Average Error: 0.4 → 0.2
Time: 12.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(\left(-\left(6 \cdot z\right) \cdot \left(y - x\right)\right) + \left(6 \cdot \frac{2}{3}\right) \cdot \left(y - x\right)\right) + x\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(\left(-\left(6 \cdot z\right) \cdot \left(y - x\right)\right) + \left(6 \cdot \frac{2}{3}\right) \cdot \left(y - x\right)\right) + x
double f(double x, double y, double z) {
        double r154287 = x;
        double r154288 = y;
        double r154289 = r154288 - r154287;
        double r154290 = 6.0;
        double r154291 = r154289 * r154290;
        double r154292 = 2.0;
        double r154293 = 3.0;
        double r154294 = r154292 / r154293;
        double r154295 = z;
        double r154296 = r154294 - r154295;
        double r154297 = r154291 * r154296;
        double r154298 = r154287 + r154297;
        return r154298;
}
↓
double f(double x, double y, double z) {
        double r154299 = 6.0;
        double r154300 = z;
        double r154301 = r154299 * r154300;
        double r154302 = y;
        double r154303 = x;
        double r154304 = r154302 - r154303;
        double r154305 = r154301 * r154304;
        double r154306 = -r154305;
        double r154307 = 2.0;
        double r154308 = 3.0;
        double r154309 = r154307 / r154308;
        double r154310 = r154299 * r154309;
        double r154311 = r154310 * r154304;
        double r154312 = r154306 + r154311;
        double r154313 = r154312 + r154303;
        return r154313;
}

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

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 
(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))))