Average Error: 6.1 → 0.1
Time: 10.2s
Precision: 64
\[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
↓
\[\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}\]
\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}
↓
\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}
double f(double x, double y) {
        double r582839 = 1.0;
        double r582840 = x;
        double r582841 = r582839 - r582840;
        double r582842 = 3.0;
        double r582843 = r582842 - r582840;
        double r582844 = r582841 * r582843;
        double r582845 = y;
        double r582846 = r582845 * r582842;
        double r582847 = r582844 / r582846;
        return r582847;
}
↓
double f(double x, double y) {
        double r582848 = 1.0;
        double r582849 = x;
        double r582850 = r582848 - r582849;
        double r582851 = y;
        double r582852 = r582850 / r582851;
        double r582853 = 3.0;
        double r582854 = r582853 - r582849;
        double r582855 = r582853 / r582854;
        double r582856 = r582852 / r582855;
        return r582856;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 6.1

    \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3}\]
  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 clear-num0.2

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(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)))