Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\mathsf{fma}\left(\log y, x, \log t - y\right) - z\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\mathsf{fma}\left(\log y, x, \log t - y\right) - z
double f(double x, double y, double z, double t) {
        double r5519642 = x;
        double r5519643 = y;
        double r5519644 = log(r5519643);
        double r5519645 = r5519642 * r5519644;
        double r5519646 = r5519645 - r5519643;
        double r5519647 = z;
        double r5519648 = r5519646 - r5519647;
        double r5519649 = t;
        double r5519650 = log(r5519649);
        double r5519651 = r5519648 + r5519650;
        return r5519651;
}
↓
double f(double x, double y, double z, double t) {
        double r5519652 = y;
        double r5519653 = log(r5519652);
        double r5519654 = x;
        double r5519655 = t;
        double r5519656 = log(r5519655);
        double r5519657 = r5519656 - r5519652;
        double r5519658 = fma(r5519653, r5519654, r5519657);
        double r5519659 = z;
        double r5519660 = r5519658 - r5519659;
        return r5519660;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \log t - y\right) - z}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\log y, x, \log t - y\right) - z\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))