Average Error: 0.3 → 0.3
Time: 32.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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(y + x\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
double f(double x, double y, double z, double t, double a) {
        double r1436168 = x;
        double r1436169 = y;
        double r1436170 = r1436168 + r1436169;
        double r1436171 = log(r1436170);
        double r1436172 = z;
        double r1436173 = log(r1436172);
        double r1436174 = r1436171 + r1436173;
        double r1436175 = t;
        double r1436176 = r1436174 - r1436175;
        double r1436177 = a;
        double r1436178 = 0.5;
        double r1436179 = r1436177 - r1436178;
        double r1436180 = log(r1436175);
        double r1436181 = r1436179 * r1436180;
        double r1436182 = r1436176 + r1436181;
        return r1436182;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1436183 = y;
        double r1436184 = x;
        double r1436185 = r1436183 + r1436184;
        double r1436186 = log(r1436185);
        double r1436187 = z;
        double r1436188 = cbrt(r1436187);
        double r1436189 = r1436188 * r1436188;
        double r1436190 = log(r1436189);
        double r1436191 = r1436186 + r1436190;
        double r1436192 = log(r1436188);
        double r1436193 = r1436191 + r1436192;
        double r1436194 = t;
        double r1436195 = r1436193 - r1436194;
        double r1436196 = a;
        double r1436197 = 0.5;
        double r1436198 = r1436196 - r1436197;
        double r1436199 = log(r1436194);
        double r1436200 = r1436198 * r1436199;
        double r1436201 = r1436195 + r1436200;
        return r1436201;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 +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))))