Average Error: 10.3 → 2.9
Time: 10.0s
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 r592740 = x;
        double r592741 = y;
        double r592742 = z;
        double r592743 = r592742 - r592740;
        double r592744 = r592741 * r592743;
        double r592745 = r592740 + r592744;
        double r592746 = r592745 / r592742;
        return r592746;
}
↓
double f(double x, double y, double z) {
        double r592747 = x;
        double r592748 = z;
        double r592749 = 1.0;
        double r592750 = y;
        double r592751 = r592749 - r592750;
        double r592752 = r592748 / r592751;
        double r592753 = r592747 / r592752;
        double r592754 = r592753 + r592750;
        return r592754;
}

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

Original10.3
Target0.0
Herbie2.9
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  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 simplification2.9

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

Reproduce

herbie shell --seed 2019294 
(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))