Average Error: 0.0 → 0.2
Time: 13.4s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{1}{\frac{z - y}{x}} - \frac{y}{z - y}\]
\frac{x - y}{z - y}
↓
\frac{1}{\frac{z - y}{x}} - \frac{y}{z - y}
double f(double x, double y, double z) {
        double r432509 = x;
        double r432510 = y;
        double r432511 = r432509 - r432510;
        double r432512 = z;
        double r432513 = r432512 - r432510;
        double r432514 = r432511 / r432513;
        return r432514;
}
↓
double f(double x, double y, double z) {
        double r432515 = 1.0;
        double r432516 = z;
        double r432517 = y;
        double r432518 = r432516 - r432517;
        double r432519 = x;
        double r432520 = r432518 / r432519;
        double r432521 = r432515 / r432520;
        double r432522 = r432517 / r432518;
        double r432523 = r432521 - r432522;
        return r432523;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.2
\[\frac{x}{z - y} - \frac{y}{z - y}\]

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. Using strategy rm

  5. Applied clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x}}} - \frac{y}{z - y}\]

  6. Final simplification0.2

    \[\leadsto \frac{1}{\frac{z - y}{x}} - \frac{y}{z - y}\]

Reproduce

herbie shell --seed 2019326 
(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)))