Average Error: 0.0 → 0.0
Time: 3.6s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\frac{\sqrt{2}}{\sqrt{\cosh x}}}{\sqrt{e^{x} + e^{-x}}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\frac{\frac{\sqrt{2}}{\sqrt{\cosh x}}}{\sqrt{e^{x} + e^{-x}}}
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (/ (/ (sqrt 2.0) (sqrt (cosh x))) (sqrt (+ (exp x) (exp (- x))))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return (sqrt(2.0) / sqrt(cosh(x))) / sqrt(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-sqrt_binary64_28280.8

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

  4. Applied associate-/r*_binary64_27500.5

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

  6. Applied cosh-undef_binary64_30000.5

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

  7. Applied sqrt-prod_binary64_28220.5

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

  8. Applied add-sqr-sqrt_binary64_28280.5

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

  9. Applied times-frac_binary64_28120.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

    \[\leadsto \frac{\frac{\sqrt{2}}{\sqrt{\cosh x}}}{\sqrt{e^{x} + e^{-x}}}\]

Reproduce

herbie shell --seed 2021050 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))