Average Error: 0.2 → 0.3
Time: 40.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{\sqrt{z}}\right)\right) + \log \left(\sqrt{\sqrt{z}}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt{z}\right)\right) + \log \left(\sqrt{\sqrt{z}}\right)\right) + \log \left(\sqrt{\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 r78397 = x;
        double r78398 = y;
        double r78399 = r78397 + r78398;
        double r78400 = log(r78399);
        double r78401 = z;
        double r78402 = log(r78401);
        double r78403 = r78400 + r78402;
        double r78404 = t;
        double r78405 = r78403 - r78404;
        double r78406 = a;
        double r78407 = 0.5;
        double r78408 = r78406 - r78407;
        double r78409 = log(r78404);
        double r78410 = r78408 * r78409;
        double r78411 = r78405 + r78410;
        return r78411;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r78412 = x;
        double r78413 = y;
        double r78414 = r78412 + r78413;
        double r78415 = log(r78414);
        double r78416 = z;
        double r78417 = sqrt(r78416);
        double r78418 = log(r78417);
        double r78419 = r78415 + r78418;
        double r78420 = sqrt(r78417);
        double r78421 = log(r78420);
        double r78422 = r78419 + r78421;
        double r78423 = r78422 + r78421;
        double r78424 = t;
        double r78425 = r78423 - r78424;
        double r78426 = a;
        double r78427 = 0.5;
        double r78428 = r78426 - r78427;
        double r78429 = log(r78424);
        double r78430 = r78428 * r78429;
        double r78431 = r78425 + r78430;
        return r78431;
}

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 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

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

  4. Applied log-prod0.2

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

  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. Using strategy rm

  7. Applied add-sqr-sqrt0.3

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

  8. Applied sqrt-prod0.3

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

  9. Applied log-prod0.3

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

  10. Applied associate-+r+0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019198 +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))))