mixedcos

Percentage Accurate: 67.0% → 97.9%

Time: 20.6s

Alternatives: 13

Speedup: 24.1×

• 32.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \end{array} \]

FPCore

(FPCore (x c s)
 :precision binary64
 (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))

C

double code(double x, double c, double s) {
	return cos((2.0 * x)) / (pow(c, 2.0) * ((x * pow(s, 2.0)) * x));
}

Fortran

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

Java

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

Python

def code(x, c, s):
	return math.cos((2.0 * x)) / (math.pow(c, 2.0) * ((x * math.pow(s, 2.0)) * x))

Julia

function code(x, c, s)
	return Float64(cos(Float64(2.0 * x)) / Float64((c ^ 2.0) * Float64(Float64(x * (s ^ 2.0)) * x)))
end

MATLAB

function tmp = code(x, c, s)
	tmp = cos((2.0 * x)) / ((c ^ 2.0) * ((x * (s ^ 2.0)) * x));
end

Wolfram

code[x_, c_, s_] := N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / N[(N[Power[c, 2.0], $MachinePrecision] * N[(N[(x * N[Power[s, 2.0], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \end{array} \]

FPCore

(FPCore (x c s)
 :precision binary64
 (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))

C

double code(double x, double c, double s) {
	return cos((2.0 * x)) / (pow(c, 2.0) * ((x * pow(s, 2.0)) * x));
}

Fortran

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

Java

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

Python

def code(x, c, s):
	return math.cos((2.0 * x)) / (math.pow(c, 2.0) * ((x * math.pow(s, 2.0)) * x))

Julia

function code(x, c, s)
	return Float64(cos(Float64(2.0 * x)) / Float64((c ^ 2.0) * Float64(Float64(x * (s ^ 2.0)) * x)))
end

MATLAB

function tmp = code(x, c, s)
	tmp = cos((2.0 * x)) / ((c ^ 2.0) * ((x * (s ^ 2.0)) * x));
end

Wolfram

code[x_, c_, s_] := N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / N[(N[Power[c, 2.0], $MachinePrecision] * N[(N[(x * N[Power[s, 2.0], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \begin{array}{l} \mathbf{if}\;{s_m}^{2} \leq 10^{+120}:\\ \;\;\;\;\frac{\cos \left(x \cdot -2\right)}{{\left(c_m \cdot \left(s_m \cdot x\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x \cdot \left(-s_m \cdot c_m\right)} \cdot \frac{\frac{\cos \left(2 \cdot x\right)}{x}}{s_m \cdot c_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (if (<= (pow s_m 2.0) 1e+120)
   (/ (cos (* x -2.0)) (pow (* c_m (* s_m x)) 2.0))
   (* (/ -1.0 (* x (- (* s_m c_m)))) (/ (/ (cos (* 2.0 x)) x) (* s_m c_m)))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	double tmp;
	if (pow(s_m, 2.0) <= 1e+120) {
		tmp = cos((x * -2.0)) / pow((c_m * (s_m * x)), 2.0);
	} else {
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((cos((2.0 * x)) / x) / (s_m * c_m));
	}
	return tmp;
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    real(8) :: tmp
    if ((s_m ** 2.0d0) <= 1d+120) then
        tmp = cos((x * (-2.0d0))) / ((c_m * (s_m * x)) ** 2.0d0)
    else
        tmp = ((-1.0d0) / (x * -(s_m * c_m))) * ((cos((2.0d0 * x)) / x) / (s_m * c_m))
    end if
    code = tmp
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	double tmp;
	if (Math.pow(s_m, 2.0) <= 1e+120) {
		tmp = Math.cos((x * -2.0)) / Math.pow((c_m * (s_m * x)), 2.0);
	} else {
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((Math.cos((2.0 * x)) / x) / (s_m * c_m));
	}
	return tmp;
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	tmp = 0
	if math.pow(s_m, 2.0) <= 1e+120:
		tmp = math.cos((x * -2.0)) / math.pow((c_m * (s_m * x)), 2.0)
	else:
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((math.cos((2.0 * x)) / x) / (s_m * c_m))
	return tmp

