Average Error: 0.3 → 0.3
Time: 32.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\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 r1067321 = x;
        double r1067322 = y;
        double r1067323 = r1067321 + r1067322;
        double r1067324 = log(r1067323);
        double r1067325 = z;
        double r1067326 = log(r1067325);
        double r1067327 = r1067324 + r1067326;
        double r1067328 = t;
        double r1067329 = r1067327 - r1067328;
        double r1067330 = a;
        double r1067331 = 0.5;
        double r1067332 = r1067330 - r1067331;
        double r1067333 = log(r1067328);
        double r1067334 = r1067332 * r1067333;
        double r1067335 = r1067329 + r1067334;
        return r1067335;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1067336 = x;
        double r1067337 = y;
        double r1067338 = r1067336 + r1067337;
        double r1067339 = log(r1067338);
        double r1067340 = z;
        double r1067341 = cbrt(r1067340);
        double r1067342 = log(r1067341);
        double r1067343 = r1067342 + r1067342;
        double r1067344 = r1067339 + r1067343;
        double r1067345 = r1067344 + r1067342;
        double r1067346 = t;
        double r1067347 = r1067345 - r1067346;
        double r1067348 = log(r1067346);
        double r1067349 = a;
        double r1067350 = 0.5;
        double r1067351 = r1067349 - r1067350;
        double r1067352 = r1067348 * r1067351;
        double r1067353 = r1067347 + r1067352;
        return r1067353;
}

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

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(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))))