Average Error: 10.6 → 0.0
Time: 1.9s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \frac{x}{z} \cdot \left(1 - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \frac{x}{z} \cdot \left(1 - y\right)
double f(double x, double y, double z) {
        double r866719 = x;
        double r866720 = y;
        double r866721 = z;
        double r866722 = r866721 - r866719;
        double r866723 = r866720 * r866722;
        double r866724 = r866719 + r866723;
        double r866725 = r866724 / r866721;
        return r866725;
}
↓
double f(double x, double y, double z) {
        double r866726 = y;
        double r866727 = x;
        double r866728 = z;
        double r866729 = r866727 / r866728;
        double r866730 = 1.0;
        double r866731 = r866730 - r866726;
        double r866732 = r866729 * r866731;
        double r866733 = r866726 + r866732;
        return r866733;
}

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

Original10.6
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.6

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

  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. Taylor expanded around 0 3.5

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

  6. Simplified0.0

    \[\leadsto \color{blue}{y + \frac{x}{z} \cdot \left(1 - y\right)}\]

  7. Final simplification0.0

    \[\leadsto y + \frac{x}{z} \cdot \left(1 - y\right)\]

Reproduce

herbie shell --seed 2020060 
(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))