invcot (example 3.9)

Percentage Accurate: 6.4% → 99.5%

Time: 14.3s

Alternatives: 5

Speedup: 35.7×

Specification

\[-0.026 < x \land x < 0.026\]

Math

\[\begin{array}{l} \\ \frac{1}{x} - \frac{1}{\tan x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 x) (/ 1.0 (tan x))))

C

double code(double x) {
	return (1.0 / x) - (1.0 / tan(x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / x) - (1.0d0 / tan(x))
end function

Java

public static double code(double x) {
	return (1.0 / x) - (1.0 / Math.tan(x));
}

Python

def code(x):
	return (1.0 / x) - (1.0 / math.tan(x))

Julia

function code(x)
	return Float64(Float64(1.0 / x) - Float64(1.0 / tan(x)))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / x) - (1.0 / tan(x));
end

Wolfram

code[x_] := N[(N[(1.0 / x), $MachinePrecision] - N[(1.0 / N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 6.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{x} - \frac{1}{\tan x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (/ 1.0 x) (/ 1.0 (tan x))))

C

double code(double x) {
	return (1.0 / x) - (1.0 / tan(x));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 / x) - (1.0d0 / tan(x))
end function

Java

public static double code(double x) {
	return (1.0 / x) - (1.0 / Math.tan(x));
}

Python

def code(x):
	return (1.0 / x) - (1.0 / math.tan(x))

Julia

function code(x)
	return Float64(Float64(1.0 / x) - Float64(1.0 / tan(x)))
end

MATLAB

function tmp = code(x)
	tmp = (1.0 / x) - (1.0 / tan(x));
end

Wolfram

code[x_] := N[(N[(1.0 / x), $MachinePrecision] - N[(1.0 / N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot x + \left(0.0021164021164021165 \cdot {x}^{5} + \left(0.022222222222222223 \cdot {x}^{3} + 0.00021164021164021165 \cdot {x}^{7}\right)\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (+
  (* 0.3333333333333333 x)
  (+
   (* 0.0021164021164021165 (pow x 5.0))
   (+
    (* 0.022222222222222223 (pow x 3.0))
    (* 0.00021164021164021165 (pow x 7.0))))))

C

double code(double x) {
	return (0.3333333333333333 * x) + ((0.0021164021164021165 * pow(x, 5.0)) + ((0.022222222222222223 * pow(x, 3.0)) + (0.00021164021164021165 * pow(x, 7.0))));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.3333333333333333d0 * x) + ((0.0021164021164021165d0 * (x ** 5.0d0)) + ((0.022222222222222223d0 * (x ** 3.0d0)) + (0.00021164021164021165d0 * (x ** 7.0d0))))
end function

Java

public static double code(double x) {
	return (0.3333333333333333 * x) + ((0.0021164021164021165 * Math.pow(x, 5.0)) + ((0.022222222222222223 * Math.pow(x, 3.0)) + (0.00021164021164021165 * Math.pow(x, 7.0))));
}

Python

def code(x):
	return (0.3333333333333333 * x) + ((0.0021164021164021165 * math.pow(x, 5.0)) + ((0.022222222222222223 * math.pow(x, 3.0)) + (0.00021164021164021165 * math.pow(x, 7.0))))

Julia

function code(x)
	return Float64(Float64(0.3333333333333333 * x) + Float64(Float64(0.0021164021164021165 * (x ^ 5.0)) + Float64(Float64(0.022222222222222223 * (x ^ 3.0)) + Float64(0.00021164021164021165 * (x ^ 7.0)))))
end

MATLAB

function tmp = code(x)
	tmp = (0.3333333333333333 * x) + ((0.0021164021164021165 * (x ^ 5.0)) + ((0.022222222222222223 * (x ^ 3.0)) + (0.00021164021164021165 * (x ^ 7.0))));
end

Wolfram

code[x_] := N[(N[(0.3333333333333333 * x), $MachinePrecision] + N[(N[(0.0021164021164021165 * N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision] + N[(N[(0.022222222222222223 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(0.00021164021164021165 * N[Power[x, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 6.3%

   \[\frac{1}{x} - \frac{1}{\tan x} \]

