Average Error: 0.4 → 0.2
Time: 8.9s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r329561 = x;
        double r329562 = y;
        double r329563 = r329562 - r329561;
        double r329564 = 6.0;
        double r329565 = r329563 * r329564;
        double r329566 = 2.0;
        double r329567 = 3.0;
        double r329568 = r329566 / r329567;
        double r329569 = z;
        double r329570 = r329568 - r329569;
        double r329571 = r329565 * r329570;
        double r329572 = r329561 + r329571;
        return r329572;
}
↓
double f(double x, double y, double z) {
        double r329573 = x;
        double r329574 = y;
        double r329575 = r329574 - r329573;
        double r329576 = 6.0;
        double r329577 = 2.0;
        double r329578 = 3.0;
        double r329579 = r329577 / r329578;
        double r329580 = z;
        double r329581 = r329579 - r329580;
        double r329582 = r329576 * r329581;
        double r329583 = r329575 * r329582;
        double r329584 = r329573 + r329583;
        return r329584;
}

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

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]

Reproduce

herbie shell --seed 2020089 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))