Average Error: 0.1 → 0.0
Time: 13.4s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)
double f(double x, double y, double z) {
        double r558444 = 4.0;
        double r558445 = x;
        double r558446 = y;
        double r558447 = r558445 - r558446;
        double r558448 = z;
        double r558449 = 0.5;
        double r558450 = r558448 * r558449;
        double r558451 = r558447 - r558450;
        double r558452 = r558444 * r558451;
        double r558453 = r558452 / r558448;
        return r558453;
}
↓
double f(double x, double y, double z) {
        double r558454 = 4.0;
        double r558455 = x;
        double r558456 = z;
        double r558457 = r558455 / r558456;
        double r558458 = y;
        double r558459 = r558458 / r558456;
        double r558460 = r558457 - r558459;
        double r558461 = 0.5;
        double r558462 = r558460 - r558461;
        double r558463 = r558454 * r558462;
        return r558463;
}

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. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 4 \cdot \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0.5\right)\]

  5. Final simplification0.0

    \[\leadsto 4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]

Reproduce

herbie shell --seed 2019325 
(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))