Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 33.2s

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 r17477854 = x;
        double r17477855 = y;
        double r17477856 = r17477854 + r17477855;
        double r17477857 = log(r17477856);
        double r17477858 = z;
        double r17477859 = log(r17477858);
        double r17477860 = r17477857 + r17477859;
        double r17477861 = t;
        double r17477862 = r17477860 - r17477861;
        double r17477863 = a;
        double r17477864 = 0.5;
        double r17477865 = r17477863 - r17477864;
        double r17477866 = log(r17477861);
        double r17477867 = r17477865 * r17477866;
        double r17477868 = r17477862 + r17477867;
        return r17477868;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r17477869 = a;
        double r17477870 = 0.5;
        double r17477871 = r17477869 - r17477870;
        double r17477872 = t;
        double r17477873 = 0.3333333333333333;
        double r17477874 = pow(r17477872, r17477873);
        double r17477875 = log(r17477874);
        double r17477876 = r17477871 * r17477875;
        double r17477877 = cbrt(r17477872);
        double r17477878 = log(r17477877);
        double r17477879 = r17477878 + r17477878;
        double r17477880 = r17477871 * r17477879;
        double r17477881 = r17477876 + r17477880;
        double r17477882 = y;
        double r17477883 = x;
        double r17477884 = r17477882 + r17477883;
        double r17477885 = log(r17477884);
        double r17477886 = z;
        double r17477887 = log(r17477886);
        double r17477888 = r17477885 + r17477887;
        double r17477889 = r17477888 - r17477872;
        double r17477890 = r17477881 + r17477889;
        return r17477890;
}

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))))