Average Error: 0.4 → 0.2
Time: 7.5s
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 r339556 = x;
        double r339557 = y;
        double r339558 = r339557 - r339556;
        double r339559 = 6.0;
        double r339560 = r339558 * r339559;
        double r339561 = 2.0;
        double r339562 = 3.0;
        double r339563 = r339561 / r339562;
        double r339564 = z;
        double r339565 = r339563 - r339564;
        double r339566 = r339560 * r339565;
        double r339567 = r339556 + r339566;
        return r339567;
}
↓
double f(double x, double y, double z) {
        double r339568 = x;
        double r339569 = y;
        double r339570 = r339569 - r339568;
        double r339571 = 6.0;
        double r339572 = 2.0;
        double r339573 = 3.0;
        double r339574 = r339572 / r339573;
        double r339575 = z;
        double r339576 = r339574 - r339575;
        double r339577 = r339571 * r339576;
        double r339578 = r339570 * r339577;
        double r339579 = r339568 + r339578;
        return r339579;
}

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 2020047 
(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))))