2. Taylor expanded in x around 0 99.5%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot x + \left(0.0021164021164021165 \cdot {x}^{5} + \left(0.022222222222222223 \cdot {x}^{3} + 0.00021164021164021165 \cdot {x}^{7}\right)\right)} \]

3. Final simplification 99.5%

   \[\leadsto 0.3333333333333333 \cdot x + \left(0.0021164021164021165 \cdot {x}^{5} + \left(0.022222222222222223 \cdot {x}^{3} + 0.00021164021164021165 \cdot {x}^{7}\right)\right) \]

Alternative 2: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot x + \left(0.0021164021164021165 \cdot {x}^{5} + 0.022222222222222223 \cdot {x}^{3}\right) \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (+
  (* 0.3333333333333333 x)
  (+
   (* 0.0021164021164021165 (pow x 5.0))
   (* 0.022222222222222223 (pow x 3.0)))))

C

double code(double x) {
	return (0.3333333333333333 * x) + ((0.0021164021164021165 * pow(x, 5.0)) + (0.022222222222222223 * pow(x, 3.0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (0.3333333333333333d0 * x) + ((0.0021164021164021165d0 * (x ** 5.0d0)) + (0.022222222222222223d0 * (x ** 3.0d0)))
end function

Java

public static double code(double x) {
	return (0.3333333333333333 * x) + ((0.0021164021164021165 * Math.pow(x, 5.0)) + (0.022222222222222223 * Math.pow(x, 3.0)));
}

Python

def code(x):
	return (0.3333333333333333 * x) + ((0.0021164021164021165 * math.pow(x, 5.0)) + (0.022222222222222223 * math.pow(x, 3.0)))

Julia

function code(x)
	return Float64(Float64(0.3333333333333333 * x) + Float64(Float64(0.0021164021164021165 * (x ^ 5.0)) + Float64(0.022222222222222223 * (x ^ 3.0))))
end

MATLAB

function tmp = code(x)
	tmp = (0.3333333333333333 * x) + ((0.0021164021164021165 * (x ^ 5.0)) + (0.022222222222222223 * (x ^ 3.0)));
end

Wolfram

code[x_] := N[(N[(0.3333333333333333 * x), $MachinePrecision] + N[(N[(0.0021164021164021165 * N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision] + N[(0.022222222222222223 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 6.3%

   \[\frac{1}{x} - \frac{1}{\tan x} \]

2. Taylor expanded in x around 0 99.4%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot x + \left(0.0021164021164021165 \cdot {x}^{5} + 0.022222222222222223 \cdot {x}^{3}\right)} \]

3. Final simplification 99.4%

   \[\leadsto 0.3333333333333333 \cdot x + \left(0.0021164021164021165 \cdot {x}^{5} + 0.022222222222222223 \cdot {x}^{3}\right) \]

Alternative 3: 99.5% accurate, 11.9× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{3}{x} + x \cdot -0.2} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 1.0 (+ (/ 3.0 x) (* x -0.2))))

C

double code(double x) {
	return 1.0 / ((3.0 / x) + (x * -0.2));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / ((3.0d0 / x) + (x * (-0.2d0)))
end function

Java

public static double code(double x) {
	return 1.0 / ((3.0 / x) + (x * -0.2));
}

Python

def code(x):
	return 1.0 / ((3.0 / x) + (x * -0.2))

Julia

function code(x)
	return Float64(1.0 / Float64(Float64(3.0 / x) + Float64(x * -0.2)))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / ((3.0 / x) + (x * -0.2));
end

Wolfram

code[x_] := N[(1.0 / N[(N[(3.0 / x), $MachinePrecision] + N[(x * -0.2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 6.3%

   \[\frac{1}{x} - \frac{1}{\tan x} \]

2. Taylor expanded in x around 0 99.3%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot x + 0.022222222222222223 \cdot {x}^{3}} \]
3. Step-by-step derivation

   1. flip-+ 53.5%

      \[\leadsto \color{blue}{\frac{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}{0.3333333333333333 \cdot x - 0.022222222222222223 \cdot {x}^{3}}} \]

   2. clear-num 53.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{0.3333333333333333 \cdot x - 0.022222222222222223 \cdot {x}^{3}}{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}}} \]

