Average Error: 0.1 → 0.0
Time: 4.1s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} - 2
double f(double x, double y, double z) {
        double r579984 = 4.0;
        double r579985 = x;
        double r579986 = y;
        double r579987 = r579985 - r579986;
        double r579988 = z;
        double r579989 = 0.5;
        double r579990 = r579988 * r579989;
        double r579991 = r579987 - r579990;
        double r579992 = r579984 * r579991;
        double r579993 = r579992 / r579988;
        return r579993;
}
↓
double f(double x, double y, double z) {
        double r579994 = 4.0;
        double r579995 = x;
        double r579996 = y;
        double r579997 = r579995 - r579996;
        double r579998 = z;
        double r579999 = r579997 / r579998;
        double r580000 = r579994 * r579999;
        double r580001 = 2.0;
        double r580002 = r580000 - r580001;
        return r580002;
}

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

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]

  4. Final simplification0.0

    \[\leadsto 4 \cdot \frac{x - y}{z} - 2\]

Reproduce

herbie shell --seed 2019208 +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))