Average Error: 39.4 → 39.4
Time: 4.8s
Precision: binary64
\[\frac{2 \cdot e^{2 \cdot x}}{{\left(1 + e^{x}\right)}^{3}} - \frac{e^{x}}{{\left(1 + e^{x}\right)}^{2}}\]
↓
\[\frac{2 \cdot e^{2 \cdot x}}{{\left(1 + e^{x}\right)}^{3}} - \frac{e^{x}}{{\left(1 + e^{x}\right)}^{2}}\]
\frac{2 \cdot e^{2 \cdot x}}{{\left(1 + e^{x}\right)}^{3}} - \frac{e^{x}}{{\left(1 + e^{x}\right)}^{2}}
↓
\frac{2 \cdot e^{2 \cdot x}}{{\left(1 + e^{x}\right)}^{3}} - \frac{e^{x}}{{\left(1 + e^{x}\right)}^{2}}
double code(double x) {
	return ((double) (((double) (((double) (2.0 * ((double) exp(((double) (2.0 * x)))))) / ((double) pow(((double) (1.0 + ((double) exp(x)))), 3.0)))) - ((double) (((double) exp(x)) / ((double) pow(((double) (1.0 + ((double) exp(x)))), 2.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (2.0 * ((double) exp(((double) (2.0 * x)))))) / ((double) pow(((double) (1.0 + ((double) exp(x)))), 3.0)))) - ((double) (((double) exp(x)) / ((double) pow(((double) (1.0 + ((double) exp(x)))), 2.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.4

    \[\frac{2 \cdot e^{2 \cdot x}}{{\left(1 + e^{x}\right)}^{3}} - \frac{e^{x}}{{\left(1 + e^{x}\right)}^{2}}\]

  2. Final simplification39.4

    \[\leadsto \frac{2 \cdot e^{2 \cdot x}}{{\left(1 + e^{x}\right)}^{3}} - \frac{e^{x}}{{\left(1 + e^{x}\right)}^{2}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (/ (* 2 (exp (* 2 x))) (pow (+ 1 (exp x)) 3)) (/ (exp x) (pow (+ 1 (exp x)) 2)))"
  :precision binary64
  (- (/ (* 2.0 (exp (* 2.0 x))) (pow (+ 1.0 (exp x)) 3.0)) (/ (exp x) (pow (+ 1.0 (exp x)) 2.0))))