Average Error: 61.4 → 0.3
Time: 35.4s
Precision: 64
\[\frac{a}{2 \cdot \log \left({e}^{a}\right)}\]
\[\frac{1}{\log e \cdot 2}\]
\frac{a}{2 \cdot \log \left({e}^{a}\right)}
\frac{1}{\log e \cdot 2}
double f(double a, double e) {
        double r2156128 = a;
        double r2156129 = 2.0;
        double r2156130 = e;
        double r2156131 = pow(r2156130, r2156128);
        double r2156132 = log(r2156131);
        double r2156133 = r2156129 * r2156132;
        double r2156134 = r2156128 / r2156133;
        return r2156134;
}

double f(double __attribute__((unused)) a, double e) {
        double r2156135 = 1.0;
        double r2156136 = e;
        double r2156137 = log(r2156136);
        double r2156138 = 2.0;
        double r2156139 = r2156137 * r2156138;
        double r2156140 = r2156135 / r2156139;
        return r2156140;
}

Error

Bits error versus a

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 61.4

    \[\frac{a}{2 \cdot \log \left({e}^{a}\right)}\]
  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{1}{\log e \cdot 2}}\]
  3. Final simplification0.3

    \[\leadsto \frac{1}{\log e \cdot 2}\]

Reproduce

herbie shell --seed 1 
(FPCore (a e)
  :name "a/(2*log(e^a))"
  :precision binary64
  (/ a (* 2 (log (pow e a)))))