Average Error: 0.1 → 0.1
Time: 11.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
double f(double x, double y, double z) {
        double r751902 = 4.0;
        double r751903 = x;
        double r751904 = y;
        double r751905 = r751903 - r751904;
        double r751906 = z;
        double r751907 = 0.5;
        double r751908 = r751906 * r751907;
        double r751909 = r751905 - r751908;
        double r751910 = r751902 * r751909;
        double r751911 = r751910 / r751906;
        return r751911;
}
↓
double f(double x, double y, double z) {
        double r751912 = 4.0;
        double r751913 = x;
        double r751914 = y;
        double r751915 = r751913 - r751914;
        double r751916 = z;
        double r751917 = 0.5;
        double r751918 = r751916 * r751917;
        double r751919 = r751915 - r751918;
        double r751920 = r751912 * r751919;
        double r751921 = r751920 / r751916;
        return r751921;
}

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
Herbie0.1
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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))