# ?

Average Error: 0.2 → 0.2
Time: 7.8s
Precision: binary64
Cost: 19328

# ?

$\frac{1}{{\cos x}^{2}}$
$\sqrt{{\cos x}^{-4}}$
(FPCore (x) :precision binary64 (/ 1.0 (pow (cos x) 2.0)))
(FPCore (x) :precision binary64 (sqrt (pow (cos x) -4.0)))
double code(double x) {
return 1.0 / pow(cos(x), 2.0);
}

double code(double x) {
return sqrt(pow(cos(x), -4.0));
}

real(8) function code(x)
real(8), intent (in) :: x
code = 1.0d0 / (cos(x) ** 2.0d0)
end function

real(8) function code(x)
real(8), intent (in) :: x
code = sqrt((cos(x) ** (-4.0d0)))
end function

public static double code(double x) {
return 1.0 / Math.pow(Math.cos(x), 2.0);
}

public static double code(double x) {
return Math.sqrt(Math.pow(Math.cos(x), -4.0));
}

def code(x):
return 1.0 / math.pow(math.cos(x), 2.0)

def code(x):
return math.sqrt(math.pow(math.cos(x), -4.0))

function code(x)
return Float64(1.0 / (cos(x) ^ 2.0))
end

function code(x)
return sqrt((cos(x) ^ -4.0))
end

function tmp = code(x)
tmp = 1.0 / (cos(x) ^ 2.0);
end

function tmp = code(x)
tmp = sqrt((cos(x) ^ -4.0));
end

code[x_] := N[(1.0 / N[Power[N[Cos[x], $MachinePrecision], 2.0],$MachinePrecision]), $MachinePrecision]  code[x_] := N[Sqrt[N[Power[N[Cos[x],$MachinePrecision], -4.0], $MachinePrecision]],$MachinePrecision]

\frac{1}{{\cos x}^{2}}

\sqrt{{\cos x}^{-4}}


# Try it out?

Results

 In Out
Enter valid numbers for all inputs

# Derivation?

1. Initial program 0.2

$\frac{1}{{\cos x}^{2}}$
2. Applied egg-rr0.2

$\leadsto \color{blue}{\sqrt{{\cos x}^{-4}}}$
3. Final simplification0.2

$\leadsto \sqrt{{\cos x}^{-4}}$

# Alternatives

Alternative 1
Error0.2
Cost12928
${\cos x}^{-2}$
Alternative 2
Error0.5
Cost6848
$\frac{2}{\cos \left(x \cdot 2\right) + 1}$
Alternative 3
Error25.6
Cost64
$1$

# Reproduce?

herbie shell --seed 1
(FPCore (x)
:name "1 / pow(cos(x), 2)"
:precision binary64
(/ 1.0 (pow (cos x) 2.0)))