Average Error: 0.3 → 0.3
Time: 47.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r4575835 = x;
        double r4575836 = y;
        double r4575837 = r4575835 + r4575836;
        double r4575838 = log(r4575837);
        double r4575839 = z;
        double r4575840 = log(r4575839);
        double r4575841 = r4575838 + r4575840;
        double r4575842 = t;
        double r4575843 = r4575841 - r4575842;
        double r4575844 = a;
        double r4575845 = 0.5;
        double r4575846 = r4575844 - r4575845;
        double r4575847 = log(r4575842);
        double r4575848 = r4575846 * r4575847;
        double r4575849 = r4575843 + r4575848;
        return r4575849;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r4575850 = t;
        double r4575851 = 0.3333333333333333;
        double r4575852 = pow(r4575850, r4575851);
        double r4575853 = log(r4575852);
        double r4575854 = a;
        double r4575855 = 0.5;
        double r4575856 = r4575854 - r4575855;
        double r4575857 = r4575853 * r4575856;
        double r4575858 = cbrt(r4575850);
        double r4575859 = r4575858 * r4575858;
        double r4575860 = log(r4575859);
        double r4575861 = r4575860 * r4575856;
        double r4575862 = y;
        double r4575863 = x;
        double r4575864 = r4575862 + r4575863;
        double r4575865 = log(r4575864);
        double r4575866 = z;
        double r4575867 = log(r4575866);
        double r4575868 = r4575865 + r4575867;
        double r4575869 = r4575868 - r4575850;
        double r4575870 = r4575861 + r4575869;
        double r4575871 = r4575857 + r4575870;
        return r4575871;
}

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. Taylor expanded around 0 0.3

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

  3. Simplified0.3

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

  5. Applied add-cube-cbrt0.3

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

  6. Applied log-prod0.3

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

  7. Applied distribute-lft-in0.3

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

  8. Applied associate-+r+0.3

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

  10. Applied pow1/30.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019104 
(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))))