Average Error: 9.0 → 0.0
Time: 13.2s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} - \frac{x}{z} \cdot y\right) + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} - \frac{x}{z} \cdot y\right) + y
double f(double x, double y, double z) {
        double r38685788 = x;
        double r38685789 = y;
        double r38685790 = z;
        double r38685791 = r38685790 - r38685788;
        double r38685792 = r38685789 * r38685791;
        double r38685793 = r38685788 + r38685792;
        double r38685794 = r38685793 / r38685790;
        return r38685794;
}
↓
double f(double x, double y, double z) {
        double r38685795 = x;
        double r38685796 = z;
        double r38685797 = r38685795 / r38685796;
        double r38685798 = y;
        double r38685799 = r38685797 * r38685798;
        double r38685800 = r38685797 - r38685799;
        double r38685801 = r38685800 + r38685798;
        return r38685801;
}

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

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

Derivation

  1. Initial program 9.0

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

  2. Taylor expanded around 0 3.1

    \[\leadsto \color{blue}{\left(y + \frac{x}{z}\right) - \frac{x \cdot y}{z}}\]
  3. Using strategy rm

  4. Applied associate--l+3.1

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(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))