Average Error: 0.0 → 0.1
Time: 12.7s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - \frac{\frac{1}{z - y}}{\frac{1}{y}}\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - \frac{\frac{1}{z - y}}{\frac{1}{y}}
double f(double x, double y, double z) {
        double r34183805 = x;
        double r34183806 = y;
        double r34183807 = r34183805 - r34183806;
        double r34183808 = z;
        double r34183809 = r34183808 - r34183806;
        double r34183810 = r34183807 / r34183809;
        return r34183810;
}
↓
double f(double x, double y, double z) {
        double r34183811 = x;
        double r34183812 = z;
        double r34183813 = y;
        double r34183814 = r34183812 - r34183813;
        double r34183815 = r34183811 / r34183814;
        double r34183816 = 1.0;
        double r34183817 = r34183816 / r34183814;
        double r34183818 = r34183816 / r34183813;
        double r34183819 = r34183817 / r34183818;
        double r34183820 = r34183815 - r34183819;
        return r34183820;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Target

Original0.0
Target0.0
Herbie0.1
\[\frac{x}{z - y} - \frac{y}{z - y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{z - y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

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

  5. Applied clear-num0.2

    \[\leadsto \frac{x}{z - y} - \color{blue}{\frac{1}{\frac{z - y}{y}}}\]
  6. Using strategy rm

  7. Applied div-inv0.2

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

  (/ (- x y) (- z y)))