Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\left(\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}} \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}\right)\right) \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\left(\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \left(\sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}} \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}\right)\right) \cdot \sqrt[3]{\sqrt{\frac{2}{e^{x} + e^{-x}}}}
double code(double x) {
	return (2.0 / (exp(x) + exp(-x)));
}
↓
double code(double x) {
	return ((sqrt((2.0 / (exp(x) + exp(-x)))) * (cbrt(sqrt((2.0 / (exp(x) + exp(-x))))) * cbrt(sqrt((2.0 / (exp(x) + exp(-x))))))) * cbrt(sqrt((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-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2 (+ (exp x) (exp (- x)))))