Average Error: 0.3 → 0.3
Time: 48.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log t \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log t \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{z}\right)\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r4014419 = x;
        double r4014420 = y;
        double r4014421 = r4014419 + r4014420;
        double r4014422 = log(r4014421);
        double r4014423 = z;
        double r4014424 = log(r4014423);
        double r4014425 = r4014422 + r4014424;
        double r4014426 = t;
        double r4014427 = r4014425 - r4014426;
        double r4014428 = a;
        double r4014429 = 0.5;
        double r4014430 = r4014428 - r4014429;
        double r4014431 = log(r4014426);
        double r4014432 = r4014430 * r4014431;
        double r4014433 = r4014427 + r4014432;
        return r4014433;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r4014434 = t;
        double r4014435 = log(r4014434);
        double r4014436 = a;
        double r4014437 = 0.5;
        double r4014438 = r4014436 - r4014437;
        double r4014439 = r4014435 * r4014438;
        double r4014440 = y;
        double r4014441 = x;
        double r4014442 = r4014440 + r4014441;
        double r4014443 = log(r4014442);
        double r4014444 = z;
        double r4014445 = sqrt(r4014444);
        double r4014446 = log(r4014445);
        double r4014447 = r4014443 + r4014446;
        double r4014448 = r4014447 + r4014446;
        double r4014449 = r4014448 - r4014434;
        double r4014450 = r4014439 + r4014449;
        return r4014450;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019120 
(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))))