Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)
double f(double x, double y) {
        double r59083 = x;
        double r59084 = y;
        double r59085 = 1.0;
        double r59086 = r59084 - r59085;
        double r59087 = r59083 * r59086;
        double r59088 = 0.5;
        double r59089 = r59084 * r59088;
        double r59090 = r59087 - r59089;
        double r59091 = 0.918938533204673;
        double r59092 = r59090 + r59091;
        return r59092;
}
↓
double f(double x, double y) {
        double r59093 = y;
        double r59094 = x;
        double r59095 = 0.918938533204673;
        double r59096 = fma(r59093, r59094, r59095);
        double r59097 = 1.0;
        double r59098 = 0.5;
        double r59099 = r59093 * r59098;
        double r59100 = fma(r59094, r59097, r59099);
        double r59101 = r59096 - r59100;
        return r59101;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2020065 +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))