Average Error: 1.4 → 1.4
Time: 999.0ms
Precision: binary64
\[\log \left(\frac{e^{x}}{1 + e^{x}}\right)\]
↓
\[\log \left(\frac{e^{x}}{1 + e^{x}}\right)\]
\log \left(\frac{e^{x}}{1 + e^{x}}\right)
↓
\log \left(\frac{e^{x}}{1 + e^{x}}\right)
double code(double x) {
	return ((double) log(((double) (((double) exp(x)) / ((double) (1.0 + ((double) exp(x))))))));
}
↓
double code(double x) {
	return ((double) log(((double) (((double) exp(x)) / ((double) (1.0 + ((double) exp(x))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.4

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

  2. Final simplification1.4

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

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(log (/ (exp x) (+ 1 (exp x))))"
  :precision binary64
  (log (/ (exp x) (+ 1.0 (exp x)))))