Average Error: 0.3 → 0.3
Time: 36.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(\log z - t\right)\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left(y + x\right)\]
\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(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(\log z - t\right)\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r1733051 = x;
        double r1733052 = y;
        double r1733053 = r1733051 + r1733052;
        double r1733054 = log(r1733053);
        double r1733055 = z;
        double r1733056 = log(r1733055);
        double r1733057 = r1733054 + r1733056;
        double r1733058 = t;
        double r1733059 = r1733057 - r1733058;
        double r1733060 = a;
        double r1733061 = 0.5;
        double r1733062 = r1733060 - r1733061;
        double r1733063 = log(r1733058);
        double r1733064 = r1733062 * r1733063;
        double r1733065 = r1733059 + r1733064;
        return r1733065;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1733066 = t;
        double r1733067 = cbrt(r1733066);
        double r1733068 = log(r1733067);
        double r1733069 = a;
        double r1733070 = 0.5;
        double r1733071 = r1733069 - r1733070;
        double r1733072 = r1733068 * r1733071;
        double r1733073 = r1733072 + r1733072;
        double r1733074 = z;
        double r1733075 = log(r1733074);
        double r1733076 = r1733075 - r1733066;
        double r1733077 = r1733073 + r1733076;
        double r1733078 = r1733077 + r1733072;
        double r1733079 = y;
        double r1733080 = x;
        double r1733081 = r1733079 + r1733080;
        double r1733082 = log(r1733081);
        double r1733083 = r1733078 + r1733082;
        return r1733083;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied distribute-lft-in0.3

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

  9. Applied associate-+r+0.3

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019135 
(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))))