Average Error: 0.3 → 0.3
Time: 37.9s
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 r52800 = x;
        double r52801 = y;
        double r52802 = r52800 + r52801;
        double r52803 = log(r52802);
        double r52804 = z;
        double r52805 = log(r52804);
        double r52806 = r52803 + r52805;
        double r52807 = t;
        double r52808 = r52806 - r52807;
        double r52809 = a;
        double r52810 = 0.5;
        double r52811 = r52809 - r52810;
        double r52812 = log(r52807);
        double r52813 = r52811 * r52812;
        double r52814 = r52808 + r52813;
        return r52814;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r52815 = x;
        double r52816 = y;
        double r52817 = r52815 + r52816;
        double r52818 = log(r52817);
        double r52819 = z;
        double r52820 = log(r52819);
        double r52821 = t;
        double r52822 = r52820 - r52821;
        double r52823 = a;
        double r52824 = 0.5;
        double r52825 = r52823 - r52824;
        double r52826 = log(r52821);
        double r52827 = r52825 * r52826;
        double r52828 = r52822 + r52827;
        double r52829 = r52818 + r52828;
        return r52829;
}

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