Average Error: 0.3 → 0.2
Time: 18.4s
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 r54068 = x;
        double r54069 = y;
        double r54070 = r54068 + r54069;
        double r54071 = log(r54070);
        double r54072 = z;
        double r54073 = log(r54072);
        double r54074 = r54071 + r54073;
        double r54075 = t;
        double r54076 = r54074 - r54075;
        double r54077 = a;
        double r54078 = 0.5;
        double r54079 = r54077 - r54078;
        double r54080 = log(r54075);
        double r54081 = r54079 * r54080;
        double r54082 = r54076 + r54081;
        return r54082;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r54083 = x;
        double r54084 = y;
        double r54085 = r54083 + r54084;
        double r54086 = log(r54085);
        double r54087 = z;
        double r54088 = log(r54087);
        double r54089 = t;
        double r54090 = r54088 - r54089;
        double r54091 = a;
        double r54092 = 0.5;
        double r54093 = r54091 - r54092;
        double r54094 = log(r54089);
        double r54095 = r54093 * r54094;
        double r54096 = r54090 + r54095;
        double r54097 = r54086 + r54096;
        return r54097;
}

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+0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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))))