Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003
double f(double x, double y) {
        double r47161 = x;
        double r47162 = y;
        double r47163 = 1.0;
        double r47164 = r47162 - r47163;
        double r47165 = r47161 * r47164;
        double r47166 = 0.5;
        double r47167 = r47162 * r47166;
        double r47168 = r47165 - r47167;
        double r47169 = 0.918938533204673;
        double r47170 = r47168 + r47169;
        return r47170;
}
↓
double f(double x, double y) {
        double r47171 = x;
        double r47172 = y;
        double r47173 = r47171 * r47172;
        double r47174 = 1.0;
        double r47175 = -r47174;
        double r47176 = r47171 * r47175;
        double r47177 = r47173 + r47176;
        double r47178 = 0.5;
        double r47179 = r47172 * r47178;
        double r47180 = r47177 - r47179;
        double r47181 = 0.918938533204673;
        double r47182 = r47180 + r47181;
        return r47182;
}

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

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto \left(x \cdot \color{blue}{\left(y + \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \left(\color{blue}{\left(x \cdot y + x \cdot \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

  5. Final simplification0.0

    \[\leadsto \left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003\]

Reproduce

herbie shell --seed 2020018 
(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))