Average Error: 9.7 → 2.7
Time: 8.4s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\frac{x}{\frac{z}{1 - y}} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\frac{x}{\frac{z}{1 - y}} + y
double f(double x, double y, double z) {
        double r501067 = x;
        double r501068 = y;
        double r501069 = z;
        double r501070 = r501069 - r501067;
        double r501071 = r501068 * r501070;
        double r501072 = r501067 + r501071;
        double r501073 = r501072 / r501069;
        return r501073;
}
↓
double f(double x, double y, double z) {
        double r501074 = x;
        double r501075 = z;
        double r501076 = 1.0;
        double r501077 = y;
        double r501078 = r501076 - r501077;
        double r501079 = r501075 / r501078;
        double r501080 = r501074 / r501079;
        double r501081 = r501080 + r501077;
        return r501081;
}

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

Original9.7
Target0.0
Herbie2.7
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.7

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

  2. Taylor expanded around 0 3.2

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

  3. Taylor expanded around 0 3.2

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

  4. Simplified0.0

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

  5. Final simplification2.7

    \[\leadsto \frac{x}{\frac{z}{1 - y}} + y\]

Reproduce

herbie shell --seed 2019298 
(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))