Average Error: 0.3 → 0.3
Time: 29.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(y + x\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - \left(t - \left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(y + x\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - \left(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)\right)
double f(double x, double y, double z, double t, double a) {
        double r970823 = x;
        double r970824 = y;
        double r970825 = r970823 + r970824;
        double r970826 = log(r970825);
        double r970827 = z;
        double r970828 = log(r970827);
        double r970829 = r970826 + r970828;
        double r970830 = t;
        double r970831 = r970829 - r970830;
        double r970832 = a;
        double r970833 = 0.5;
        double r970834 = r970832 - r970833;
        double r970835 = log(r970830);
        double r970836 = r970834 * r970835;
        double r970837 = r970831 + r970836;
        return r970837;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r970838 = y;
        double r970839 = x;
        double r970840 = r970838 + r970839;
        double r970841 = log(r970840);
        double r970842 = z;
        double r970843 = sqrt(r970842);
        double r970844 = log(r970843);
        double r970845 = r970841 + r970844;
        double r970846 = r970845 + r970844;
        double r970847 = t;
        double r970848 = a;
        double r970849 = 0.5;
        double r970850 = r970848 - r970849;
        double r970851 = 0.3333333333333333;
        double r970852 = pow(r970847, r970851);
        double r970853 = log(r970852);
        double r970854 = r970850 * r970853;
        double r970855 = cbrt(r970847);
        double r970856 = log(r970855);
        double r970857 = r970856 + r970856;
        double r970858 = r970850 * r970857;
        double r970859 = r970854 + r970858;
        double r970860 = r970847 - r970859;
        double r970861 = r970846 - r970860;
        return r970861;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 associate-+l-0.3

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.3

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

  7. Applied distribute-lft-in0.3

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

  8. Simplified0.3

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

  10. Applied pow1/30.3

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

  12. Applied add-sqr-sqrt0.3

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

  13. Applied log-prod0.3

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

  14. Applied associate-+r+0.3

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

  15. Final simplification0.3

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

Reproduce

herbie shell --seed 2019154 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))