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	tmp = 0.0
	if ((s_m ^ 2.0) <= 1e+120)
		tmp = Float64(cos(Float64(x * -2.0)) / (Float64(c_m * Float64(s_m * x)) ^ 2.0));
	else
		tmp = Float64(Float64(-1.0 / Float64(x * Float64(-Float64(s_m * c_m)))) * Float64(Float64(cos(Float64(2.0 * x)) / x) / Float64(s_m * c_m)));
	end
	return tmp
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp_2 = code(x, c_m, s_m)
	tmp = 0.0;
	if ((s_m ^ 2.0) <= 1e+120)
		tmp = cos((x * -2.0)) / ((c_m * (s_m * x)) ^ 2.0);
	else
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((cos((2.0 * x)) / x) / (s_m * c_m));
	end
	tmp_2 = tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := If[LessEqual[N[Power[s$95$m, 2.0], $MachinePrecision], 1e+120], N[(N[Cos[N[(x * -2.0), $MachinePrecision]], $MachinePrecision] / N[Power[N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(x * (-N[(s$95$m * c$95$m), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision] / N[(s$95$m * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 96.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \begin{array}{l} t_0 := \cos \left(2 \cdot x\right)\\ \mathbf{if}\;{s_m}^{2} \leq 10^{+76}:\\ \;\;\;\;\frac{1}{\left(c_m \cdot \left(s_m \cdot x\right)\right) \cdot \frac{c_m}{\frac{t_0}{s_m \cdot x}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x \cdot \left(-s_m \cdot c_m\right)} \cdot \frac{\frac{t_0}{s_m}}{x \cdot c_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (let* ((t_0 (cos (* 2.0 x))))
   (if (<= (pow s_m 2.0) 1e+76)
     (/ 1.0 (* (* c_m (* s_m x)) (/ c_m (/ t_0 (* s_m x)))))
     (* (/ -1.0 (* x (- (* s_m c_m)))) (/ (/ t_0 s_m) (* x c_m))))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	double t_0 = cos((2.0 * x));
	double tmp;
	if (pow(s_m, 2.0) <= 1e+76) {
		tmp = 1.0 / ((c_m * (s_m * x)) * (c_m / (t_0 / (s_m * x))));
	} else {
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / s_m) / (x * c_m));
	}
	return tmp;
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = cos((2.0d0 * x))
    if ((s_m ** 2.0d0) <= 1d+76) then
        tmp = 1.0d0 / ((c_m * (s_m * x)) * (c_m / (t_0 / (s_m * x))))
    else
        tmp = ((-1.0d0) / (x * -(s_m * c_m))) * ((t_0 / s_m) / (x * c_m))
    end if
    code = tmp
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	double t_0 = Math.cos((2.0 * x));
	double tmp;
	if (Math.pow(s_m, 2.0) <= 1e+76) {
		tmp = 1.0 / ((c_m * (s_m * x)) * (c_m / (t_0 / (s_m * x))));
	} else {
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / s_m) / (x * c_m));
	}
	return tmp;
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	t_0 = math.cos((2.0 * x))
	tmp = 0
	if math.pow(s_m, 2.0) <= 1e+76:
		tmp = 1.0 / ((c_m * (s_m * x)) * (c_m / (t_0 / (s_m * x))))
	else:
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / s_m) / (x * c_m))
	return tmp

