Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[-8 \le x \le 8\]
\[\log \left(1 + e^{x}\right)\]
\[\log \left(1 + e^{x}\right)\]
\log \left(1 + e^{x}\right)
\log \left(1 + e^{x}\right)
double f(double x) {
        double r68712 = 1.0;
        double r68713 = x;
        double r68714 = exp(r68713);
        double r68715 = r68712 + r68714;
        double r68716 = log(r68715);
        return r68716;
}

double f(double x) {
        double r68717 = 1.0;
        double r68718 = x;
        double r68719 = exp(r68718);
        double r68720 = r68717 + r68719;
        double r68721 = log(r68720);
        return r68721;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\log \left(1 + e^{x}\right)\]
  2. Final simplification0.0

    \[\leadsto \log \left(1 + e^{x}\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "logexp"
  :pre (<= -8.0 x 8.0)
  (log (+ 1.0 (exp x))))