Average Error: 9.4 → 0.0
Time: 11.5s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} - \frac{x}{z} \cdot y\right) + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} - \frac{x}{z} \cdot y\right) + y
double f(double x, double y, double z) {
        double r34606510 = x;
        double r34606511 = y;
        double r34606512 = z;
        double r34606513 = r34606512 - r34606510;
        double r34606514 = r34606511 * r34606513;
        double r34606515 = r34606510 + r34606514;
        double r34606516 = r34606515 / r34606512;
        return r34606516;
}
↓
double f(double x, double y, double z) {
        double r34606517 = x;
        double r34606518 = z;
        double r34606519 = r34606517 / r34606518;
        double r34606520 = y;
        double r34606521 = r34606519 * r34606520;
        double r34606522 = r34606519 - r34606521;
        double r34606523 = r34606522 + r34606520;
        return r34606523;
}

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

Original9.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.4

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

  2. Taylor expanded around 0 3.3

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

  4. Applied associate--l+3.3

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(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))