Average Error: 10.4 → 2.9
Time: 8.5s
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 r661883 = x;
        double r661884 = y;
        double r661885 = z;
        double r661886 = r661885 - r661883;
        double r661887 = r661884 * r661886;
        double r661888 = r661883 + r661887;
        double r661889 = r661888 / r661885;
        return r661889;
}
↓
double f(double x, double y, double z) {
        double r661890 = x;
        double r661891 = z;
        double r661892 = 1.0;
        double r661893 = y;
        double r661894 = r661892 - r661893;
        double r661895 = r661891 / r661894;
        double r661896 = r661890 / r661895;
        double r661897 = r661896 + r661893;
        return r661897;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original10.4
Target0.0
Herbie2.9
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around 0 3.4

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

  3. Taylor expanded around 0 3.4

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

  4. Simplified0.0

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

  5. Final simplification2.9

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

Reproduce

herbie shell --seed 2019291 
(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))