Average Error: 0.1 → 0.0
Time: 13.7s
Precision: 64
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x}{z} - \left(0.5 + \frac{y}{z}\right)\right) \cdot 4.0\]
\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x}{z} - \left(0.5 + \frac{y}{z}\right)\right) \cdot 4.0
double f(double x, double y, double z) {
        double r40111874 = 4.0;
        double r40111875 = x;
        double r40111876 = y;
        double r40111877 = r40111875 - r40111876;
        double r40111878 = z;
        double r40111879 = 0.5;
        double r40111880 = r40111878 * r40111879;
        double r40111881 = r40111877 - r40111880;
        double r40111882 = r40111874 * r40111881;
        double r40111883 = r40111882 / r40111878;
        return r40111883;
}
↓
double f(double x, double y, double z) {
        double r40111884 = x;
        double r40111885 = z;
        double r40111886 = r40111884 / r40111885;
        double r40111887 = 0.5;
        double r40111888 = y;
        double r40111889 = r40111888 / r40111885;
        double r40111890 = r40111887 + r40111889;
        double r40111891 = r40111886 - r40111890;
        double r40111892 = 4.0;
        double r40111893 = r40111891 * r40111892;
        return r40111893;
}

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
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4.0}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0.5\right) \cdot 4.0\]

  5. Applied associate--l-0.0

    \[\leadsto \color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)} \cdot 4.0\]

  6. Final simplification0.0

    \[\leadsto \left(\frac{x}{z} - \left(0.5 + \frac{y}{z}\right)\right) \cdot 4.0\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))