Average Error: 10.4 → 0.0
Time: 15.3s
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 r34524651 = x;
        double r34524652 = y;
        double r34524653 = z;
        double r34524654 = r34524653 - r34524651;
        double r34524655 = r34524652 * r34524654;
        double r34524656 = r34524651 + r34524655;
        double r34524657 = r34524656 / r34524653;
        return r34524657;
}
↓
double f(double x, double y, double z) {
        double r34524658 = x;
        double r34524659 = z;
        double r34524660 = r34524658 / r34524659;
        double r34524661 = y;
        double r34524662 = r34524660 * r34524661;
        double r34524663 = r34524660 - r34524662;
        double r34524664 = r34524663 + r34524661;
        return r34524664;
}

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

Original10.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around 0 3.5

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

  4. Applied associate--l+3.5

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(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))