?

Average Error: 0.0 → 0.0
Time: 10.9s
Precision: binary64
Cost: 12992

?

\[-1000 \leq x \land x \leq 1000\]
\[\frac{1}{\tan x} \]
\[\frac{\cos x}{\sin x} \]
(FPCore (x) :precision binary64 (/ 1.0 (tan x)))
(FPCore (x) :precision binary64 (/ (cos x) (sin x)))
double code(double x) {
	return 1.0 / tan(x);
}
double code(double x) {
	return cos(x) / sin(x);
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / tan(x)
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = cos(x) / sin(x)
end function
public static double code(double x) {
	return 1.0 / Math.tan(x);
}
public static double code(double x) {
	return Math.cos(x) / Math.sin(x);
}
def code(x):
	return 1.0 / math.tan(x)
def code(x):
	return math.cos(x) / math.sin(x)
function code(x)
	return Float64(1.0 / tan(x))
end
function code(x)
	return Float64(cos(x) / sin(x))
end
function tmp = code(x)
	tmp = 1.0 / tan(x);
end
function tmp = code(x)
	tmp = cos(x) / sin(x);
end
code[x_] := N[(1.0 / N[Tan[x], $MachinePrecision]), $MachinePrecision]
code[x_] := N[(N[Cos[x], $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]
\frac{1}{\tan x}
\frac{\cos x}{\sin x}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.0

    \[\frac{1}{\tan x} \]
  2. Taylor expanded in x around inf 0.0

    \[\leadsto \color{blue}{\frac{\cos x}{\sin x}} \]
  3. Final simplification0.0

    \[\leadsto \frac{\cos x}{\sin x} \]

Alternatives

Alternative 1
Error0.0
Cost6592
\[\frac{1}{\tan x} \]
Alternative 2
Error0.8
Cost1088
\[\frac{x \cdot \left(\left(x \cdot x\right) \cdot 0.022222222222222223\right)}{-1} + \left(x \cdot -0.3333333333333333 + \frac{1}{x}\right) \]
Alternative 3
Error1.0
Cost448
\[x \cdot -0.3333333333333333 + \frac{1}{x} \]
Alternative 4
Error63.0
Cost192
\[x \cdot -0.3333333333333333 \]
Alternative 5
Error1.3
Cost192
\[\frac{1}{x} \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (x)
  :name "1 / tan(x)"
  :precision binary64
  :pre (and (<= -1000.0 x) (<= x 1000.0))
  (/ 1.0 (tan x)))