Average Error: 10.5 → 0.0
Time: 2.2s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y + \frac{x}{z} \cdot \left(1 - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y + \frac{x}{z} \cdot \left(1 - y\right)
double f(double x, double y, double z) {
        double r832914 = x;
        double r832915 = y;
        double r832916 = z;
        double r832917 = r832916 - r832914;
        double r832918 = r832915 * r832917;
        double r832919 = r832914 + r832918;
        double r832920 = r832919 / r832916;
        return r832920;
}
↓
double f(double x, double y, double z) {
        double r832921 = y;
        double r832922 = x;
        double r832923 = z;
        double r832924 = r832922 / r832923;
        double r832925 = 1.0;
        double r832926 = r832925 - r832921;
        double r832927 = r832924 * r832926;
        double r832928 = r832921 + r832927;
        return r832928;
}

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 3.6

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

  3. Taylor expanded around 0 3.6

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

  4. Simplified0.0

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

  5. Taylor expanded around 0 3.6

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

  6. Simplified0.0

    \[\leadsto \color{blue}{y + \frac{x}{z} \cdot \left(1 - y\right)}\]

  7. Final simplification0.0

    \[\leadsto y + \frac{x}{z} \cdot \left(1 - y\right)\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))