Average Error: 0.1 → 0.0
Time: 13.1s
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 r507628 = 4.0;
        double r507629 = x;
        double r507630 = y;
        double r507631 = r507629 - r507630;
        double r507632 = z;
        double r507633 = 0.5;
        double r507634 = r507632 * r507633;
        double r507635 = r507631 - r507634;
        double r507636 = r507628 * r507635;
        double r507637 = r507636 / r507632;
        return r507637;
}
↓
double f(double x, double y, double z) {
        double r507638 = 4.0;
        double r507639 = x;
        double r507640 = y;
        double r507641 = r507639 - r507640;
        double r507642 = z;
        double r507643 = r507641 / r507642;
        double r507644 = 0.5;
        double r507645 = r507643 - r507644;
        double r507646 = r507638 * r507645;
        return r507646;
}

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 2019326 +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))