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	t_0 = cos(Float64(2.0 * x))
	tmp = 0.0
	if ((s_m ^ 2.0) <= 1e+76)
		tmp = Float64(1.0 / Float64(Float64(c_m * Float64(s_m * x)) * Float64(c_m / Float64(t_0 / Float64(s_m * x)))));
	else
		tmp = Float64(Float64(-1.0 / Float64(x * Float64(-Float64(s_m * c_m)))) * Float64(Float64(t_0 / s_m) / Float64(x * c_m)));
	end
	return tmp
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp_2 = code(x, c_m, s_m)
	t_0 = cos((2.0 * x));
	tmp = 0.0;
	if ((s_m ^ 2.0) <= 1e+76)
		tmp = 1.0 / ((c_m * (s_m * x)) * (c_m / (t_0 / (s_m * x))));
	else
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / s_m) / (x * c_m));
	end
	tmp_2 = tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := Block[{t$95$0 = N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Power[s$95$m, 2.0], $MachinePrecision], 1e+76], N[(1.0 / N[(N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision] * N[(c$95$m / N[(t$95$0 / N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(x * (-N[(s$95$m * c$95$m), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$0 / s$95$m), $MachinePrecision] / N[(x * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 98.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \begin{array}{l} t_0 := \cos \left(2 \cdot x\right)\\ t_1 := c_m \cdot \left(s_m \cdot x\right)\\ \mathbf{if}\;{s_m}^{2} \leq 10^{+120}:\\ \;\;\;\;\frac{\frac{t_0}{t_1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{x \cdot \left(-s_m \cdot c_m\right)} \cdot \frac{\frac{t_0}{x}}{s_m \cdot c_m}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (let* ((t_0 (cos (* 2.0 x))) (t_1 (* c_m (* s_m x))))
   (if (<= (pow s_m 2.0) 1e+120)
     (/ (/ t_0 t_1) t_1)
     (* (/ -1.0 (* x (- (* s_m c_m)))) (/ (/ t_0 x) (* s_m c_m))))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	double t_0 = cos((2.0 * x));
	double t_1 = c_m * (s_m * x);
	double tmp;
	if (pow(s_m, 2.0) <= 1e+120) {
		tmp = (t_0 / t_1) / t_1;
	} else {
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / x) / (s_m * c_m));
	}
	return tmp;
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((2.0d0 * x))
    t_1 = c_m * (s_m * x)
    if ((s_m ** 2.0d0) <= 1d+120) then
        tmp = (t_0 / t_1) / t_1
    else
        tmp = ((-1.0d0) / (x * -(s_m * c_m))) * ((t_0 / x) / (s_m * c_m))
    end if
    code = tmp
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	double t_0 = Math.cos((2.0 * x));
	double t_1 = c_m * (s_m * x);
	double tmp;
	if (Math.pow(s_m, 2.0) <= 1e+120) {
		tmp = (t_0 / t_1) / t_1;
	} else {
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / x) / (s_m * c_m));
	}
	return tmp;
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	t_0 = math.cos((2.0 * x))
	t_1 = c_m * (s_m * x)
	tmp = 0
	if math.pow(s_m, 2.0) <= 1e+120:
		tmp = (t_0 / t_1) / t_1
	else:
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / x) / (s_m * c_m))
	return tmp

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	t_0 = cos(Float64(2.0 * x))
	t_1 = Float64(c_m * Float64(s_m * x))
	tmp = 0.0
	if ((s_m ^ 2.0) <= 1e+120)
		tmp = Float64(Float64(t_0 / t_1) / t_1);
	else
		tmp = Float64(Float64(-1.0 / Float64(x * Float64(-Float64(s_m * c_m)))) * Float64(Float64(t_0 / x) / Float64(s_m * c_m)));
	end
	return tmp
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp_2 = code(x, c_m, s_m)
	t_0 = cos((2.0 * x));
	t_1 = c_m * (s_m * x);
	tmp = 0.0;
	if ((s_m ^ 2.0) <= 1e+120)
		tmp = (t_0 / t_1) / t_1;
	else
		tmp = (-1.0 / (x * -(s_m * c_m))) * ((t_0 / x) / (s_m * c_m));
	end
	tmp_2 = tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := Block[{t$95$0 = N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Power[s$95$m, 2.0], $MachinePrecision], 1e+120], N[(N[(t$95$0 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(-1.0 / N[(x * (-N[(s$95$m * c$95$m), $MachinePrecision])), $MachinePrecision]), $MachinePrecision] * N[(N[(t$95$0 / x), $MachinePrecision] / N[(s$95$m * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 95.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(s_m \cdot x\right)\\ t_1 := \cos \left(2 \cdot x\right)\\ \mathbf{if}\;c_m \leq 8 \cdot 10^{-198}:\\ \;\;\;\;\frac{\frac{t_1}{c_m}}{\left(s_m \cdot x\right) \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_1}{c_m \cdot t_0}}{s_m \cdot x}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (let* ((t_0 (* c_m (* s_m x))) (t_1 (cos (* 2.0 x))))
   (if (<= c_m 8e-198)
     (/ (/ t_1 c_m) (* (* s_m x) t_0))
     (/ (/ t_1 (* c_m t_0)) (* s_m x)))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	double t_0 = c_m * (s_m * x);
	double t_1 = cos((2.0 * x));
	double tmp;
	if (c_m <= 8e-198) {
		tmp = (t_1 / c_m) / ((s_m * x) * t_0);
	} else {
		tmp = (t_1 / (c_m * t_0)) / (s_m * x);
	}
	return tmp;
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = c_m * (s_m * x)
    t_1 = cos((2.0d0 * x))
    if (c_m <= 8d-198) then
        tmp = (t_1 / c_m) / ((s_m * x) * t_0)
    else
        tmp = (t_1 / (c_m * t_0)) / (s_m * x)
    end if
    code = tmp
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	double t_0 = c_m * (s_m * x);
	double t_1 = Math.cos((2.0 * x));
	double tmp;
	if (c_m <= 8e-198) {
		tmp = (t_1 / c_m) / ((s_m * x) * t_0);
	} else {
		tmp = (t_1 / (c_m * t_0)) / (s_m * x);
	}
	return tmp;
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	t_0 = c_m * (s_m * x)
	t_1 = math.cos((2.0 * x))
	tmp = 0
	if c_m <= 8e-198:
		tmp = (t_1 / c_m) / ((s_m * x) * t_0)
	else:
		tmp = (t_1 / (c_m * t_0)) / (s_m * x)
	return tmp

