Average Error: 10.2 → 3.2
Time: 9.8s
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 r511085 = x;
        double r511086 = y;
        double r511087 = z;
        double r511088 = r511087 - r511085;
        double r511089 = r511086 * r511088;
        double r511090 = r511085 + r511089;
        double r511091 = r511090 / r511087;
        return r511091;
}
↓
double f(double x, double y, double z) {
        double r511092 = x;
        double r511093 = z;
        double r511094 = 1.0;
        double r511095 = y;
        double r511096 = r511094 - r511095;
        double r511097 = r511093 / r511096;
        double r511098 = r511092 / r511097;
        double r511099 = r511098 + r511095;
        return r511099;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.7

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

  3. Taylor expanded around 0 3.7

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

  4. Simplified0.0

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

  5. Final simplification3.2

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

Reproduce

herbie shell --seed 2019303 
(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))