Average Error: 0.4 → 0.2
Time: 14.6s
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 r147451 = x;
        double r147452 = y;
        double r147453 = r147452 - r147451;
        double r147454 = 6.0;
        double r147455 = r147453 * r147454;
        double r147456 = 2.0;
        double r147457 = 3.0;
        double r147458 = r147456 / r147457;
        double r147459 = z;
        double r147460 = r147458 - r147459;
        double r147461 = r147455 * r147460;
        double r147462 = r147451 + r147461;
        return r147462;
}
↓
double f(double x, double y, double z) {
        double r147463 = 6.0;
        double r147464 = -r147463;
        double r147465 = z;
        double r147466 = r147464 * r147465;
        double r147467 = y;
        double r147468 = x;
        double r147469 = r147467 - r147468;
        double r147470 = r147466 * r147469;
        double r147471 = 2.0;
        double r147472 = 3.0;
        double r147473 = r147471 / r147472;
        double r147474 = r147473 * r147463;
        double r147475 = r147469 * r147474;
        double r147476 = r147470 + r147475;
        double r147477 = r147476 + r147468;
        return r147477;
}

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 sub-neg0.4

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

  4. Applied distribute-lft-in0.4

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  7. 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 2019174 +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))))