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 r378096 = x;
        double r378097 = y;
        double r378098 = r378096 + r378097;
        double r378099 = log(r378098);
        double r378100 = z;
        double r378101 = log(r378100);
        double r378102 = r378099 + r378101;
        double r378103 = t;
        double r378104 = r378102 - r378103;
        double r378105 = a;
        double r378106 = 0.5;
        double r378107 = r378105 - r378106;
        double r378108 = log(r378103);
        double r378109 = r378107 * r378108;
        double r378110 = r378104 + r378109;
        return r378110;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r378111 = t;
        double r378112 = log(r378111);
        double r378113 = a;
        double r378114 = 0.5;
        double r378115 = r378113 - r378114;
        double r378116 = x;
        double r378117 = y;
        double r378118 = r378116 + r378117;
        double r378119 = log(r378118);
        double r378120 = z;
        double r378121 = log(r378120);
        double r378122 = r378121 - r378111;
        double r378123 = r378119 + r378122;
        double r378124 = fma(r378112, r378115, r378123);
        return r378124;
}

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))))