Average Error: 10.3 → 0.0
Time: 20.7s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y
double f(double x, double y, double z) {
        double r622000 = x;
        double r622001 = y;
        double r622002 = z;
        double r622003 = r622002 - r622000;
        double r622004 = r622001 * r622003;
        double r622005 = r622000 + r622004;
        double r622006 = r622005 / r622002;
        return r622006;
}
↓
double f(double x, double y, double z) {
        double r622007 = y;
        double r622008 = -r622007;
        double r622009 = 1.0;
        double r622010 = r622008 + r622009;
        double r622011 = x;
        double r622012 = z;
        double r622013 = r622011 / r622012;
        double r622014 = r622010 * r622013;
        double r622015 = r622014 + r622007;
        return r622015;
}

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

Original10.3
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.3

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

  2. Simplified10.3

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z - x, y, x\right)}{z}}\]

  3. Taylor expanded around 0 3.5

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

  4. Taylor expanded around 0 3.5

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(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))