Average Error: 0.1 → 0.0
Time: 15.1s
Precision: 64
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4.0 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4.0 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r38650728 = 4.0;
        double r38650729 = x;
        double r38650730 = y;
        double r38650731 = r38650729 - r38650730;
        double r38650732 = z;
        double r38650733 = 0.5;
        double r38650734 = r38650732 * r38650733;
        double r38650735 = r38650731 - r38650734;
        double r38650736 = r38650728 * r38650735;
        double r38650737 = r38650736 / r38650732;
        return r38650737;
}
↓
double f(double x, double y, double z) {
        double r38650738 = 4.0;
        double r38650739 = x;
        double r38650740 = y;
        double r38650741 = r38650739 - r38650740;
        double r38650742 = z;
        double r38650743 = r38650741 / r38650742;
        double r38650744 = 0.5;
        double r38650745 = r38650743 - r38650744;
        double r38650746 = r38650738 * r38650745;
        return r38650746;
}

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
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4.0}\]

  3. Final simplification0.0

    \[\leadsto 4.0 \cdot \left(\frac{x - y}{z} - 0.5\right)\]

Reproduce

herbie shell --seed 2019168 +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))