Average Error: 0.3 → 0.3
Time: 17.6s
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 r63034 = x;
        double r63035 = y;
        double r63036 = r63034 + r63035;
        double r63037 = log(r63036);
        double r63038 = z;
        double r63039 = log(r63038);
        double r63040 = r63037 + r63039;
        double r63041 = t;
        double r63042 = r63040 - r63041;
        double r63043 = a;
        double r63044 = 0.5;
        double r63045 = r63043 - r63044;
        double r63046 = log(r63041);
        double r63047 = r63045 * r63046;
        double r63048 = r63042 + r63047;
        return r63048;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r63049 = x;
        double r63050 = y;
        double r63051 = r63049 + r63050;
        double r63052 = log(r63051);
        double r63053 = z;
        double r63054 = log(r63053);
        double r63055 = t;
        double r63056 = r63054 - r63055;
        double r63057 = a;
        double r63058 = 0.5;
        double r63059 = r63057 - r63058;
        double r63060 = log(r63055);
        double r63061 = r63059 * r63060;
        double r63062 = r63056 + r63061;
        double r63063 = r63052 + r63062;
        return r63063;
}

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 2020045 
(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))))