Average Error: 9.2 → 0.0
Time: 8.6s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(y - \frac{x}{z} \cdot y\right) + \frac{x}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(y - \frac{x}{z} \cdot y\right) + \frac{x}{z}
double f(double x, double y, double z) {
        double r13020633 = x;
        double r13020634 = y;
        double r13020635 = z;
        double r13020636 = r13020635 - r13020633;
        double r13020637 = r13020634 * r13020636;
        double r13020638 = r13020633 + r13020637;
        double r13020639 = r13020638 / r13020635;
        return r13020639;
}
↓
double f(double x, double y, double z) {
        double r13020640 = y;
        double r13020641 = x;
        double r13020642 = z;
        double r13020643 = r13020641 / r13020642;
        double r13020644 = r13020643 * r13020640;
        double r13020645 = r13020640 - r13020644;
        double r13020646 = r13020645 + r13020643;
        return r13020646;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

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Target

Original9.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.2

    \[\frac{x + y \cdot \left(z - x\right)}{z}\]

  2. Simplified9.2

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, z - x, x\right)}{z}}\]

  3. Taylor expanded around 0 2.9

    \[\leadsto \color{blue}{\left(y + \frac{x}{z}\right) - \frac{x \cdot y}{z}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{\frac{x}{z} + \left(y - \frac{x}{z} \cdot y\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(y - \frac{x}{z} \cdot y\right) + \frac{x}{z}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))