Average Error: 0.0 → 0.0
Time: 10.2s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - \frac{y}{z - y}\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - \frac{y}{z - y}
double f(double x, double y, double z) {
        double r414648 = x;
        double r414649 = y;
        double r414650 = r414648 - r414649;
        double r414651 = z;
        double r414652 = r414651 - r414649;
        double r414653 = r414650 / r414652;
        return r414653;
}
↓
double f(double x, double y, double z) {
        double r414654 = x;
        double r414655 = z;
        double r414656 = y;
        double r414657 = r414655 - r414656;
        double r414658 = r414654 / r414657;
        double r414659 = r414656 / r414657;
        double r414660 = r414658 - r414659;
        return r414660;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

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

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. Final simplification0.0

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

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)))