Average Error: 0.3 → 0.3
Time: 40.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)
double f(double x, double y, double z, double t, double a) {
        double r58765 = x;
        double r58766 = y;
        double r58767 = r58765 + r58766;
        double r58768 = log(r58767);
        double r58769 = z;
        double r58770 = log(r58769);
        double r58771 = r58768 + r58770;
        double r58772 = t;
        double r58773 = r58771 - r58772;
        double r58774 = a;
        double r58775 = 0.5;
        double r58776 = r58774 - r58775;
        double r58777 = log(r58772);
        double r58778 = r58776 * r58777;
        double r58779 = r58773 + r58778;
        return r58779;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r58780 = x;
        double r58781 = y;
        double r58782 = r58780 + r58781;
        double r58783 = log(r58782);
        double r58784 = z;
        double r58785 = log(r58784);
        double r58786 = r58783 + r58785;
        double r58787 = t;
        double r58788 = r58786 - r58787;
        double r58789 = 2.0;
        double r58790 = cbrt(r58787);
        double r58791 = log(r58790);
        double r58792 = r58789 * r58791;
        double r58793 = a;
        double r58794 = 0.5;
        double r58795 = r58793 - r58794;
        double r58796 = r58792 * r58795;
        double r58797 = r58788 + r58796;
        double r58798 = 1.0;
        double r58799 = r58798 / r58787;
        double r58800 = -0.3333333333333333;
        double r58801 = pow(r58799, r58800);
        double r58802 = log(r58801);
        double r58803 = r58795 * r58802;
        double r58804 = r58797 + r58803;
        return r58804;
}

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Simplified0.3

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

  8. Taylor expanded around inf 0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))