Average Error: 0.0 → 0.0
Time: 2.7s
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 r768217 = x;
        double r768218 = y;
        double r768219 = r768217 - r768218;
        double r768220 = z;
        double r768221 = r768220 - r768218;
        double r768222 = r768219 / r768221;
        return r768222;
}
↓
double f(double x, double y, double z) {
        double r768223 = x;
        double r768224 = z;
        double r768225 = y;
        double r768226 = r768224 - r768225;
        double r768227 = r768223 / r768226;
        double r768228 = r768225 / r768226;
        double r768229 = r768227 - r768228;
        return r768229;
}

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 2020060 
(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)))