Average Error: 0.0 → 0.0
Time: 2.6s
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 r612809 = x;
        double r612810 = y;
        double r612811 = r612809 - r612810;
        double r612812 = z;
        double r612813 = r612812 - r612810;
        double r612814 = r612811 / r612813;
        return r612814;
}
↓
double f(double x, double y, double z) {
        double r612815 = x;
        double r612816 = z;
        double r612817 = y;
        double r612818 = r612816 - r612817;
        double r612819 = r612815 / r612818;
        double r612820 = r612817 / r612818;
        double r612821 = r612819 - r612820;
        return r612821;
}

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 2020100 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

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

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