Average Error: 10.3 → 0.0
Time: 36.5s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(-y\right) \cdot \frac{x}{z} + \left(\frac{x}{z} + y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(-y\right) \cdot \frac{x}{z} + \left(\frac{x}{z} + y\right)
double f(double x, double y, double z) {
        double r34499801 = x;
        double r34499802 = y;
        double r34499803 = z;
        double r34499804 = r34499803 - r34499801;
        double r34499805 = r34499802 * r34499804;
        double r34499806 = r34499801 + r34499805;
        double r34499807 = r34499806 / r34499803;
        return r34499807;
}
↓
double f(double x, double y, double z) {
        double r34499808 = y;
        double r34499809 = -r34499808;
        double r34499810 = x;
        double r34499811 = z;
        double r34499812 = r34499810 / r34499811;
        double r34499813 = r34499809 * r34499812;
        double r34499814 = r34499812 + r34499808;
        double r34499815 = r34499813 + r34499814;
        return r34499815;
}

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

Original10.3
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  2. Taylor expanded around 0 3.7

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

  4. Applied sub-neg3.7

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(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))