Average Error: 0.1 → 0.0
Time: 18.3s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r761352 = 4.0;
        double r761353 = x;
        double r761354 = y;
        double r761355 = r761353 - r761354;
        double r761356 = z;
        double r761357 = 0.5;
        double r761358 = r761356 * r761357;
        double r761359 = r761355 - r761358;
        double r761360 = r761352 * r761359;
        double r761361 = r761360 / r761356;
        return r761361;
}
↓
double f(double x, double y, double z) {
        double r761362 = 4.0;
        double r761363 = x;
        double r761364 = y;
        double r761365 = r761363 - r761364;
        double r761366 = z;
        double r761367 = r761365 / r761366;
        double r761368 = 0.5;
        double r761369 = r761367 - r761368;
        double r761370 = r761362 * r761369;
        return r761370;
}

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

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \left(\frac{x - y}{z} - 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))