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	t_0 = Float64(c_m * Float64(s_m * x))
	t_1 = cos(Float64(2.0 * x))
	tmp = 0.0
	if (c_m <= 8e-198)
		tmp = Float64(Float64(t_1 / c_m) / Float64(Float64(s_m * x) * t_0));
	else
		tmp = Float64(Float64(t_1 / Float64(c_m * t_0)) / Float64(s_m * x));
	end
	return tmp
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp_2 = code(x, c_m, s_m)
	t_0 = c_m * (s_m * x);
	t_1 = cos((2.0 * x));
	tmp = 0.0;
	if (c_m <= 8e-198)
		tmp = (t_1 / c_m) / ((s_m * x) * t_0);
	else
		tmp = (t_1 / (c_m * t_0)) / (s_m * x);
	end
	tmp_2 = tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := Block[{t$95$0 = N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[c$95$m, 8e-198], N[(N[(t$95$1 / c$95$m), $MachinePrecision] / N[(N[(s$95$m * x), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 / N[(c$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 91.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \frac{\frac{\cos \left(2 \cdot x\right)}{c_m}}{s_m \cdot \left(x \cdot \left(c_m \cdot \left(s_m \cdot x\right)\right)\right)} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (/ (/ (cos (* 2.0 x)) c_m) (* s_m (* x (* c_m (* s_m x))))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return (cos((2.0 * x)) / c_m) / (s_m * (x * (c_m * (s_m * x))));
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = (cos((2.0d0 * x)) / c_m) / (s_m * (x * (c_m * (s_m * x))))
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return (Math.cos((2.0 * x)) / c_m) / (s_m * (x * (c_m * (s_m * x))));
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return (math.cos((2.0 * x)) / c_m) / (s_m * (x * (c_m * (s_m * x))))

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(Float64(cos(Float64(2.0 * x)) / c_m) / Float64(s_m * Float64(x * Float64(c_m * Float64(s_m * x)))))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = (cos((2.0 * x)) / c_m) / (s_m * (x * (c_m * (s_m * x))));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[(N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / c$95$m), $MachinePrecision] / N[(s$95$m * N[(x * N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 93.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \frac{\frac{\cos \left(2 \cdot x\right)}{c_m}}{\left(s_m \cdot x\right) \cdot \left(c_m \cdot \left(s_m \cdot x\right)\right)} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (/ (/ (cos (* 2.0 x)) c_m) (* (* s_m x) (* c_m (* s_m x)))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return (cos((2.0 * x)) / c_m) / ((s_m * x) * (c_m * (s_m * x)));
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = (cos((2.0d0 * x)) / c_m) / ((s_m * x) * (c_m * (s_m * x)))
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return (Math.cos((2.0 * x)) / c_m) / ((s_m * x) * (c_m * (s_m * x)));
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return (math.cos((2.0 * x)) / c_m) / ((s_m * x) * (c_m * (s_m * x)))

