Average Error: 0.1 → 0.1
Time: 23.1s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)
double f(double x, double y, double z) {
        double r13414797 = x;
        double r13414798 = y;
        double r13414799 = 0.5;
        double r13414800 = r13414798 + r13414799;
        double r13414801 = log(r13414798);
        double r13414802 = r13414800 * r13414801;
        double r13414803 = r13414797 - r13414802;
        double r13414804 = r13414803 + r13414798;
        double r13414805 = z;
        double r13414806 = r13414804 - r13414805;
        return r13414806;
}
↓
double f(double x, double y, double z) {
        double r13414807 = x;
        double r13414808 = y;
        double r13414809 = log(r13414808);
        double r13414810 = 0.5;
        double r13414811 = r13414808 + r13414810;
        double r13414812 = z;
        double r13414813 = r13414812 - r13414808;
        double r13414814 = fma(r13414809, r13414811, r13414813);
        double r13414815 = r13414807 - r13414814;
        return r13414815;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x - \mathsf{fma}\left(\log y, 0.5 + y, z - y\right)}\]

  3. Final simplification0.1

    \[\leadsto x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))