Average Error: 10.5 → 0.0
Time: 14.0s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\frac{x}{z} + \left(y - \frac{x}{z} \cdot y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\frac{x}{z} + \left(y - \frac{x}{z} \cdot y\right)
double f(double x, double y, double z) {
        double r39559625 = x;
        double r39559626 = y;
        double r39559627 = z;
        double r39559628 = r39559627 - r39559625;
        double r39559629 = r39559626 * r39559628;
        double r39559630 = r39559625 + r39559629;
        double r39559631 = r39559630 / r39559627;
        return r39559631;
}
↓
double f(double x, double y, double z) {
        double r39559632 = x;
        double r39559633 = z;
        double r39559634 = r39559632 / r39559633;
        double r39559635 = y;
        double r39559636 = r39559634 * r39559635;
        double r39559637 = r39559635 - r39559636;
        double r39559638 = r39559634 + r39559637;
        return r39559638;
}

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

Original10.5
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.5

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

  2. Taylor expanded around 0 3.5

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

  3. Taylor expanded around 0 3.5

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(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))