Average Error: 0.3 → 0.3
Time: 18.4s
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 r29677 = x;
        double r29678 = y;
        double r29679 = r29677 + r29678;
        double r29680 = log(r29679);
        double r29681 = z;
        double r29682 = log(r29681);
        double r29683 = r29680 + r29682;
        double r29684 = t;
        double r29685 = r29683 - r29684;
        double r29686 = a;
        double r29687 = 0.5;
        double r29688 = r29686 - r29687;
        double r29689 = log(r29684);
        double r29690 = r29688 * r29689;
        double r29691 = r29685 + r29690;
        return r29691;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29692 = x;
        double r29693 = y;
        double r29694 = r29692 + r29693;
        double r29695 = log(r29694);
        double r29696 = z;
        double r29697 = log(r29696);
        double r29698 = t;
        double r29699 = r29697 - r29698;
        double r29700 = a;
        double r29701 = 0.5;
        double r29702 = r29700 - r29701;
        double r29703 = log(r29698);
        double r29704 = r29702 * r29703;
        double r29705 = r29699 + r29704;
        double r29706 = r29695 + r29705;
        return r29706;
}

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 2020045 
(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))))