Average Error: 0.2 → 0.0
Time: 1.5s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r880669 = 4.0;
        double r880670 = x;
        double r880671 = y;
        double r880672 = r880670 - r880671;
        double r880673 = z;
        double r880674 = 0.5;
        double r880675 = r880673 * r880674;
        double r880676 = r880672 - r880675;
        double r880677 = r880669 * r880676;
        double r880678 = r880677 / r880673;
        return r880678;
}
↓
double f(double x, double y, double z) {
        double r880679 = 4.0;
        double r880680 = x;
        double r880681 = y;
        double r880682 = r880680 - r880681;
        double r880683 = z;
        double r880684 = r880682 / r880683;
        double r880685 = r880679 * r880684;
        double r880686 = 2.0;
        double r880687 = -r880686;
        double r880688 = r880685 + r880687;
        return r880688;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020003 
(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))