Average Error: 0.3 → 0.3
Time: 33.0s
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 r240822 = x;
        double r240823 = y;
        double r240824 = r240822 + r240823;
        double r240825 = log(r240824);
        double r240826 = z;
        double r240827 = log(r240826);
        double r240828 = r240825 + r240827;
        double r240829 = t;
        double r240830 = r240828 - r240829;
        double r240831 = a;
        double r240832 = 0.5;
        double r240833 = r240831 - r240832;
        double r240834 = log(r240829);
        double r240835 = r240833 * r240834;
        double r240836 = r240830 + r240835;
        return r240836;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r240837 = x;
        double r240838 = y;
        double r240839 = r240837 + r240838;
        double r240840 = log(r240839);
        double r240841 = z;
        double r240842 = log(r240841);
        double r240843 = t;
        double r240844 = r240842 - r240843;
        double r240845 = a;
        double r240846 = 0.5;
        double r240847 = r240845 - r240846;
        double r240848 = log(r240843);
        double r240849 = r240847 * r240848;
        double r240850 = r240844 + r240849;
        double r240851 = r240840 + r240850;
        return r240851;
}

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 2019303 
(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))))