Average Error: 0.0 → 0.2
Time: 17.5s
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 r478106 = x;
        double r478107 = y;
        double r478108 = r478106 - r478107;
        double r478109 = z;
        double r478110 = r478109 - r478107;
        double r478111 = r478108 / r478110;
        return r478111;
}
↓
double f(double x, double y, double z) {
        double r478112 = x;
        double r478113 = z;
        double r478114 = y;
        double r478115 = r478113 - r478114;
        double r478116 = r478112 / r478115;
        double r478117 = 1.0;
        double r478118 = -1.0;
        double r478119 = r478113 / r478114;
        double r478120 = r478118 + r478119;
        double r478121 = r478117 / r478120;
        double r478122 = r478116 - r478121;
        return r478122;
}

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

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

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 +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)))