Average Error: 0.0 → 0.0
Time: 934.0ms
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
double f(double x, double y) {
        double r58461 = x;
        double r58462 = y;
        double r58463 = 1.0;
        double r58464 = r58462 - r58463;
        double r58465 = r58461 * r58464;
        double r58466 = 0.5;
        double r58467 = r58462 * r58466;
        double r58468 = r58465 - r58467;
        double r58469 = 0.918938533204673;
        double r58470 = r58468 + r58469;
        return r58470;
}
↓
double f(double x, double y) {
        double r58471 = x;
        double r58472 = y;
        double r58473 = r58471 * r58472;
        double r58474 = 1.0;
        double r58475 = -r58474;
        double r58476 = r58471 * r58475;
        double r58477 = r58473 + r58476;
        double r58478 = 0.5;
        double r58479 = r58472 * r58478;
        double r58480 = r58477 - r58479;
        double r58481 = 0.918938533204673;
        double r58482 = r58480 + r58481;
        return r58482;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto \left(x \cdot \color{blue}{\left(y + \left(-1\right)\right)} - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \left(\color{blue}{\left(x \cdot y + x \cdot \left(-1\right)\right)} - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

  5. Final simplification0.0

    \[\leadsto \left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

Reproduce

herbie shell --seed 2019352 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1)) (* y 0.5)) 0.918938533204673))