Average Error: 0.2 → 0.0
Time: 12.7s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2
double f(double x, double y, double z) {
        double r38765350 = 4.0;
        double r38765351 = x;
        double r38765352 = y;
        double r38765353 = r38765351 - r38765352;
        double r38765354 = z;
        double r38765355 = 0.5;
        double r38765356 = r38765354 * r38765355;
        double r38765357 = r38765353 - r38765356;
        double r38765358 = r38765350 * r38765357;
        double r38765359 = r38765358 / r38765354;
        return r38765359;
}
↓
double f(double x, double y, double z) {
        double r38765360 = 4.0;
        double r38765361 = x;
        double r38765362 = z;
        double r38765363 = r38765361 / r38765362;
        double r38765364 = y;
        double r38765365 = r38765364 / r38765362;
        double r38765366 = r38765363 - r38765365;
        double r38765367 = r38765360 * r38765366;
        double r38765368 = 2.0;
        double r38765369 = r38765367 - r38765368;
        return r38765369;
}

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

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

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 2\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))