Average Error: 9.4 → 0.0
Time: 11.9s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \left(\frac{x}{z} - \frac{x}{z} \cdot y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \left(\frac{x}{z} - \frac{x}{z} \cdot y\right)
double f(double x, double y, double z) {
        double r36033864 = x;
        double r36033865 = y;
        double r36033866 = z;
        double r36033867 = r36033866 - r36033864;
        double r36033868 = r36033865 * r36033867;
        double r36033869 = r36033864 + r36033868;
        double r36033870 = r36033869 / r36033866;
        return r36033870;
}
↓
double f(double x, double y, double z) {
        double r36033871 = y;
        double r36033872 = x;
        double r36033873 = z;
        double r36033874 = r36033872 / r36033873;
        double r36033875 = r36033874 * r36033871;
        double r36033876 = r36033874 - r36033875;
        double r36033877 = r36033871 + r36033876;
        return r36033877;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.4

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

  2. Taylor expanded around 0 3.3

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

  3. Taylor expanded around 0 3.3

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(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))