Average Error: 10.7 → 0.0
Time: 12.6s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(-\frac{x}{z}\right) \cdot y + \left(\frac{x}{z} + y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(-\frac{x}{z}\right) \cdot y + \left(\frac{x}{z} + y\right)
double f(double x, double y, double z) {
        double r727709 = x;
        double r727710 = y;
        double r727711 = z;
        double r727712 = r727711 - r727709;
        double r727713 = r727710 * r727712;
        double r727714 = r727709 + r727713;
        double r727715 = r727714 / r727711;
        return r727715;
}
↓
double f(double x, double y, double z) {
        double r727716 = x;
        double r727717 = z;
        double r727718 = r727716 / r727717;
        double r727719 = -r727718;
        double r727720 = y;
        double r727721 = r727719 * r727720;
        double r727722 = r727718 + r727720;
        double r727723 = r727721 + r727722;
        return r727723;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.7
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.7

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

  2. Taylor expanded around 0 3.4

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

  3. Simplified3.4

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

  5. Applied sub-neg3.4

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(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))