Average Error: 9.2 → 0.0
Time: 7.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(y + \frac{x}{z}\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(y + \frac{x}{z}\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r16117288 = x;
        double r16117289 = y;
        double r16117290 = z;
        double r16117291 = r16117290 - r16117288;
        double r16117292 = r16117289 * r16117291;
        double r16117293 = r16117288 + r16117292;
        double r16117294 = r16117293 / r16117290;
        return r16117294;
}
↓
double f(double x, double y, double z) {
        double r16117295 = y;
        double r16117296 = x;
        double r16117297 = z;
        double r16117298 = r16117296 / r16117297;
        double r16117299 = r16117295 + r16117298;
        double r16117300 = r16117298 * r16117295;
        double r16117301 = r16117299 - r16117300;
        return r16117301;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Taylor expanded around 0 2.9

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(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))