Average Error: 0.3 → 0.3
Time: 38.5s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r59722 = x;
        double r59723 = y;
        double r59724 = r59722 + r59723;
        double r59725 = log(r59724);
        double r59726 = z;
        double r59727 = log(r59726);
        double r59728 = r59725 + r59727;
        double r59729 = t;
        double r59730 = r59728 - r59729;
        double r59731 = a;
        double r59732 = 0.5;
        double r59733 = r59731 - r59732;
        double r59734 = log(r59729);
        double r59735 = r59733 * r59734;
        double r59736 = r59730 + r59735;
        return r59736;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r59737 = x;
        double r59738 = y;
        double r59739 = r59737 + r59738;
        double r59740 = log(r59739);
        double r59741 = z;
        double r59742 = log(r59741);
        double r59743 = t;
        double r59744 = r59742 - r59743;
        double r59745 = a;
        double r59746 = 0.5;
        double r59747 = r59745 - r59746;
        double r59748 = log(r59743);
        double r59749 = r59747 * r59748;
        double r59750 = r59744 + r59749;
        double r59751 = r59740 + r59750;
        return r59751;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(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))))