Average Error: 0.0 → 0.0
Time: 10.0s
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 r418602 = x;
        double r418603 = y;
        double r418604 = r418602 - r418603;
        double r418605 = z;
        double r418606 = r418605 - r418603;
        double r418607 = r418604 / r418606;
        return r418607;
}
↓
double f(double x, double y, double z) {
        double r418608 = x;
        double r418609 = z;
        double r418610 = y;
        double r418611 = r418609 - r418610;
        double r418612 = r418608 / r418611;
        double r418613 = r418610 / r418611;
        double r418614 = r418612 - r418613;
        return r418614;
}

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

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 2019199 +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)))