Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\left(\left(y \cdot x + \left(-1\right) \cdot x\right) - y \cdot 0.5\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\left(\left(y \cdot x + \left(-1\right) \cdot x\right) - y \cdot 0.5\right) + 0.918938533204673003
double f(double x, double y) {
        double r60240 = x;
        double r60241 = y;
        double r60242 = 1.0;
        double r60243 = r60241 - r60242;
        double r60244 = r60240 * r60243;
        double r60245 = 0.5;
        double r60246 = r60241 * r60245;
        double r60247 = r60244 - r60246;
        double r60248 = 0.918938533204673;
        double r60249 = r60247 + r60248;
        return r60249;
}
↓
double f(double x, double y) {
        double r60250 = y;
        double r60251 = x;
        double r60252 = r60250 * r60251;
        double r60253 = 1.0;
        double r60254 = -r60253;
        double r60255 = r60254 * r60251;
        double r60256 = r60252 + r60255;
        double r60257 = 0.5;
        double r60258 = r60250 * r60257;
        double r60259 = r60256 - r60258;
        double r60260 = 0.918938533204673;
        double r60261 = r60259 + r60260;
        return r60261;
}

Error

Bits error versus x

Bits error versus y

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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. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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))