Average Error: 0.1 → 0.0
Time: 1.2s
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 r701721 = 4.0;
        double r701722 = x;
        double r701723 = y;
        double r701724 = r701722 - r701723;
        double r701725 = z;
        double r701726 = 0.5;
        double r701727 = r701725 * r701726;
        double r701728 = r701724 - r701727;
        double r701729 = r701721 * r701728;
        double r701730 = r701729 / r701725;
        return r701730;
}
↓
double f(double x, double y, double z) {
        double r701731 = 4.0;
        double r701732 = x;
        double r701733 = y;
        double r701734 = r701732 - r701733;
        double r701735 = z;
        double r701736 = r701734 / r701735;
        double r701737 = r701731 * r701736;
        double r701738 = 2.0;
        double r701739 = -r701738;
        double r701740 = r701737 + r701739;
        return r701740;
}

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. 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 2019362 
(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))