Average Error: 5.4 → 0.1
Time: 9.8s
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 r744836 = 1.0;
        double r744837 = x;
        double r744838 = r744836 - r744837;
        double r744839 = 3.0;
        double r744840 = r744839 - r744837;
        double r744841 = r744838 * r744840;
        double r744842 = y;
        double r744843 = r744842 * r744839;
        double r744844 = r744841 / r744843;
        return r744844;
}
↓
double f(double x, double y) {
        double r744845 = 1.0;
        double r744846 = x;
        double r744847 = r744845 - r744846;
        double r744848 = 3.0;
        double r744849 = r744848 - r744846;
        double r744850 = r744849 / r744848;
        double r744851 = y;
        double r744852 = r744850 / r744851;
        double r744853 = r744847 * r744852;
        return r744853;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original5.4
Target0.1
Herbie0.1
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Derivation

  1. Initial program 5.4

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 2020043 +o rules:numerics
(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)))