Average Error: 0.4 → 0.2
Time: 23.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(\left(\left(-6\right) \cdot z\right) \cdot \left(y - x\right) + \left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right)\right) + x\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(\left(\left(-6\right) \cdot z\right) \cdot \left(y - x\right) + \left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right)\right) + x
double f(double x, double y, double z) {
        double r13484407 = x;
        double r13484408 = y;
        double r13484409 = r13484408 - r13484407;
        double r13484410 = 6.0;
        double r13484411 = r13484409 * r13484410;
        double r13484412 = 2.0;
        double r13484413 = 3.0;
        double r13484414 = r13484412 / r13484413;
        double r13484415 = z;
        double r13484416 = r13484414 - r13484415;
        double r13484417 = r13484411 * r13484416;
        double r13484418 = r13484407 + r13484417;
        return r13484418;
}
↓
double f(double x, double y, double z) {
        double r13484419 = 6.0;
        double r13484420 = -r13484419;
        double r13484421 = z;
        double r13484422 = r13484420 * r13484421;
        double r13484423 = y;
        double r13484424 = x;
        double r13484425 = r13484423 - r13484424;
        double r13484426 = r13484422 * r13484425;
        double r13484427 = 2.0;
        double r13484428 = 3.0;
        double r13484429 = r13484427 / r13484428;
        double r13484430 = r13484429 * r13484419;
        double r13484431 = r13484425 * r13484430;
        double r13484432 = r13484426 + r13484431;
        double r13484433 = r13484432 + r13484424;
        return r13484433;
}

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. Using strategy rm

  5. Applied sub-neg0.2

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

  6. Applied distribute-rgt-in0.2

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

  7. Applied distribute-rgt-in0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(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))))