 forecast rows.

## Output

Largest difference: **1.2e-11** (< 0.0001% of the input's range).

Every forecast row from both libraries.

| Date | Effect Prophet | Python Prophet | Difference |
| --- | ---: | ---: | ---: |
| 2020-03-29 | 109.2537 | 109.2537 | 1.2e-11 |
| 2020-03-30 | 109.2406 | 109.2406 | 1.2e-11 |
| 2020-03-31 | 109.4134 | 109.4134 | 1.2e-11 |
| 2020-04-01 | 109.7283 | 109.7283 | 1.2e-11 |
| 2020-04-02 | 110.0413 | 110.0413 | 1.2e-11 |
| 2020-04-03 | 110.2101 | 110.2101 | 1.2e-11 |
| 2020-04-04 | 110.1943 | 110.1943 | 1.2e-11 |
| 2020-04-05 | 110.0950 | 110.0950 | 1.2e-11 |

## Timing

Median of all measured repetitions.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Convert input rows | 16 µs | 472 µs | 29× faster |
| Save model to JSON | 27 µs | 431 µs | 16× faster |
| Load model from JSON | 175 µs | 2.50 ms | 14× faster |
| Simulate uncertainty | 331 µs | 19.8 ms | Not compared: different work |
| First simulation in a new process | 175 ms | 1.48 s | Not compared: different work |
| Load and simulate in a new process | 163 ms | 1.46 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, Load and simulate 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.

```json
{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "linear-output-first-v4"
  },
  "configuration": {
    "growth": "linear",
    "scaling": "absmax",
    "seasonalityMode": "additive",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "explicit",
      "timestamps": [
        "2020-02-10T00:00:00.000Z"
      ]
    },
    "changepointPriorScale": 0.2,
    "seasonalities": [
      {
        "name": "weekly-custom",
        "periodDays": 7,
        "fourierOrder": 2,
        "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
  },
  "uncertainty": {
    "seed": 19,
    "samples": 128,
    "intervalWidth": 0.8,
    "output": "intervals",
    "algorithm": "scalar-continuous-time",
    "evidence": "docs/validation/uncertainty.md#evidence-classes",
    "samplerMemoryLimitBytes": 67108864
  }
}
```