Average Error: 10.3 → 0.0
Time: 2.9s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r750888 = x;
        double r750889 = y;
        double r750890 = z;
        double r750891 = r750890 - r750888;
        double r750892 = r750889 * r750891;
        double r750893 = r750888 + r750892;
        double r750894 = r750893 / r750890;
        return r750894;
}
↓
double f(double x, double y, double z) {
        double r750895 = x;
        double r750896 = z;
        double r750897 = r750895 / r750896;
        double r750898 = y;
        double r750899 = r750897 + r750898;
        double r750900 = r750897 * r750898;
        double r750901 = r750899 - r750900;
        return r750901;
}

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

Original10.3
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  2. Taylor expanded around 0 3.5

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

  3. Taylor expanded around 0 3.5

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

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

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