Average Error: 0.2 → 0.0
Time: 11.0s
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 r1048933 = 4.0;
        double r1048934 = x;
        double r1048935 = y;
        double r1048936 = r1048934 - r1048935;
        double r1048937 = z;
        double r1048938 = 0.5;
        double r1048939 = r1048937 * r1048938;
        double r1048940 = r1048936 - r1048939;
        double r1048941 = r1048933 * r1048940;
        double r1048942 = r1048941 / r1048937;
        return r1048942;
}
↓
double f(double x, double y, double z) {
        double r1048943 = 4.0;
        double r1048944 = x;
        double r1048945 = z;
        double r1048946 = r1048944 / r1048945;
        double r1048947 = y;
        double r1048948 = r1048947 / r1048945;
        double r1048949 = r1048946 - r1048948;
        double r1048950 = 0.5;
        double r1048951 = r1048949 - r1048950;
        double r1048952 = r1048943 * r1048951;
        return r1048952;
}

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

Original0.2
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

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

  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 2020042 +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))