Average Error: 3.5 → 0.4
Time: 2.2s
Precision: binary64
\[1.99 \leq x \land x \leq 2.01\]
\[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]
↓
\[\cos x \cdot \sqrt{{\left({\left(e^{20}\right)}^{x}\right)}^{x}} \]
(FPCore (x) :precision binary64 (* (cos x) (exp (* 10.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (* (cos x) (sqrt (pow (pow (exp 20.0) x) x))))
double code(double x) {
	return cos(x) * exp((10.0 * (x * x)));
}
↓
double code(double x) {
	return cos(x) * sqrt(pow(pow(exp(20.0), x), x));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * exp((10.0d0 * (x * x)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) * sqrt(((exp(20.0d0) ** x) ** x))
end function

public static double code(double x) {
	return Math.cos(x) * Math.exp((10.0 * (x * x)));
}
↓
public static double code(double x) {
	return Math.cos(x) * Math.sqrt(Math.pow(Math.pow(Math.exp(20.0), x), x));
}

def code(x):
	return math.cos(x) * math.exp((10.0 * (x * x)))
↓
def code(x):
	return math.cos(x) * math.sqrt(math.pow(math.pow(math.exp(20.0), x), x))

function code(x)
	return Float64(cos(x) * exp(Float64(10.0 * Float64(x * x))))
end
↓
function code(x)
	return Float64(cos(x) * sqrt(((exp(20.0) ^ x) ^ x)))
end

function tmp = code(x)
	tmp = cos(x) * exp((10.0 * (x * x)));
end
↓
function tmp = code(x)
	tmp = cos(x) * sqrt(((exp(20.0) ^ x) ^ x));
end

code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Exp[N[(10.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[Cos[x], $MachinePrecision] * N[Sqrt[N[Power[N[Power[N[Exp[20.0], $MachinePrecision], x], $MachinePrecision], x], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\cos x \cdot e^{10 \cdot \left(x \cdot x\right)}
↓
\cos x \cdot \sqrt{{\left({\left(e^{20}\right)}^{x}\right)}^{x}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.5

    \[\cos x \cdot e^{10 \cdot \left(x \cdot x\right)} \]

  2. Simplified3.2

    \[\leadsto \color{blue}{\cos x \cdot {\left(e^{x \cdot 10}\right)}^{x}} \]

  3. Taylor expanded in x around inf 3.2

    \[\leadsto \cos x \cdot {\color{blue}{\left(e^{10 \cdot x}\right)}}^{x} \]

  4. Simplified1.3

    \[\leadsto \cos x \cdot {\color{blue}{\left({\left(e^{10}\right)}^{x}\right)}}^{x} \]

  5. Applied egg-rr0.5

    \[\leadsto \cos x \cdot {\color{blue}{\left(\sqrt{{\left(e^{20}\right)}^{x}}\right)}}^{x} \]

  6. Applied egg-rr0.4

    \[\leadsto \cos x \cdot \color{blue}{\sqrt{{\left({\left(e^{20}\right)}^{x}\right)}^{x}}} \]

  7. Final simplification0.4

    \[\leadsto \cos x \cdot \sqrt{{\left({\left(e^{20}\right)}^{x}\right)}^{x}} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x)
  :name "ENA, Section 1.4, Exercise 1"
  :precision binary64
  :pre (and (<= 1.99 x) (<= x 2.01))
  (* (cos x) (exp (* 10.0 (* x x)))))