Average Error: 0.1 → 0.0
Time: 10.2s
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 r804619 = 4.0;
        double r804620 = x;
        double r804621 = y;
        double r804622 = r804620 - r804621;
        double r804623 = z;
        double r804624 = 0.5;
        double r804625 = r804623 * r804624;
        double r804626 = r804622 - r804625;
        double r804627 = r804619 * r804626;
        double r804628 = r804627 / r804623;
        return r804628;
}
↓
double f(double x, double y, double z) {
        double r804629 = 4.0;
        double r804630 = x;
        double r804631 = y;
        double r804632 = r804630 - r804631;
        double r804633 = z;
        double r804634 = r804632 / r804633;
        double r804635 = 0.5;
        double r804636 = r804634 - r804635;
        double r804637 = r804629 * r804636;
        return r804637;
}

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 +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))