Average Error: 10.2 → 0.0
Time: 3.1s
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 r838537 = x;
        double r838538 = y;
        double r838539 = z;
        double r838540 = r838539 - r838537;
        double r838541 = r838538 * r838540;
        double r838542 = r838537 + r838541;
        double r838543 = r838542 / r838539;
        return r838543;
}
↓
double f(double x, double y, double z) {
        double r838544 = 1.0;
        double r838545 = y;
        double r838546 = r838544 - r838545;
        double r838547 = x;
        double r838548 = z;
        double r838549 = r838547 / r838548;
        double r838550 = r838546 * r838549;
        double r838551 = r838550 + r838545;
        return r838551;
}

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

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  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 2020047 +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))