Average Error: 0.1 → 0.0
Time: 13.0s
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 r541296 = 4.0;
        double r541297 = x;
        double r541298 = y;
        double r541299 = r541297 - r541298;
        double r541300 = z;
        double r541301 = 0.5;
        double r541302 = r541300 * r541301;
        double r541303 = r541299 - r541302;
        double r541304 = r541296 * r541303;
        double r541305 = r541304 / r541300;
        return r541305;
}
↓
double f(double x, double y, double z) {
        double r541306 = 4.0;
        double r541307 = x;
        double r541308 = y;
        double r541309 = r541307 - r541308;
        double r541310 = z;
        double r541311 = r541309 / r541310;
        double r541312 = 0.5;
        double r541313 = r541311 - r541312;
        double r541314 = r541306 * r541313;
        return r541314;
}

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 
(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))