Average Error: 9.8 → 0.0
Time: 13.2s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{x}{z} \cdot y
double f(double x, double y, double z) {
        double r34217070 = x;
        double r34217071 = y;
        double r34217072 = z;
        double r34217073 = r34217072 - r34217070;
        double r34217074 = r34217071 * r34217073;
        double r34217075 = r34217070 + r34217074;
        double r34217076 = r34217075 / r34217072;
        return r34217076;
}
↓
double f(double x, double y, double z) {
        double r34217077 = x;
        double r34217078 = z;
        double r34217079 = r34217077 / r34217078;
        double r34217080 = y;
        double r34217081 = r34217079 + r34217080;
        double r34217082 = r34217079 * r34217080;
        double r34217083 = r34217081 - r34217082;
        return r34217083;
}

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

Original9.8
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.8

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

  2. Taylor expanded around 0 3.2

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

  3. Taylor expanded around 0 3.2

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(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))