Average Error: 0.0 → 0.1
Time: 954.0ms
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{8}{{\left(e^{x} + e^{-x}\right)}^{3}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{\frac{8}{{\left(e^{x} + e^{-x}\right)}^{3}}}
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (cbrt (/ 8.0 (pow (+ (exp x) (exp (- x))) 3.0))))
double code(double x) {
	return (2.0 / ((double) (((double) exp(x)) + ((double) exp(((double) -(x)))))));
}
↓
double code(double x) {
	return ((double) cbrt((8.0 / ((double) pow(((double) (((double) exp(x)) + ((double) exp(((double) -(x)))))), 3.0)))));
}

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_binary640.1

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

  4. Applied add-cbrt-cube_binary640.1

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

  5. Applied cbrt-undiv_binary640.1

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

  6. Simplified0.1

    \[\leadsto \sqrt[3]{\color{blue}{\frac{8}{{\left(e^{x} + e^{-x}\right)}^{3}}}}\]

  7. Final simplification0.1

    \[\leadsto \sqrt[3]{\frac{8}{{\left(e^{x} + e^{-x}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020219 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))