Average Error: 0.3 → 0.3
Time: 28.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right) + \log \left(x + y\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right) + \log \left(x + y\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r1016981 = x;
        double r1016982 = y;
        double r1016983 = r1016981 + r1016982;
        double r1016984 = log(r1016983);
        double r1016985 = z;
        double r1016986 = log(r1016985);
        double r1016987 = r1016984 + r1016986;
        double r1016988 = t;
        double r1016989 = r1016987 - r1016988;
        double r1016990 = a;
        double r1016991 = 0.5;
        double r1016992 = r1016990 - r1016991;
        double r1016993 = log(r1016988);
        double r1016994 = r1016992 * r1016993;
        double r1016995 = r1016989 + r1016994;
        return r1016995;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1016996 = z;
        double r1016997 = cbrt(r1016996);
        double r1016998 = log(r1016997);
        double r1016999 = r1016998 + r1016998;
        double r1017000 = x;
        double r1017001 = y;
        double r1017002 = r1017000 + r1017001;
        double r1017003 = log(r1017002);
        double r1017004 = r1016999 + r1017003;
        double r1017005 = r1017004 + r1016998;
        double r1017006 = t;
        double r1017007 = r1017005 - r1017006;
        double r1017008 = log(r1017006);
        double r1017009 = a;
        double r1017010 = 0.5;
        double r1017011 = r1017009 - r1017010;
        double r1017012 = r1017008 * r1017011;
        double r1017013 = r1017007 + r1017012;
        return r1017013;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019154 +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))))