Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 35.9s

Precision: 64

Math

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

↓

\[\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r19868983 = x;
        double r19868984 = y;
        double r19868985 = r19868983 + r19868984;
        double r19868986 = log(r19868985);
        double r19868987 = z;
        double r19868988 = log(r19868987);
        double r19868989 = r19868986 + r19868988;
        double r19868990 = t;
        double r19868991 = r19868989 - r19868990;
        double r19868992 = a;
        double r19868993 = 0.5;
        double r19868994 = r19868992 - r19868993;
        double r19868995 = log(r19868990);
        double r19868996 = r19868994 * r19868995;
        double r19868997 = r19868991 + r19868996;
        return r19868997;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r19868998 = a;
        double r19868999 = 0.5;
        double r19869000 = r19868998 - r19868999;
        double r19869001 = t;
        double r19869002 = 0.3333333333333333;
        double r19869003 = pow(r19869001, r19869002);
        double r19869004 = log(r19869003);
        double r19869005 = r19869000 * r19869004;
        double r19869006 = cbrt(r19869001);
        double r19869007 = log(r19869006);
        double r19869008 = r19869007 + r19869007;
        double r19869009 = r19869000 * r19869008;
        double r19869010 = r19869005 + r19869009;
        double r19869011 = y;
        double r19869012 = x;
        double r19869013 = r19869011 + r19869012;
        double r19869014 = log(r19869013);
        double r19869015 = z;
        double r19869016 = log(r19869015);
        double r19869017 = r19869014 + r19869016;
        double r19869018 = r19869017 - r19869001;
        double r19869019 = r19869010 + r19869018;
        return r19869019;
}

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. Using strategy rm

3. Applied add-cube-cbrt 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

4. Applied log-prod 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\]

5. Applied distribute-rgt-in 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)}\]

6. Simplified 0.3

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

8. Applied pow1/3 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right) + \log \color{blue}{\left({t}^{\frac{1}{3}}\right)} \cdot \left(a - 0.5\right)\right)\]

9. Final simplification 0.3

   \[\leadsto \left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

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

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