Average Error: 10.3 → 0.0
Time: 28.6s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[y - \left(\frac{x}{z} \cdot y - \frac{x}{z}\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
y - \left(\frac{x}{z} \cdot y - \frac{x}{z}\right)
double f(double x, double y, double z) {
        double r17463466 = x;
        double r17463467 = y;
        double r17463468 = z;
        double r17463469 = r17463468 - r17463466;
        double r17463470 = r17463467 * r17463469;
        double r17463471 = r17463466 + r17463470;
        double r17463472 = r17463471 / r17463468;
        return r17463472;
}
↓
double f(double x, double y, double z) {
        double r17463473 = y;
        double r17463474 = x;
        double r17463475 = z;
        double r17463476 = r17463474 / r17463475;
        double r17463477 = r17463476 * r17463473;
        double r17463478 = r17463477 - r17463476;
        double r17463479 = r17463473 - r17463478;
        return r17463479;
}

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

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

  3. Taylor expanded around 0 3.7

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))