Average Error: 9.8 → 0.0
Time: 3.7s
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 r792510 = x;
        double r792511 = y;
        double r792512 = z;
        double r792513 = r792512 - r792510;
        double r792514 = r792511 * r792513;
        double r792515 = r792510 + r792514;
        double r792516 = r792515 / r792512;
        return r792516;
}
↓
double f(double x, double y, double z) {
        double r792517 = 1.0;
        double r792518 = y;
        double r792519 = r792517 - r792518;
        double r792520 = x;
        double r792521 = z;
        double r792522 = r792520 / r792521;
        double r792523 = r792519 * r792522;
        double r792524 = r792523 + r792518;
        return r792524;
}

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

Original9.8
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.8

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

  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 2020100 +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))