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 r749683 = x;
        double r749684 = y;
        double r749685 = r749683 - r749684;
        double r749686 = z;
        double r749687 = r749686 - r749684;
        double r749688 = r749685 / r749687;
        return r749688;
}
↓
double f(double x, double y, double z) {
        double r749689 = x;
        double r749690 = z;
        double r749691 = y;
        double r749692 = r749690 - r749691;
        double r749693 = r749689 / r749692;
        double r749694 = r749691 / r749692;
        double r749695 = r749693 - r749694;
        return r749695;
}

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 2020036 
(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)))