   3. cancel-sign-sub-inv 53.4%

      \[\leadsto \frac{1}{\frac{\color{blue}{0.3333333333333333 \cdot x + \left(-0.022222222222222223\right) \cdot {x}^{3}}}{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}} \]

   4. metadata-eval 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + \color{blue}{-0.022222222222222223} \cdot {x}^{3}}{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}} \]

   5. pow2 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{\color{blue}{{\left(0.3333333333333333 \cdot x\right)}^{2}} - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}} \]

   6. swap-sqr 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - \color{blue}{\left(0.022222222222222223 \cdot 0.022222222222222223\right) \cdot \left({x}^{3} \cdot {x}^{3}\right)}}} \]

   7. metadata-eval 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - \color{blue}{0.0004938271604938272} \cdot \left({x}^{3} \cdot {x}^{3}\right)}} \]

   8. pow-prod-up 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - 0.0004938271604938272 \cdot \color{blue}{{x}^{\left(3 + 3\right)}}}} \]

   9. metadata-eval 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - 0.0004938271604938272 \cdot {x}^{\color{blue}{6}}}} \]

4. Applied egg-rr 53.4%

   \[\leadsto \color{blue}{\frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - 0.0004938271604938272 \cdot {x}^{6}}}} \]

5. Taylor expanded in x around 0 99.2%

   \[\leadsto \frac{1}{\color{blue}{3 \cdot \frac{1}{x} + -0.2 \cdot x}} \]
6. Step-by-step derivation

   1. associate-*r/ 99.4%

      \[\leadsto \frac{1}{\color{blue}{\frac{3 \cdot 1}{x}} + -0.2 \cdot x} \]

   2. metadata-eval 99.4%

      \[\leadsto \frac{1}{\frac{\color{blue}{3}}{x} + -0.2 \cdot x} \]

   3. *-commutative 99.4%

      \[\leadsto \frac{1}{\frac{3}{x} + \color{blue}{x \cdot -0.2}} \]

7. Simplified 99.4%

   \[\leadsto \frac{1}{\color{blue}{\frac{3}{x} + x \cdot -0.2}} \]

8. Final simplification 99.4%

   \[\leadsto \frac{1}{\frac{3}{x} + x \cdot -0.2} \]

Alternative 4: 99.0% accurate, 21.4× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{3}{x}} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ 1.0 (/ 3.0 x)))

C

double code(double x) {
	return 1.0 / (3.0 / x);
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / (3.0d0 / x)
end function

Java

public static double code(double x) {
	return 1.0 / (3.0 / x);
}

Python

def code(x):
	return 1.0 / (3.0 / x)

Julia

function code(x)
	return Float64(1.0 / Float64(3.0 / x))
end

MATLAB

function tmp = code(x)
	tmp = 1.0 / (3.0 / x);
end

Wolfram

code[x_] := N[(1.0 / N[(3.0 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 6.3%

   \[\frac{1}{x} - \frac{1}{\tan x} \]

2. Taylor expanded in x around 0 99.3%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot x + 0.022222222222222223 \cdot {x}^{3}} \]
3. Step-by-step derivation

   1. flip-+ 53.5%

      \[\leadsto \color{blue}{\frac{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}{0.3333333333333333 \cdot x - 0.022222222222222223 \cdot {x}^{3}}} \]

   2. clear-num 53.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{0.3333333333333333 \cdot x - 0.022222222222222223 \cdot {x}^{3}}{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}}} \]

   3. cancel-sign-sub-inv 53.4%

      \[\leadsto \frac{1}{\frac{\color{blue}{0.3333333333333333 \cdot x + \left(-0.022222222222222223\right) \cdot {x}^{3}}}{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}} \]

   4. metadata-eval 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + \color{blue}{-0.022222222222222223} \cdot {x}^{3}}{\left(0.3333333333333333 \cdot x\right) \cdot \left(0.3333333333333333 \cdot x\right) - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}} \]

   5. pow2 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{\color{blue}{{\left(0.3333333333333333 \cdot x\right)}^{2}} - \left(0.022222222222222223 \cdot {x}^{3}\right) \cdot \left(0.022222222222222223 \cdot {x}^{3}\right)}} \]

   6. swap-sqr 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - \color{blue}{\left(0.022222222222222223 \cdot 0.022222222222222223\right) \cdot \left({x}^{3} \cdot {x}^{3}\right)}}} \]

