Average Error: 0.2 → 0.0
Time: 13.6s
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 r775612 = 4.0;
        double r775613 = x;
        double r775614 = y;
        double r775615 = r775613 - r775614;
        double r775616 = z;
        double r775617 = 0.5;
        double r775618 = r775616 * r775617;
        double r775619 = r775615 - r775618;
        double r775620 = r775612 * r775619;
        double r775621 = r775620 / r775616;
        return r775621;
}
↓
double f(double x, double y, double z) {
        double r775622 = 4.0;
        double r775623 = x;
        double r775624 = y;
        double r775625 = r775623 - r775624;
        double r775626 = z;
        double r775627 = r775625 / r775626;
        double r775628 = 0.5;
        double r775629 = r775627 - r775628;
        double r775630 = r775622 * r775629;
        return r775630;
}

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. 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 2019351 +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))