Average Error: 0.3 → 0.3
Time: 37.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \left(\log z - t\right)\right) + \log \left(y + x\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \left(\log z - t\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r2007859 = x;
        double r2007860 = y;
        double r2007861 = r2007859 + r2007860;
        double r2007862 = log(r2007861);
        double r2007863 = z;
        double r2007864 = log(r2007863);
        double r2007865 = r2007862 + r2007864;
        double r2007866 = t;
        double r2007867 = r2007865 - r2007866;
        double r2007868 = a;
        double r2007869 = 0.5;
        double r2007870 = r2007868 - r2007869;
        double r2007871 = log(r2007866);
        double r2007872 = r2007870 * r2007871;
        double r2007873 = r2007867 + r2007872;
        return r2007873;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2007874 = t;
        double r2007875 = sqrt(r2007874);
        double r2007876 = log(r2007875);
        double r2007877 = a;
        double r2007878 = 0.5;
        double r2007879 = r2007877 - r2007878;
        double r2007880 = r2007876 * r2007879;
        double r2007881 = r2007880 + r2007880;
        double r2007882 = z;
        double r2007883 = log(r2007882);
        double r2007884 = r2007883 - r2007874;
        double r2007885 = r2007881 + r2007884;
        double r2007886 = y;
        double r2007887 = x;
        double r2007888 = r2007886 + r2007887;
        double r2007889 = log(r2007888);
        double r2007890 = r2007885 + r2007889;
        return r2007890;
}

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. Using strategy rm

  6. Applied add-sqr-sqrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied distribute-rgt-in0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019133 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))