Average Error: 0.0 → 0.0
Time: 7.9s
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 r38454 = x;
        double r38455 = y;
        double r38456 = 1.0;
        double r38457 = r38455 - r38456;
        double r38458 = r38454 * r38457;
        double r38459 = 0.5;
        double r38460 = r38455 * r38459;
        double r38461 = r38458 - r38460;
        double r38462 = 0.918938533204673;
        double r38463 = r38461 + r38462;
        return r38463;
}
↓
double f(double x, double y) {
        double r38464 = x;
        double r38465 = y;
        double r38466 = r38464 * r38465;
        double r38467 = 1.0;
        double r38468 = -r38467;
        double r38469 = r38464 * r38468;
        double r38470 = r38466 + r38469;
        double r38471 = 0.5;
        double r38472 = r38465 * r38471;
        double r38473 = r38470 - r38472;
        double r38474 = 0.918938533204673;
        double r38475 = r38473 + r38474;
        return r38475;
}

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 2019323 +o rules:numerics
(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))