Average Error: 0.3 → 0.3
Time: 17.4s
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 r336725 = x;
        double r336726 = y;
        double r336727 = r336725 + r336726;
        double r336728 = log(r336727);
        double r336729 = z;
        double r336730 = log(r336729);
        double r336731 = r336728 + r336730;
        double r336732 = t;
        double r336733 = r336731 - r336732;
        double r336734 = a;
        double r336735 = 0.5;
        double r336736 = r336734 - r336735;
        double r336737 = log(r336732);
        double r336738 = r336736 * r336737;
        double r336739 = r336733 + r336738;
        return r336739;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r336740 = x;
        double r336741 = y;
        double r336742 = r336740 + r336741;
        double r336743 = log(r336742);
        double r336744 = z;
        double r336745 = log(r336744);
        double r336746 = t;
        double r336747 = r336745 - r336746;
        double r336748 = a;
        double r336749 = 0.5;
        double r336750 = r336748 - r336749;
        double r336751 = log(r336746);
        double r336752 = r336750 * r336751;
        double r336753 = r336747 + r336752;
        double r336754 = r336743 + r336753;
        return r336754;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))