Average Error: 0.1 → 0.0
Time: 9.1s
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 r859602 = 4.0;
        double r859603 = x;
        double r859604 = y;
        double r859605 = r859603 - r859604;
        double r859606 = z;
        double r859607 = 0.5;
        double r859608 = r859606 * r859607;
        double r859609 = r859605 - r859608;
        double r859610 = r859602 * r859609;
        double r859611 = r859610 / r859606;
        return r859611;
}
↓
double f(double x, double y, double z) {
        double r859612 = 4.0;
        double r859613 = x;
        double r859614 = y;
        double r859615 = r859613 - r859614;
        double r859616 = z;
        double r859617 = r859615 / r859616;
        double r859618 = 0.5;
        double r859619 = r859617 - r859618;
        double r859620 = r859612 * r859619;
        return r859620;
}

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. 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 2019350 
(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))