Average Error: 0.0 → 0.0
Time: 2.2s
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 r658163 = x;
        double r658164 = y;
        double r658165 = r658163 - r658164;
        double r658166 = z;
        double r658167 = r658166 - r658164;
        double r658168 = r658165 / r658167;
        return r658168;
}
↓
double f(double x, double y, double z) {
        double r658169 = x;
        double r658170 = z;
        double r658171 = y;
        double r658172 = r658170 - r658171;
        double r658173 = r658169 / r658172;
        double r658174 = r658171 / r658172;
        double r658175 = r658173 - r658174;
        return r658175;
}

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 2020018 
(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)))