Average Error: 0.3 → 0.3
Time: 39.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right) + \left(\left(\left(\log z + \log \left(\sqrt{y + x}\right)\right) + \log \left(\sqrt{y + x}\right)\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right) + \left(\left(\left(\log z + \log \left(\sqrt{y + x}\right)\right) + \log \left(\sqrt{y + x}\right)\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r2263563 = x;
        double r2263564 = y;
        double r2263565 = r2263563 + r2263564;
        double r2263566 = log(r2263565);
        double r2263567 = z;
        double r2263568 = log(r2263567);
        double r2263569 = r2263566 + r2263568;
        double r2263570 = t;
        double r2263571 = r2263569 - r2263570;
        double r2263572 = a;
        double r2263573 = 0.5;
        double r2263574 = r2263572 - r2263573;
        double r2263575 = log(r2263570);
        double r2263576 = r2263574 * r2263575;
        double r2263577 = r2263571 + r2263576;
        return r2263577;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2263578 = a;
        double r2263579 = 0.5;
        double r2263580 = r2263578 - r2263579;
        double r2263581 = t;
        double r2263582 = sqrt(r2263581);
        double r2263583 = log(r2263582);
        double r2263584 = r2263580 * r2263583;
        double r2263585 = r2263584 + r2263584;
        double r2263586 = z;
        double r2263587 = log(r2263586);
        double r2263588 = y;
        double r2263589 = x;
        double r2263590 = r2263588 + r2263589;
        double r2263591 = sqrt(r2263590);
        double r2263592 = log(r2263591);
        double r2263593 = r2263587 + r2263592;
        double r2263594 = r2263593 + r2263592;
        double r2263595 = r2263594 - r2263581;
        double r2263596 = r2263585 + r2263595;
        return r2263596;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied add-sqr-sqrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied distribute-lft-in0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019149 
(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))))