Average Error: 0.0 → 0.1
Time: 2.3s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{2}{e^{x} + e^{-x}} \cdot \left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right)}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\frac{2}{e^{x} + e^{-x}} \cdot \left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right)}
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (cbrt
  (*
   (/ 2.0 (+ (exp x) (exp (- x))))
   (* (/ 2.0 (+ (exp x) (exp (- x)))) (/ 2.0 (+ (exp x) (exp (- x))))))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return cbrt((2.0 / (exp(x) + exp(-x))) * ((2.0 / (exp(x) + exp(-x))) * (2.0 / (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 add-cbrt-cube_binary64_31830.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021043 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))