Average Error: 0.3 → 0.3
Time: 39.9s
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 r57661 = x;
        double r57662 = y;
        double r57663 = r57661 + r57662;
        double r57664 = log(r57663);
        double r57665 = z;
        double r57666 = log(r57665);
        double r57667 = r57664 + r57666;
        double r57668 = t;
        double r57669 = r57667 - r57668;
        double r57670 = a;
        double r57671 = 0.5;
        double r57672 = r57670 - r57671;
        double r57673 = log(r57668);
        double r57674 = r57672 * r57673;
        double r57675 = r57669 + r57674;
        return r57675;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r57676 = x;
        double r57677 = y;
        double r57678 = r57676 + r57677;
        double r57679 = log(r57678);
        double r57680 = z;
        double r57681 = log(r57680);
        double r57682 = t;
        double r57683 = r57681 - r57682;
        double r57684 = a;
        double r57685 = 0.5;
        double r57686 = r57684 - r57685;
        double r57687 = log(r57682);
        double r57688 = r57686 * r57687;
        double r57689 = r57683 + r57688;
        double r57690 = r57679 + r57689;
        return r57690;
}

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 2019326 
(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))))