Average Error: 0.3 → 0.3
Time: 36.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log \left(\sqrt{\sqrt[3]{t}} \cdot \sqrt{\sqrt[3]{t}}\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]
\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(\sqrt{\sqrt[3]{t}} \cdot \sqrt{\sqrt[3]{t}}\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)
double f(double x, double y, double z, double t, double a) {
        double r1269796 = x;
        double r1269797 = y;
        double r1269798 = r1269796 + r1269797;
        double r1269799 = log(r1269798);
        double r1269800 = z;
        double r1269801 = log(r1269800);
        double r1269802 = r1269799 + r1269801;
        double r1269803 = t;
        double r1269804 = r1269802 - r1269803;
        double r1269805 = a;
        double r1269806 = 0.5;
        double r1269807 = r1269805 - r1269806;
        double r1269808 = log(r1269803);
        double r1269809 = r1269807 * r1269808;
        double r1269810 = r1269804 + r1269809;
        return r1269810;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1269811 = a;
        double r1269812 = 0.5;
        double r1269813 = r1269811 - r1269812;
        double r1269814 = t;
        double r1269815 = cbrt(r1269814);
        double r1269816 = sqrt(r1269815);
        double r1269817 = r1269816 * r1269816;
        double r1269818 = log(r1269817);
        double r1269819 = r1269813 * r1269818;
        double r1269820 = log(r1269815);
        double r1269821 = r1269820 + r1269820;
        double r1269822 = r1269813 * r1269821;
        double r1269823 = r1269819 + r1269822;
        double r1269824 = y;
        double r1269825 = x;
        double r1269826 = r1269824 + r1269825;
        double r1269827 = log(r1269826);
        double r1269828 = z;
        double r1269829 = log(r1269828);
        double r1269830 = r1269827 + r1269829;
        double r1269831 = r1269830 - r1269814;
        double r1269832 = r1269823 + r1269831;
        return r1269832;
}

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-rgt-in0.3

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

  6. Simplified0.3

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

  8. Applied add-sqr-sqrt0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019151 
(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))))