Average Error: 10.3 → 0.0
Time: 2.4s
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 r876555 = x;
        double r876556 = y;
        double r876557 = z;
        double r876558 = r876557 - r876555;
        double r876559 = r876556 * r876558;
        double r876560 = r876555 + r876559;
        double r876561 = r876560 / r876557;
        return r876561;
}
↓
double f(double x, double y, double z) {
        double r876562 = 1.0;
        double r876563 = y;
        double r876564 = r876562 - r876563;
        double r876565 = x;
        double r876566 = z;
        double r876567 = r876565 / r876566;
        double r876568 = r876564 * r876567;
        double r876569 = r876568 + r876563;
        return r876569;
}

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. 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 2020020 +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))