Average Error: 9.4 → 0.0
Time: 12.1s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\frac{x}{z} - \left(\frac{x}{z} \cdot y - y\right)\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\frac{x}{z} - \left(\frac{x}{z} \cdot y - y\right)
double f(double x, double y, double z) {
        double r30083427 = x;
        double r30083428 = y;
        double r30083429 = z;
        double r30083430 = r30083429 - r30083427;
        double r30083431 = r30083428 * r30083430;
        double r30083432 = r30083427 + r30083431;
        double r30083433 = r30083432 / r30083429;
        return r30083433;
}
↓
double f(double x, double y, double z) {
        double r30083434 = x;
        double r30083435 = z;
        double r30083436 = r30083434 / r30083435;
        double r30083437 = y;
        double r30083438 = r30083436 * r30083437;
        double r30083439 = r30083438 - r30083437;
        double r30083440 = r30083436 - r30083439;
        return r30083440;
}

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

Original9.4
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 9.4

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

  2. Simplified9.4

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

  3. Taylor expanded around 0 3.3

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 +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))