Average Error: 0.3 → 0.3
Time: 42.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\left(\log \left(\sqrt[3]{z}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\left(\log \left(\sqrt[3]{z}\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r3808204 = x;
        double r3808205 = y;
        double r3808206 = r3808204 + r3808205;
        double r3808207 = log(r3808206);
        double r3808208 = z;
        double r3808209 = log(r3808208);
        double r3808210 = r3808207 + r3808209;
        double r3808211 = t;
        double r3808212 = r3808210 - r3808211;
        double r3808213 = a;
        double r3808214 = 0.5;
        double r3808215 = r3808213 - r3808214;
        double r3808216 = log(r3808211);
        double r3808217 = r3808215 * r3808216;
        double r3808218 = r3808212 + r3808217;
        return r3808218;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r3808219 = x;
        double r3808220 = y;
        double r3808221 = r3808219 + r3808220;
        double r3808222 = log(r3808221);
        double r3808223 = z;
        double r3808224 = cbrt(r3808223);
        double r3808225 = r3808224 * r3808224;
        double r3808226 = log(r3808225);
        double r3808227 = log(r3808224);
        double r3808228 = t;
        double r3808229 = r3808227 - r3808228;
        double r3808230 = a;
        double r3808231 = 0.5;
        double r3808232 = r3808230 - r3808231;
        double r3808233 = log(r3808228);
        double r3808234 = r3808232 * r3808233;
        double r3808235 = r3808229 + r3808234;
        double r3808236 = r3808226 + r3808235;
        double r3808237 = r3808222 + r3808236;
        return r3808237;
}

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

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

  7. Applied log-prod0.3

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

  8. Applied associate--l+0.3

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

  9. Applied associate-+l+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019173 
(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))))