Average Error: 1.2 → 0
Time: 1.0s
Precision: binary64
\[\frac{e^{x}}{e^{x} + e^{x + 1}}\]
↓
\[\frac{1}{e^{1} + 1}\]
\frac{e^{x}}{e^{x} + e^{x + 1}}
↓
\frac{1}{e^{1} + 1}
double code(double x) {
	return ((double) (((double) exp(x)) / ((double) (((double) exp(x)) + ((double) exp(((double) (x + 1.0))))))));
}
↓
double code(double x) {
	return ((double) (1.0 / ((double) (((double) exp(1.0)) + 1.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.2

    \[\frac{e^{x}}{e^{x} + e^{x + 1}}\]

  2. Simplified0

    \[\leadsto \color{blue}{\frac{1}{e^{1} + 1}}\]

  3. Final simplification0

    \[\leadsto \frac{1}{e^{1} + 1}\]

Reproduce

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