Average Error: 0.0 → 0.1
Time: 15.8s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - \frac{1}{-1 + \frac{z}{y}}\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - \frac{1}{-1 + \frac{z}{y}}
double f(double x, double y, double z) {
        double r389104 = x;
        double r389105 = y;
        double r389106 = r389104 - r389105;
        double r389107 = z;
        double r389108 = r389107 - r389105;
        double r389109 = r389106 / r389108;
        return r389109;
}
↓
double f(double x, double y, double z) {
        double r389110 = x;
        double r389111 = z;
        double r389112 = y;
        double r389113 = r389111 - r389112;
        double r389114 = r389110 / r389113;
        double r389115 = 1.0;
        double r389116 = -1.0;
        double r389117 = r389111 / r389112;
        double r389118 = r389116 + r389117;
        double r389119 = r389115 / r389118;
        double r389120 = r389114 - r389119;
        return r389120;
}

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
Herbie0.1
\[\frac{x}{z - y} - \frac{y}{z - y}\]

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-num0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

  (/ (- x y) (- z y)))