Average Error: 0.4 → 0.4
Time: 14.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
↓
\[\left(6.0 \cdot \left(z \cdot \left(x - y\right)\right) + \frac{2.0}{3.0} \cdot \left(\left(y - x\right) \cdot 6.0\right)\right) + x\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)
↓
\left(6.0 \cdot \left(z \cdot \left(x - y\right)\right) + \frac{2.0}{3.0} \cdot \left(\left(y - x\right) \cdot 6.0\right)\right) + x
double f(double x, double y, double z) {
        double r16474976 = x;
        double r16474977 = y;
        double r16474978 = r16474977 - r16474976;
        double r16474979 = 6.0;
        double r16474980 = r16474978 * r16474979;
        double r16474981 = 2.0;
        double r16474982 = 3.0;
        double r16474983 = r16474981 / r16474982;
        double r16474984 = z;
        double r16474985 = r16474983 - r16474984;
        double r16474986 = r16474980 * r16474985;
        double r16474987 = r16474976 + r16474986;
        return r16474987;
}
↓
double f(double x, double y, double z) {
        double r16474988 = 6.0;
        double r16474989 = z;
        double r16474990 = x;
        double r16474991 = y;
        double r16474992 = r16474990 - r16474991;
        double r16474993 = r16474989 * r16474992;
        double r16474994 = r16474988 * r16474993;
        double r16474995 = 2.0;
        double r16474996 = 3.0;
        double r16474997 = r16474995 / r16474996;
        double r16474998 = r16474991 - r16474990;
        double r16474999 = r16474998 * r16474988;
        double r16475000 = r16474997 * r16474999;
        double r16475001 = r16474994 + r16475000;
        double r16475002 = r16475001 + r16474990;
        return r16475002;
}

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

Derivation

  1. Initial program 0.4

    \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.4

    \[\leadsto x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \color{blue}{\left(\frac{2.0}{3.0} + \left(-z\right)\right)}\]

  4. Applied distribute-lft-in0.4

    \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6.0\right) \cdot \frac{2.0}{3.0} + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(-z\right)\right)}\]

  5. Taylor expanded around inf 0.4

    \[\leadsto x + \left(\left(\left(y - x\right) \cdot 6.0\right) \cdot \frac{2.0}{3.0} + \color{blue}{\left(6.0 \cdot \left(x \cdot z\right) - 6.0 \cdot \left(z \cdot y\right)\right)}\right)\]

  6. Simplified0.4

    \[\leadsto x + \left(\left(\left(y - x\right) \cdot 6.0\right) \cdot \frac{2.0}{3.0} + \color{blue}{6.0 \cdot \left(z \cdot \left(x - y\right)\right)}\right)\]

  7. Final simplification0.4

    \[\leadsto \left(6.0 \cdot \left(z \cdot \left(x - y\right)\right) + \frac{2.0}{3.0} \cdot \left(\left(y - x\right) \cdot 6.0\right)\right) + x\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))