Average Error: 0.0 → 0.2
Time: 3.7s
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 r639011 = x;
        double r639012 = y;
        double r639013 = r639011 - r639012;
        double r639014 = z;
        double r639015 = r639014 - r639012;
        double r639016 = r639013 / r639015;
        return r639016;
}
↓
double f(double x, double y, double z) {
        double r639017 = 1.0;
        double r639018 = z;
        double r639019 = y;
        double r639020 = r639018 - r639019;
        double r639021 = x;
        double r639022 = r639020 / r639021;
        double r639023 = r639017 / r639022;
        double r639024 = r639019 / r639020;
        double r639025 = r639023 - r639024;
        return r639025;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020021 
(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)))