Average Error: 9.5 → 0.0
Time: 9.7s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y
double f(double x, double y, double z) {
        double r532747 = x;
        double r532748 = y;
        double r532749 = z;
        double r532750 = r532749 - r532747;
        double r532751 = r532748 * r532750;
        double r532752 = r532747 + r532751;
        double r532753 = r532752 / r532749;
        return r532753;
}
↓
double f(double x, double y, double z) {
        double r532754 = y;
        double r532755 = -r532754;
        double r532756 = 1.0;
        double r532757 = r532755 + r532756;
        double r532758 = x;
        double r532759 = z;
        double r532760 = r532758 / r532759;
        double r532761 = r532757 * r532760;
        double r532762 = r532761 + r532754;
        return r532762;
}

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

Original9.5
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.5

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

  2. Taylor expanded around 0 3.2

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

  3. Taylor expanded around 0 3.2

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(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))