Average Error: 0.4 → 0.2
Time: 3.0s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(\left(\left(\left(-z\right) \cdot 6\right) \cdot y + x\right) + \left(\frac{2}{3} \cdot 6\right) \cdot \left(y - x\right)\right) + \left(\left(-z\right) \cdot 6\right) \cdot \left(-x\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(\left(\left(\left(-z\right) \cdot 6\right) \cdot y + x\right) + \left(\frac{2}{3} \cdot 6\right) \cdot \left(y - x\right)\right) + \left(\left(-z\right) \cdot 6\right) \cdot \left(-x\right)
double f(double x, double y, double z) {
        double r290308 = x;
        double r290309 = y;
        double r290310 = r290309 - r290308;
        double r290311 = 6.0;
        double r290312 = r290310 * r290311;
        double r290313 = 2.0;
        double r290314 = 3.0;
        double r290315 = r290313 / r290314;
        double r290316 = z;
        double r290317 = r290315 - r290316;
        double r290318 = r290312 * r290317;
        double r290319 = r290308 + r290318;
        return r290319;
}
↓
double f(double x, double y, double z) {
        double r290320 = z;
        double r290321 = -r290320;
        double r290322 = 6.0;
        double r290323 = r290321 * r290322;
        double r290324 = y;
        double r290325 = r290323 * r290324;
        double r290326 = x;
        double r290327 = r290325 + r290326;
        double r290328 = 2.0;
        double r290329 = 3.0;
        double r290330 = r290328 / r290329;
        double r290331 = r290330 * r290322;
        double r290332 = r290324 - r290326;
        double r290333 = r290331 * r290332;
        double r290334 = r290327 + r290333;
        double r290335 = -r290326;
        double r290336 = r290323 * r290335;
        double r290337 = r290334 + r290336;
        return r290337;
}

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. Applied associate-+r+0.2

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

  10. Applied sub-neg0.2

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

  11. Applied distribute-rgt-in0.2

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

  12. Applied associate-+r+0.2

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

  14. Applied sub-neg0.2

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

  15. Applied distribute-lft-in0.2

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

  16. Applied associate-+r+0.2

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

  17. Simplified0.2

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

  18. Final simplification0.2

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

Reproduce

herbie shell --seed 2020064 
(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))))