Average Error: 0.4 → 0.2
Time: 19.9s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
↓
\[\left(6.0 \cdot \left(-\left(y - x\right)\right)\right) \cdot z + \left(x + \left(6.0 \cdot \frac{2.0}{3.0}\right) \cdot \left(y - x\right)\right)\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)
↓
\left(6.0 \cdot \left(-\left(y - x\right)\right)\right) \cdot z + \left(x + \left(6.0 \cdot \frac{2.0}{3.0}\right) \cdot \left(y - x\right)\right)
double f(double x, double y, double z) {
        double r15436240 = x;
        double r15436241 = y;
        double r15436242 = r15436241 - r15436240;
        double r15436243 = 6.0;
        double r15436244 = r15436242 * r15436243;
        double r15436245 = 2.0;
        double r15436246 = 3.0;
        double r15436247 = r15436245 / r15436246;
        double r15436248 = z;
        double r15436249 = r15436247 - r15436248;
        double r15436250 = r15436244 * r15436249;
        double r15436251 = r15436240 + r15436250;
        return r15436251;
}
↓
double f(double x, double y, double z) {
        double r15436252 = 6.0;
        double r15436253 = y;
        double r15436254 = x;
        double r15436255 = r15436253 - r15436254;
        double r15436256 = -r15436255;
        double r15436257 = r15436252 * r15436256;
        double r15436258 = z;
        double r15436259 = r15436257 * r15436258;
        double r15436260 = 2.0;
        double r15436261 = 3.0;
        double r15436262 = r15436260 / r15436261;
        double r15436263 = r15436252 * r15436262;
        double r15436264 = r15436263 * r15436255;
        double r15436265 = r15436254 + r15436264;
        double r15436266 = r15436259 + r15436265;
        return r15436266;
}

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 associate-*l*0.2

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

  5. Applied sub-neg0.2

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

  6. Applied distribute-lft-in0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Applied associate-+r+0.2

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

  10. Applied neg-mul-10.2

    \[\leadsto \left(x + \left(y - x\right) \cdot \left(6.0 \cdot \frac{2.0}{3.0}\right)\right) + \left(y - x\right) \cdot \left(6.0 \cdot \color{blue}{\left(-1 \cdot z\right)}\right)\]

  11. Applied associate-*r*0.2

    \[\leadsto \left(x + \left(y - x\right) \cdot \left(6.0 \cdot \frac{2.0}{3.0}\right)\right) + \left(y - x\right) \cdot \color{blue}{\left(\left(6.0 \cdot -1\right) \cdot z\right)}\]

  12. Applied associate-*r*0.2

    \[\leadsto \left(x + \left(y - x\right) \cdot \left(6.0 \cdot \frac{2.0}{3.0}\right)\right) + \color{blue}{\left(\left(y - x\right) \cdot \left(6.0 \cdot -1\right)\right) \cdot z}\]

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(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))))