Average Error: 0.1 → 0.0
Time: 1.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r776874 = 4.0;
        double r776875 = x;
        double r776876 = y;
        double r776877 = r776875 - r776876;
        double r776878 = z;
        double r776879 = 0.5;
        double r776880 = r776878 * r776879;
        double r776881 = r776877 - r776880;
        double r776882 = r776874 * r776881;
        double r776883 = r776882 / r776878;
        return r776883;
}
↓
double f(double x, double y, double z) {
        double r776884 = 4.0;
        double r776885 = x;
        double r776886 = y;
        double r776887 = r776885 - r776886;
        double r776888 = z;
        double r776889 = r776887 / r776888;
        double r776890 = r776884 * r776889;
        double r776891 = 2.0;
        double r776892 = -r776891;
        double r776893 = r776890 + r776892;
        return r776893;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} + \left(-2\right)}\]

  4. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - y}{z} + \left(-2\right)\]

Reproduce

herbie shell --seed 2020100 
(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))