Average Error: 0.0 → 0.1
Time: 2.0s
Precision: binary64
Cost: 26048
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{{\left(\frac{2}{e^{x} + e^{-x}}\right)}^{3}}\]
\frac{2}{e^{x} + e^{-x}}
↓
\sqrt[3]{{\left(\frac{2}{e^{x} + e^{-x}}\right)}^{3}}
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x)
 :precision binary64
 (cbrt (pow (/ 2.0 (+ (exp x) (exp (- x)))) 3.0)))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return cbrt(pow((2.0 / (exp(x) + exp(-x))), 3.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.1
Cost19584
\[\sqrt[3]{{\left(0.5 \cdot \frac{2}{\cosh x}\right)}^{3}}\]
Alternative 2
Error0.1
Cost19456
\[\sqrt[3]{{\left(\frac{1}{\cosh x}\right)}^{3}}\]
Alternative 3
Error0.0
Cost13184
\[\frac{2}{e^{x} + e^{-x}}\]
Alternative 4
Error0.0
Cost6720
\[0.5 \cdot \frac{2}{\cosh x}\]
Alternative 5
Error0.0
Cost6592
\[\frac{1}{\cosh x}\]
Alternative 6
Error31.8
Cost64
\[1\]
Alternative 7
Error31.0
Cost64
\[0\]
Alternative 8
Error62.5
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube_binary64_18190.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021022 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))