Average Error: 0.3 → 0.3
Time: 43.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\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
double f(double x, double y, double z, double t, double a) {
        double r64606 = x;
        double r64607 = y;
        double r64608 = r64606 + r64607;
        double r64609 = log(r64608);
        double r64610 = z;
        double r64611 = log(r64610);
        double r64612 = r64609 + r64611;
        double r64613 = t;
        double r64614 = r64612 - r64613;
        double r64615 = a;
        double r64616 = 0.5;
        double r64617 = r64615 - r64616;
        double r64618 = log(r64613);
        double r64619 = r64617 * r64618;
        double r64620 = r64614 + r64619;
        return r64620;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r64621 = x;
        double r64622 = y;
        double r64623 = r64621 + r64622;
        double r64624 = log(r64623);
        double r64625 = z;
        double r64626 = log(r64625);
        double r64627 = r64624 + r64626;
        double r64628 = t;
        double r64629 = r64627 - r64628;
        double r64630 = a;
        double r64631 = 0.5;
        double r64632 = r64630 - r64631;
        double r64633 = log(r64628);
        double r64634 = r64632 * r64633;
        double r64635 = r64629 + r64634;
        return r64635;
}

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 *-un-lft-identity0.3

    \[\leadsto \color{blue}{1 \cdot \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019199 +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))))