Average Error: 0.1 → 0.1
Time: 11.8s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)
double f(double x, double y, double z) {
        double r1766 = x;
        double r1767 = y;
        double r1768 = 0.5;
        double r1769 = r1767 + r1768;
        double r1770 = log(r1767);
        double r1771 = r1769 * r1770;
        double r1772 = r1766 - r1771;
        double r1773 = r1772 + r1767;
        double r1774 = z;
        double r1775 = r1773 - r1774;
        return r1775;
}
↓
double f(double x, double y, double z) {
        double r1776 = x;
        double r1777 = y;
        double r1778 = log(r1777);
        double r1779 = 0.5;
        double r1780 = r1777 + r1779;
        double r1781 = z;
        double r1782 = fma(r1778, r1780, r1781);
        double r1783 = r1782 - r1777;
        double r1784 = r1776 - r1783;
        return r1784;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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