Average Error: 0.0 → 0.1
Time: 15.9s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - \frac{1}{z - y} \cdot y\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - \frac{1}{z - y} \cdot y
double f(double x, double y, double z) {
        double r28017173 = x;
        double r28017174 = y;
        double r28017175 = r28017173 - r28017174;
        double r28017176 = z;
        double r28017177 = r28017176 - r28017174;
        double r28017178 = r28017175 / r28017177;
        return r28017178;
}
↓
double f(double x, double y, double z) {
        double r28017179 = x;
        double r28017180 = z;
        double r28017181 = y;
        double r28017182 = r28017180 - r28017181;
        double r28017183 = r28017179 / r28017182;
        double r28017184 = 1.0;
        double r28017185 = r28017184 / r28017182;
        double r28017186 = r28017185 * r28017181;
        double r28017187 = r28017183 - r28017186;
        return r28017187;
}

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 div-inv0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 +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)))