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(Float64(cos(Float64(2.0 * x)) / c_m) / Float64(Float64(s_m * x) * Float64(c_m * Float64(s_m * x))))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = (cos((2.0 * x)) / c_m) / ((s_m * x) * (c_m * (s_m * x)));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[(N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / c$95$m), $MachinePrecision] / N[(N[(s$95$m * x), $MachinePrecision] * N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 97.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(s_m \cdot x\right)\\ \frac{\frac{\cos \left(2 \cdot x\right)}{t_0}}{t_0} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (let* ((t_0 (* c_m (* s_m x)))) (/ (/ (cos (* 2.0 x)) t_0) t_0)))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	double t_0 = c_m * (s_m * x);
	return (cos((2.0 * x)) / t_0) / t_0;
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    real(8) :: t_0
    t_0 = c_m * (s_m * x)
    code = (cos((2.0d0 * x)) / t_0) / t_0
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	double t_0 = c_m * (s_m * x);
	return (Math.cos((2.0 * x)) / t_0) / t_0;
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	t_0 = c_m * (s_m * x)
	return (math.cos((2.0 * x)) / t_0) / t_0

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	t_0 = Float64(c_m * Float64(s_m * x))
	return Float64(Float64(cos(Float64(2.0 * x)) / t_0) / t_0)
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	t_0 = c_m * (s_m * x);
	tmp = (cos((2.0 * x)) / t_0) / t_0;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := Block[{t$95$0 = N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 80.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ {\left(\frac{c_m}{\frac{\frac{1}{x}}{s_m}}\right)}^{-2} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m) :precision binary64 (pow (/ c_m (/ (/ 1.0 x) s_m)) -2.0))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return pow((c_m / ((1.0 / x) / s_m)), -2.0);
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = (c_m / ((1.0d0 / x) / s_m)) ** (-2.0d0)
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return Math.pow((c_m / ((1.0 / x) / s_m)), -2.0);
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return math.pow((c_m / ((1.0 / x) / s_m)), -2.0)

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(c_m / Float64(Float64(1.0 / x) / s_m)) ^ -2.0
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = (c_m / ((1.0 / x) / s_m)) ^ -2.0;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[Power[N[(c$95$m / N[(N[(1.0 / x), $MachinePrecision] / s$95$m), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 80.0% accurate, 20.9× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \frac{1}{c_m \cdot \left(s_m \cdot x\right)} \cdot \frac{\frac{1}{s_m \cdot x}}{c_m} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (* (/ 1.0 (* c_m (* s_m x))) (/ (/ 1.0 (* s_m x)) c_m)))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return (1.0 / (c_m * (s_m * x))) * ((1.0 / (s_m * x)) / c_m);
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = (1.0d0 / (c_m * (s_m * x))) * ((1.0d0 / (s_m * x)) / c_m)
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return (1.0 / (c_m * (s_m * x))) * ((1.0 / (s_m * x)) / c_m);
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return (1.0 / (c_m * (s_m * x))) * ((1.0 / (s_m * x)) / c_m)

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(Float64(1.0 / Float64(c_m * Float64(s_m * x))) * Float64(Float64(1.0 / Float64(s_m * x)) / c_m))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = (1.0 / (c_m * (s_m * x))) * ((1.0 / (s_m * x)) / c_m);
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[(N[(1.0 / N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 / N[(s$95$m * x), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 76.6% accurate, 24.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \frac{1}{\left(s_m \cdot c_m\right) \cdot \left(x \cdot \left(c_m \cdot \left(s_m \cdot x\right)\right)\right)} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (/ 1.0 (* (* s_m c_m) (* x (* c_m (* s_m x))))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return 1.0 / ((s_m * c_m) * (x * (c_m * (s_m * x))));
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = 1.0d0 / ((s_m * c_m) * (x * (c_m * (s_m * x))))
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return 1.0 / ((s_m * c_m) * (x * (c_m * (s_m * x))));
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return 1.0 / ((s_m * c_m) * (x * (c_m * (s_m * x))))

