Average Error: 0.0 → 0.0
Time: 2.5s
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 r677289 = x;
        double r677290 = y;
        double r677291 = r677289 - r677290;
        double r677292 = z;
        double r677293 = r677292 - r677290;
        double r677294 = r677291 / r677293;
        return r677294;
}
↓
double f(double x, double y, double z) {
        double r677295 = x;
        double r677296 = z;
        double r677297 = y;
        double r677298 = r677296 - r677297;
        double r677299 = r677295 / r677298;
        double r677300 = r677297 / r677298;
        double r677301 = r677299 - r677300;
        return r677301;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

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 2020049 
(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)))