Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 11.6s

Precision: 64

Math

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

↓

\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(e^{\log \left({t}^{\frac{1}{3}}\right)}\right)\right)\]

C

double f(double x, double y, double z, double t, double a) {
        double r358736 = x;
        double r358737 = y;
        double r358738 = r358736 + r358737;
        double r358739 = log(r358738);
        double r358740 = z;
        double r358741 = log(r358740);
        double r358742 = r358739 + r358741;
        double r358743 = t;
        double r358744 = r358742 - r358743;
        double r358745 = a;
        double r358746 = 0.5;
        double r358747 = r358745 - r358746;
        double r358748 = log(r358743);
        double r358749 = r358747 * r358748;
        double r358750 = r358744 + r358749;
        return r358750;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r358751 = x;
        double r358752 = y;
        double r358753 = r358751 + r358752;
        double r358754 = log(r358753);
        double r358755 = z;
        double r358756 = log(r358755);
        double r358757 = r358754 + r358756;
        double r358758 = t;
        double r358759 = r358757 - r358758;
        double r358760 = a;
        double r358761 = 0.5;
        double r358762 = r358760 - r358761;
        double r358763 = 2.0;
        double r358764 = cbrt(r358758);
        double r358765 = log(r358764);
        double r358766 = r358763 * r358765;
        double r358767 = r358762 * r358766;
        double r358768 = 0.3333333333333333;
        double r358769 = pow(r358758, r358768);
        double r358770 = log(r358769);
        double r358771 = exp(r358770);
        double r358772 = log(r358771);
        double r358773 = r358762 * r358772;
        double r358774 = r358767 + r358773;
        double r358775 = r358759 + r358774;
        return r358775;
}

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-lft-in 0.3

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

6. Simplified 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\color{blue}{\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]
7. Using strategy rm

8. Applied add-exp-log 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(e^{\log \left(\sqrt[3]{t}\right)}\right)}\right)\]

9. Simplified 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(e^{\color{blue}{\log \left({t}^{\frac{1}{3}}\right)}}\right)\right)\]

10. Final simplification 0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(e^{\log \left({t}^{\frac{1}{3}}\right)}\right)\right)\]

Reproduce

herbie shell --seed 2020064 
(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))))