Average Error: 6.0 → 0.1
Time: 2.8s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\left(1 - x\right) \cdot \frac{\frac{3 - x}{3}}{y}
double f(double x, double y) {
        double r776928 = 1.0;
        double r776929 = x;
        double r776930 = r776928 - r776929;
        double r776931 = 3.0;
        double r776932 = r776931 - r776929;
        double r776933 = r776930 * r776932;
        double r776934 = y;
        double r776935 = r776934 * r776931;
        double r776936 = r776933 / r776935;
        return r776936;
}
↓
double f(double x, double y) {
        double r776937 = 1.0;
        double r776938 = x;
        double r776939 = r776937 - r776938;
        double r776940 = 3.0;
        double r776941 = r776940 - r776938;
        double r776942 = r776941 / r776940;
        double r776943 = y;
        double r776944 = r776942 / r776943;
        double r776945 = r776939 * r776944;
        return r776945;
}

Error

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Bits error versus y

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Results

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Target

Original6.0
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 6.0

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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-inv0.2

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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)))