Average Error: 10.2 → 3.4
Time: 16.5s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \left(x \cdot y - x\right) \cdot \frac{1}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \left(x \cdot y - x\right) \cdot \frac{1}{z}
double f(double x, double y, double z) {
        double r474910 = x;
        double r474911 = y;
        double r474912 = z;
        double r474913 = r474912 - r474910;
        double r474914 = r474911 * r474913;
        double r474915 = r474910 + r474914;
        double r474916 = r474915 / r474912;
        return r474916;
}
↓
double f(double x, double y, double z) {
        double r474917 = y;
        double r474918 = x;
        double r474919 = r474918 * r474917;
        double r474920 = r474919 - r474918;
        double r474921 = 1.0;
        double r474922 = z;
        double r474923 = r474921 / r474922;
        double r474924 = r474920 * r474923;
        double r474925 = r474917 - r474924;
        return r474925;
}

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

Original10.2
Target0.0
Herbie3.4
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.3

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

  3. Simplified3.3

    \[\leadsto \color{blue}{y - \frac{x \cdot y - x}{z}}\]
  4. Using strategy rm

  5. Applied div-inv3.4

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

  6. Final simplification3.4

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

Reproduce

herbie shell --seed 2019323 
(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))