Average Error: 0.3 → 0.3
Time: 41.4s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{y + x} \cdot \sqrt[3]{y + x}\right) + \left(\log z + \log \left(\sqrt[3]{y + x}\right)\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r1849991 = x;
        double r1849992 = y;
        double r1849993 = r1849991 + r1849992;
        double r1849994 = log(r1849993);
        double r1849995 = z;
        double r1849996 = log(r1849995);
        double r1849997 = r1849994 + r1849996;
        double r1849998 = t;
        double r1849999 = r1849997 - r1849998;
        double r1850000 = a;
        double r1850001 = 0.5;
        double r1850002 = r1850000 - r1850001;
        double r1850003 = log(r1849998);
        double r1850004 = r1850002 * r1850003;
        double r1850005 = r1849999 + r1850004;
        return r1850005;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1850006 = y;
        double r1850007 = x;
        double r1850008 = r1850006 + r1850007;
        double r1850009 = cbrt(r1850008);
        double r1850010 = r1850009 * r1850009;
        double r1850011 = log(r1850010);
        double r1850012 = z;
        double r1850013 = log(r1850012);
        double r1850014 = log(r1850009);
        double r1850015 = r1850013 + r1850014;
        double r1850016 = r1850011 + r1850015;
        double r1850017 = t;
        double r1850018 = r1850016 - r1850017;
        double r1850019 = a;
        double r1850020 = 0.5;
        double r1850021 = r1850019 - r1850020;
        double r1850022 = log(r1850017);
        double r1850023 = r1850021 * r1850022;
        double r1850024 = r1850018 + r1850023;
        return r1850024;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019144 +o rules:numerics
(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))))