Average Error: 0.3 → 0.3
Time: 38.1s
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 r301812 = x;
        double r301813 = y;
        double r301814 = r301812 + r301813;
        double r301815 = log(r301814);
        double r301816 = z;
        double r301817 = log(r301816);
        double r301818 = r301815 + r301817;
        double r301819 = t;
        double r301820 = r301818 - r301819;
        double r301821 = a;
        double r301822 = 0.5;
        double r301823 = r301821 - r301822;
        double r301824 = log(r301819);
        double r301825 = r301823 * r301824;
        double r301826 = r301820 + r301825;
        return r301826;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r301827 = x;
        double r301828 = y;
        double r301829 = r301827 + r301828;
        double r301830 = log(r301829);
        double r301831 = z;
        double r301832 = log(r301831);
        double r301833 = t;
        double r301834 = r301832 - r301833;
        double r301835 = a;
        double r301836 = 0.5;
        double r301837 = r301835 - r301836;
        double r301838 = log(r301833);
        double r301839 = r301837 * r301838;
        double r301840 = r301834 + r301839;
        double r301841 = r301830 + r301840;
        return r301841;
}

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 2019323 
(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))))