Average Error: 5.9 → 0.1
Time: 14.5s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{1 - x}{y} \cdot \frac{3 - x}{3}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{1 - x}{y} \cdot \frac{3 - x}{3}
double f(double x, double y) {
        double r44416101 = 1.0;
        double r44416102 = x;
        double r44416103 = r44416101 - r44416102;
        double r44416104 = 3.0;
        double r44416105 = r44416104 - r44416102;
        double r44416106 = r44416103 * r44416105;
        double r44416107 = y;
        double r44416108 = r44416107 * r44416104;
        double r44416109 = r44416106 / r44416108;
        return r44416109;
}
↓
double f(double x, double y) {
        double r44416110 = 1.0;
        double r44416111 = x;
        double r44416112 = r44416110 - r44416111;
        double r44416113 = y;
        double r44416114 = r44416112 / r44416113;
        double r44416115 = 3.0;
        double r44416116 = r44416115 - r44416111;
        double r44416117 = r44416116 / r44416115;
        double r44416118 = r44416114 * r44416117;
        return r44416118;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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. Final simplification0.1

    \[\leadsto \frac{1 - x}{y} \cdot \frac{3 - x}{3}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))