Average Error: 0.0 → 0.0
Time: 2.9s
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 r599361 = x;
        double r599362 = y;
        double r599363 = r599361 - r599362;
        double r599364 = z;
        double r599365 = r599364 - r599362;
        double r599366 = r599363 / r599365;
        return r599366;
}
↓
double f(double x, double y, double z) {
        double r599367 = x;
        double r599368 = z;
        double r599369 = y;
        double r599370 = r599368 - r599369;
        double r599371 = r599367 / r599370;
        double r599372 = r599369 / r599370;
        double r599373 = r599371 - r599372;
        return r599373;
}

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

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 2020062 
(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)))