Average Error: 0.3 → 0.3
Time: 40.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{\log \left(x + y\right) \cdot \log \left(x + y\right) - \log z \cdot \log z}{\log \left(x + y\right) - \log z} - t\right) + \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\frac{\log \left(x + y\right) \cdot \log \left(x + y\right) - \log z \cdot \log z}{\log \left(x + y\right) - \log z} - t\right) + \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r55432 = x;
        double r55433 = y;
        double r55434 = r55432 + r55433;
        double r55435 = log(r55434);
        double r55436 = z;
        double r55437 = log(r55436);
        double r55438 = r55435 + r55437;
        double r55439 = t;
        double r55440 = r55438 - r55439;
        double r55441 = a;
        double r55442 = 0.5;
        double r55443 = r55441 - r55442;
        double r55444 = log(r55439);
        double r55445 = r55443 * r55444;
        double r55446 = r55440 + r55445;
        return r55446;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r55447 = x;
        double r55448 = y;
        double r55449 = r55447 + r55448;
        double r55450 = log(r55449);
        double r55451 = r55450 * r55450;
        double r55452 = z;
        double r55453 = log(r55452);
        double r55454 = r55453 * r55453;
        double r55455 = r55451 - r55454;
        double r55456 = r55450 - r55453;
        double r55457 = r55455 / r55456;
        double r55458 = t;
        double r55459 = r55457 - r55458;
        double r55460 = sqrt(r55458);
        double r55461 = log(r55460);
        double r55462 = a;
        double r55463 = 0.5;
        double r55464 = r55462 - r55463;
        double r55465 = r55461 * r55464;
        double r55466 = r55465 + r55465;
        double r55467 = r55459 + r55466;
        return r55467;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  6. Simplified0.3

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

  7. Simplified0.3

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

  9. Applied flip-+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))