Average Error: 0.0 → 0.2
Time: 1.7s
Precision: binary64
\[\frac{2}{e^{x} + e^{-x}} \]
↓
\[\log \left(e^{\sqrt[3]{{\left(\frac{1}{\cosh x}\right)}^{3}}}\right) \]
(FPCore (x) :precision binary64 (/ 2.0 (+ (exp x) (exp (- x)))))
↓
(FPCore (x) :precision binary64 (log (exp (cbrt (pow (/ 1.0 (cosh x)) 3.0)))))
double code(double x) {
	return 2.0 / (exp(x) + exp(-x));
}
↓
double code(double x) {
	return log(exp(cbrt(pow((1.0 / cosh(x)), 3.0))));
}

public static double code(double x) {
	return 2.0 / (Math.exp(x) + Math.exp(-x));
}
↓
public static double code(double x) {
	return Math.log(Math.exp(Math.cbrt(Math.pow((1.0 / Math.cosh(x)), 3.0))));
}

function code(x)
	return Float64(2.0 / Float64(exp(x) + exp(Float64(-x))))
end
↓
function code(x)
	return log(exp(cbrt((Float64(1.0 / cosh(x)) ^ 3.0))))
end

code[x_] := N[(2.0 / N[(N[Exp[x], $MachinePrecision] + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[Log[N[Exp[N[Power[N[Power[N[(1.0 / N[Cosh[x], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]

\frac{2}{e^{x} + e^{-x}}
↓
\log \left(e^{\sqrt[3]{{\left(\frac{1}{\cosh x}\right)}^{3}}}\right)

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  2. Applied egg-rr0.2

    \[\leadsto \color{blue}{\log \left(e^{\frac{2}{2 \cdot \cosh x}}\right)} \]

  3. Applied egg-rr0.2

    \[\leadsto \log \left(e^{\color{blue}{\sqrt[3]{{\left(\frac{1}{\cosh x}\right)}^{3}}}}\right) \]

  4. Final simplification0.2

    \[\leadsto \log \left(e^{\sqrt[3]{{\left(\frac{1}{\cosh x}\right)}^{3}}}\right) \]

Reproduce

herbie shell --seed 2022209 
(FPCore (x)
  :name "Hyperbolic secant"
  :precision binary64
  (/ 2.0 (+ (exp x) (exp (- x)))))