Average Error: 10.2 → 0.0
Time: 14.9s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \left(y \cdot \frac{x}{z} - \frac{x}{z}\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \left(y \cdot \frac{x}{z} - \frac{x}{z}\right)
double f(double x, double y, double z) {
        double r506686 = x;
        double r506687 = y;
        double r506688 = z;
        double r506689 = r506688 - r506686;
        double r506690 = r506687 * r506689;
        double r506691 = r506686 + r506690;
        double r506692 = r506691 / r506688;
        return r506692;
}
↓
double f(double x, double y, double z) {
        double r506693 = y;
        double r506694 = x;
        double r506695 = z;
        double r506696 = r506694 / r506695;
        double r506697 = r506693 * r506696;
        double r506698 = r506697 - r506696;
        double r506699 = r506693 - r506698;
        return r506699;
}

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

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.4

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

  3. Simplified3.4

    \[\leadsto \color{blue}{y - \frac{x \cdot y - x}{z}}\]
  4. Using strategy rm

  5. Applied div-sub3.4

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

  6. Taylor expanded around 0 3.4

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(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))