Average Error: 10.6 → 0.0
Time: 2.9s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(1 - y\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(1 - y\right) \cdot \frac{x}{z} + y
double f(double x, double y, double z) {
        double r812103 = x;
        double r812104 = y;
        double r812105 = z;
        double r812106 = r812105 - r812103;
        double r812107 = r812104 * r812106;
        double r812108 = r812103 + r812107;
        double r812109 = r812108 / r812105;
        return r812109;
}
↓
double f(double x, double y, double z) {
        double r812110 = 1.0;
        double r812111 = y;
        double r812112 = r812110 - r812111;
        double r812113 = x;
        double r812114 = z;
        double r812115 = r812113 / r812114;
        double r812116 = r812112 * r812115;
        double r812117 = r812116 + r812111;
        return r812117;
}

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

Original10.6
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.6

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 - y, \frac{x}{z}, y\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 +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))