Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 11.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r410838 = x;
        double r410839 = y;
        double r410840 = r410838 + r410839;
        double r410841 = log(r410840);
        double r410842 = z;
        double r410843 = log(r410842);
        double r410844 = r410841 + r410843;
        double r410845 = t;
        double r410846 = r410844 - r410845;
        double r410847 = a;
        double r410848 = 0.5;
        double r410849 = r410847 - r410848;
        double r410850 = log(r410845);
        double r410851 = r410849 * r410850;
        double r410852 = r410846 + r410851;
        return r410852;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r410853 = t;
        double r410854 = log(r410853);
        double r410855 = a;
        double r410856 = 0.5;
        double r410857 = r410855 - r410856;
        double r410858 = x;
        double r410859 = y;
        double r410860 = r410858 + r410859;
        double r410861 = log(r410860);
        double r410862 = z;
        double r410863 = log(r410862);
        double r410864 = r410863 - r410853;
        double r410865 = r410861 + r410864;
        double r410866 = fma(r410854, r410857, r410865);
        return r410866;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.3
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 0.3

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

2. Simplified 0.3

   \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)}\]
3. Using strategy rm

4. Applied associate--l+ 0.3

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

5. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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