Average Error: 0.1 → 0.1
Time: 24.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\mathsf{fma}\left(x, \log y, \log t - z\right) - y\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\mathsf{fma}\left(x, \log y, \log t - z\right) - y
double f(double x, double y, double z, double t) {
        double r98707 = x;
        double r98708 = y;
        double r98709 = log(r98708);
        double r98710 = r98707 * r98709;
        double r98711 = r98710 - r98708;
        double r98712 = z;
        double r98713 = r98711 - r98712;
        double r98714 = t;
        double r98715 = log(r98714);
        double r98716 = r98713 + r98715;
        return r98716;
}
↓
double f(double x, double y, double z, double t) {
        double r98717 = x;
        double r98718 = y;
        double r98719 = log(r98718);
        double r98720 = t;
        double r98721 = log(r98720);
        double r98722 = z;
        double r98723 = r98721 - r98722;
        double r98724 = fma(r98717, r98719, r98723);
        double r98725 = r98724 - r98718;
        return r98725;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))