Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[2 \cdot \frac{1}{e^{x} + e^{-x}}\]
\frac{2}{e^{x} + e^{-x}}
↓
2 \cdot \frac{1}{e^{x} + e^{-x}}
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x) :precision binary64 (* 2.0 (/ 1.0 (+ (exp x) (exp (- x))))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return 2.0 * (1.0 / (exp(x) + 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 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied div-inv_binary64_10980.0

    \[\leadsto \color{blue}{2 \cdot \frac{1}{e^{x} + e^{-x}}}\]

  4. Final simplification0.0

    \[\leadsto 2 \cdot \frac{1}{e^{x} + e^{-x}}\]

Reproduce

herbie shell --seed 2021075 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))