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(1.0 / Float64(Float64(s_m * c_m) * Float64(x * Float64(c_m * Float64(s_m * x)))))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = 1.0 / ((s_m * c_m) * (x * (c_m * (s_m * x))));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[(1.0 / N[(N[(s$95$m * c$95$m), $MachinePrecision] * N[(x * N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 11: 76.7% accurate, 24.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \frac{1}{\left(s_m \cdot c_m\right) \cdot \left(x \cdot \left(x \cdot \left(s_m \cdot c_m\right)\right)\right)} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (/ 1.0 (* (* s_m c_m) (* x (* x (* s_m c_m))))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return 1.0 / ((s_m * c_m) * (x * (x * (s_m * c_m))));
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = 1.0d0 / ((s_m * c_m) * (x * (x * (s_m * c_m))))
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return 1.0 / ((s_m * c_m) * (x * (x * (s_m * c_m))));
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return 1.0 / ((s_m * c_m) * (x * (x * (s_m * c_m))))

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(1.0 / Float64(Float64(s_m * c_m) * Float64(x * Float64(x * Float64(s_m * c_m)))))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = 1.0 / ((s_m * c_m) * (x * (x * (s_m * c_m))));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[(1.0 / N[(N[(s$95$m * c$95$m), $MachinePrecision] * N[(x * N[(x * N[(s$95$m * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 79.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(s_m \cdot x\right)\\ \frac{1}{t_0 \cdot t_0} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (let* ((t_0 (* c_m (* s_m x)))) (/ 1.0 (* t_0 t_0))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	double t_0 = c_m * (s_m * x);
	return 1.0 / (t_0 * t_0);
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    real(8) :: t_0
    t_0 = c_m * (s_m * x)
    code = 1.0d0 / (t_0 * t_0)
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	double t_0 = c_m * (s_m * x);
	return 1.0 / (t_0 * t_0);
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	t_0 = c_m * (s_m * x)
	return 1.0 / (t_0 * t_0)

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	t_0 = Float64(c_m * Float64(s_m * x))
	return Float64(1.0 / Float64(t_0 * t_0))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	t_0 = c_m * (s_m * x);
	tmp = 1.0 / (t_0 * t_0);
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := Block[{t$95$0 = N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]}, N[(1.0 / N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 79.3% accurate, 24.1× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ s_m = \left|s\right| \\ [x, c_m, s_m] = \mathsf{sort}([x, c_m, s_m])\\ \\ \frac{\frac{1}{c_m}}{\left(s_m \cdot x\right) \cdot \left(c_m \cdot \left(s_m \cdot x\right)\right)} \end{array} \]

FPCore

c_m = (fabs.f64 c)
s_m = (fabs.f64 s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
(FPCore (x c_m s_m)
 :precision binary64
 (/ (/ 1.0 c_m) (* (* s_m x) (* c_m (* s_m x)))))

C

c_m = fabs(c);
s_m = fabs(s);
assert(x < c_m && c_m < s_m);
double code(double x, double c_m, double s_m) {
	return (1.0 / c_m) / ((s_m * x) * (c_m * (s_m * x)));
}

Fortran

c_m = abs(c)
s_m = abs(s)
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s_m
    code = (1.0d0 / c_m) / ((s_m * x) * (c_m * (s_m * x)))
end function

Java

c_m = Math.abs(c);
s_m = Math.abs(s);
assert x < c_m && c_m < s_m;
public static double code(double x, double c_m, double s_m) {
	return (1.0 / c_m) / ((s_m * x) * (c_m * (s_m * x)));
}

Python

c_m = math.fabs(c)
s_m = math.fabs(s)
[x, c_m, s_m] = sort([x, c_m, s_m])
def code(x, c_m, s_m):
	return (1.0 / c_m) / ((s_m * x) * (c_m * (s_m * x)))

Julia

c_m = abs(c)
s_m = abs(s)
x, c_m, s_m = sort([x, c_m, s_m])
function code(x, c_m, s_m)
	return Float64(Float64(1.0 / c_m) / Float64(Float64(s_m * x) * Float64(c_m * Float64(s_m * x))))
end

MATLAB

c_m = abs(c);
s_m = abs(s);
x, c_m, s_m = num2cell(sort([x, c_m, s_m])){:}
function tmp = code(x, c_m, s_m)
	tmp = (1.0 / c_m) / ((s_m * x) * (c_m * (s_m * x)));
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
s_m = N[Abs[s], $MachinePrecision]
NOTE: x, c_m, and s_m should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s$95$m_] := N[(N[(1.0 / c$95$m), $MachinePrecision] / N[(N[(s$95$m * x), $MachinePrecision] * N[(c$95$m * N[(s$95$m * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))