   7. metadata-eval 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - \color{blue}{0.0004938271604938272} \cdot \left({x}^{3} \cdot {x}^{3}\right)}} \]

   8. pow-prod-up 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - 0.0004938271604938272 \cdot \color{blue}{{x}^{\left(3 + 3\right)}}}} \]

   9. metadata-eval 53.4%

      \[\leadsto \frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - 0.0004938271604938272 \cdot {x}^{\color{blue}{6}}}} \]

4. Applied egg-rr 53.4%

   \[\leadsto \color{blue}{\frac{1}{\frac{0.3333333333333333 \cdot x + -0.022222222222222223 \cdot {x}^{3}}{{\left(0.3333333333333333 \cdot x\right)}^{2} - 0.0004938271604938272 \cdot {x}^{6}}}} \]

5. Taylor expanded in x around 0 99.0%

   \[\leadsto \frac{1}{\color{blue}{\frac{3}{x}}} \]

6. Final simplification 99.0%

   \[\leadsto \frac{1}{\frac{3}{x}} \]

Alternative 5: 98.9% accurate, 35.7× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot x \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 0.3333333333333333 x))

C

double code(double x) {
	return 0.3333333333333333 * x;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.3333333333333333d0 * x
end function

Java

public static double code(double x) {
	return 0.3333333333333333 * x;
}

Python

def code(x):
	return 0.3333333333333333 * x

Julia

function code(x)
	return Float64(0.3333333333333333 * x)
end

MATLAB

function tmp = code(x)
	tmp = 0.3333333333333333 * x;
end

Wolfram

code[x_] := N[(0.3333333333333333 * x), $MachinePrecision]

Derivation

1. Initial program 6.3%

   \[\frac{1}{x} - \frac{1}{\tan x} \]

2. Taylor expanded in x around 0 98.9%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot x} \]

3. Final simplification 98.9%

   \[\leadsto 0.3333333333333333 \cdot x \]

Developer target: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left|x\right| < 0.026:\\ \;\;\;\;\frac{x}{3} \cdot \left(1 + \frac{x \cdot x}{15}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x} - \frac{1}{\tan x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (< (fabs x) 0.026)
   (* (/ x 3.0) (+ 1.0 (/ (* x x) 15.0)))
   (- (/ 1.0 x) (/ 1.0 (tan x)))))

C

double code(double x) {
	double tmp;
	if (fabs(x) < 0.026) {
		tmp = (x / 3.0) * (1.0 + ((x * x) / 15.0));
	} else {
		tmp = (1.0 / x) - (1.0 / tan(x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (abs(x) < 0.026d0) then
        tmp = (x / 3.0d0) * (1.0d0 + ((x * x) / 15.0d0))
    else
        tmp = (1.0d0 / x) - (1.0d0 / tan(x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (Math.abs(x) < 0.026) {
		tmp = (x / 3.0) * (1.0 + ((x * x) / 15.0));
	} else {
		tmp = (1.0 / x) - (1.0 / Math.tan(x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if math.fabs(x) < 0.026:
		tmp = (x / 3.0) * (1.0 + ((x * x) / 15.0))
	else:
		tmp = (1.0 / x) - (1.0 / math.tan(x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (abs(x) < 0.026)
		tmp = Float64(Float64(x / 3.0) * Float64(1.0 + Float64(Float64(x * x) / 15.0)));
	else
		tmp = Float64(Float64(1.0 / x) - Float64(1.0 / tan(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (abs(x) < 0.026)
		tmp = (x / 3.0) * (1.0 + ((x * x) / 15.0));
	else
		tmp = (1.0 / x) - (1.0 / tan(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Less[N[Abs[x], $MachinePrecision], 0.026], N[(N[(x / 3.0), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] / 15.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / x), $MachinePrecision] - N[(1.0 / N[Tan[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x)
  :name "invcot (example 3.9)"
  :precision binary64
  :pre (and (< -0.026 x) (< x 0.026))

  :herbie-target
  (if (< (fabs x) 0.026) (* (/ x 3.0) (+ 1.0 (/ (* x x) 15.0))) (- (/ 1.0 x) (/ 1.0 (tan x))))

  (- (/ 1.0 x) (/ 1.0 (tan x))))