Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
\[\frac{x - y}{z - y}\]
↓
\[\frac{x}{z - y} - \frac{y}{z - y}\]
\frac{x - y}{z - y}
↓
\frac{x}{z - y} - \frac{y}{z - y}
double f(double x, double y, double z) {
        double r615577 = x;
        double r615578 = y;
        double r615579 = r615577 - r615578;
        double r615580 = z;
        double r615581 = r615580 - r615578;
        double r615582 = r615579 / r615581;
        return r615582;
}
↓
double f(double x, double y, double z) {
        double r615583 = x;
        double r615584 = z;
        double r615585 = y;
        double r615586 = r615584 - r615585;
        double r615587 = r615583 / r615586;
        double r615588 = r615585 / r615586;
        double r615589 = r615587 - r615588;
        return r615589;
}

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

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +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)))