Average Error: 5.9 → 0.2
Time: 2.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \left(1 - \frac{x}{3}\right)\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \left(1 - \frac{x}{3}\right)
double f(double x, double y) {
        double r903276 = 1.0;
        double r903277 = x;
        double r903278 = r903276 - r903277;
        double r903279 = 3.0;
        double r903280 = r903279 - r903277;
        double r903281 = r903278 * r903280;
        double r903282 = y;
        double r903283 = r903282 * r903279;
        double r903284 = r903281 / r903283;
        return r903284;
}
↓
double f(double x, double y) {
        double r903285 = 1.0;
        double r903286 = x;
        double r903287 = r903285 - r903286;
        double r903288 = 1.0;
        double r903289 = y;
        double r903290 = r903288 / r903289;
        double r903291 = r903287 * r903290;
        double r903292 = 3.0;
        double r903293 = r903286 / r903292;
        double r903294 = r903288 - r903293;
        double r903295 = r903291 * r903294;
        return r903295;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.9
Target0.1
Herbie0.2
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.9

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}}\]
  4. Using strategy rm

  5. Applied div-sub0.1

    \[\leadsto \frac{1 - x}{y} \cdot \color{blue}{\left(\frac{3}{3} - \frac{x}{3}\right)}\]

  6. Simplified0.1

    \[\leadsto \frac{1 - x}{y} \cdot \left(\color{blue}{1} - \frac{x}{3}\right)\]
  7. Using strategy rm

  8. Applied div-inv0.2

    \[\leadsto \color{blue}{\left(\left(1 - x\right) \cdot \frac{1}{y}\right)} \cdot \left(1 - \frac{x}{3}\right)\]

  9. Final simplification0.2

    \[\leadsto \left(\left(1 - x\right) \cdot \frac{1}{y}\right) \cdot \left(1 - \frac{x}{3}\right)\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1 x) y) (/ (- 3 x) 3))

  (/ (* (- 1 x) (- 3 x)) (* y 3)))