Average Error: 0.3 → 0.3
Time: 11.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{\sqrt{z}} \cdot \sqrt[3]{\sqrt{z}}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{\sqrt{z}} \cdot \sqrt[3]{\sqrt{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 r342419 = x;
        double r342420 = y;
        double r342421 = r342419 + r342420;
        double r342422 = log(r342421);
        double r342423 = z;
        double r342424 = log(r342423);
        double r342425 = r342422 + r342424;
        double r342426 = t;
        double r342427 = r342425 - r342426;
        double r342428 = a;
        double r342429 = 0.5;
        double r342430 = r342428 - r342429;
        double r342431 = log(r342426);
        double r342432 = r342430 * r342431;
        double r342433 = r342427 + r342432;
        return r342433;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r342434 = x;
        double r342435 = y;
        double r342436 = r342434 + r342435;
        double r342437 = log(r342436);
        double r342438 = z;
        double r342439 = cbrt(r342438);
        double r342440 = r342439 * r342439;
        double r342441 = log(r342440);
        double r342442 = r342437 + r342441;
        double r342443 = sqrt(r342438);
        double r342444 = cbrt(r342443);
        double r342445 = r342444 * r342444;
        double r342446 = log(r342445);
        double r342447 = r342442 + r342446;
        double r342448 = t;
        double r342449 = r342447 - r342448;
        double r342450 = a;
        double r342451 = 0.5;
        double r342452 = r342450 - r342451;
        double r342453 = log(r342448);
        double r342454 = r342452 * r342453;
        double r342455 = r342449 + r342454;
        return r342455;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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. Using strategy rm

  7. Applied add-sqr-sqrt0.3

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

  8. Applied cbrt-prod0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019356 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))