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 r424778 = x;
        double r424779 = y;
        double r424780 = r424778 + r424779;
        double r424781 = log(r424780);
        double r424782 = z;
        double r424783 = log(r424782);
        double r424784 = r424781 + r424783;
        double r424785 = t;
        double r424786 = r424784 - r424785;
        double r424787 = a;
        double r424788 = 0.5;
        double r424789 = r424787 - r424788;
        double r424790 = log(r424785);
        double r424791 = r424789 * r424790;
        double r424792 = r424786 + r424791;
        return r424792;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r424793 = x;
        double r424794 = y;
        double r424795 = r424793 + r424794;
        double r424796 = log(r424795);
        double r424797 = z;
        double r424798 = log(r424797);
        double r424799 = t;
        double r424800 = r424798 - r424799;
        double r424801 = a;
        double r424802 = 0.5;
        double r424803 = r424801 - r424802;
        double r424804 = log(r424799);
        double r424805 = r424803 * r424804;
        double r424806 = r424800 + r424805;
        double r424807 = r424796 + r424806;
        return r424807;
}

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 2020047 
(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))))