mixedcos

Percentage Accurate: 66.6% → 97.1%

Time: 10.9s

Alternatives: 8

Speedup: 24.1×

• 31.3% 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: 66.6% 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: 97.1% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 86.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{-38}:\\ \;\;\;\;{\left(\frac{s \cdot x}{\frac{1}{c_m}}\right)}^{-2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos \left(x \cdot -2\right)}{\left(c_m \cdot x\right) \cdot \left(s \cdot \left(c_m \cdot \left(s \cdot x\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
(FPCore (x c_m s)
 :precision binary64
 (if (<= x 8e-38)
   (pow (/ (* s x) (/ 1.0 c_m)) -2.0)
   (/ (cos (* x -2.0)) (* (* c_m x) (* s (* c_m (* s x)))))))

C

c_m = fabs(c);
assert(x < c_m && c_m < s);
double code(double x, double c_m, double s) {
	double tmp;
	if (x <= 8e-38) {
		tmp = pow(((s * x) / (1.0 / c_m)), -2.0);
	} else {
		tmp = cos((x * -2.0)) / ((c_m * x) * (s * (c_m * (s * x))));
	}
	return tmp;
}

Fortran

c_m = abs(c)
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s
    real(8) :: tmp
    if (x <= 8d-38) then
        tmp = ((s * x) / (1.0d0 / c_m)) ** (-2.0d0)
    else
        tmp = cos((x * (-2.0d0))) / ((c_m * x) * (s * (c_m * (s * x))))
    end if
    code = tmp
end function

Java

c_m = Math.abs(c);
assert x < c_m && c_m < s;
public static double code(double x, double c_m, double s) {
	double tmp;
	if (x <= 8e-38) {
		tmp = Math.pow(((s * x) / (1.0 / c_m)), -2.0);
	} else {
		tmp = Math.cos((x * -2.0)) / ((c_m * x) * (s * (c_m * (s * x))));
	}
	return tmp;
}

Python

c_m = math.fabs(c)
[x, c_m, s] = sort([x, c_m, s])
def code(x, c_m, s):
	tmp = 0
	if x <= 8e-38:
		tmp = math.pow(((s * x) / (1.0 / c_m)), -2.0)
	else:
		tmp = math.cos((x * -2.0)) / ((c_m * x) * (s * (c_m * (s * x))))
	return tmp

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	tmp = 0.0
	if (x <= 8e-38)
		tmp = Float64(Float64(s * x) / Float64(1.0 / c_m)) ^ -2.0;
	else
		tmp = Float64(cos(Float64(x * -2.0)) / Float64(Float64(c_m * x) * Float64(s * Float64(c_m * Float64(s * x)))));
	end
	return tmp
end

MATLAB

c_m = abs(c);
x, c_m, s = num2cell(sort([x, c_m, s])){:}
function tmp_2 = code(x, c_m, s)
	tmp = 0.0;
	if (x <= 8e-38)
		tmp = ((s * x) / (1.0 / c_m)) ^ -2.0;
	else
		tmp = cos((x * -2.0)) / ((c_m * x) * (s * (c_m * (s * x))));
	end
	tmp_2 = tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s_] := If[LessEqual[x, 8e-38], N[Power[N[(N[(s * x), $MachinePrecision] / N[(1.0 / c$95$m), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision], N[(N[Cos[N[(x * -2.0), $MachinePrecision]], $MachinePrecision] / N[(N[(c$95$m * x), $MachinePrecision] * N[(s * N[(c$95$m * N[(s * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 97.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(s \cdot x\right)\\ \frac{1}{t_0} \cdot \frac{\cos \left(x \cdot 2\right)}{t_0} \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
(FPCore (x c_m s)
 :precision binary64
 (let* ((t_0 (* c_m (* s x)))) (* (/ 1.0 t_0) (/ (cos (* x 2.0)) t_0))))

C

c_m = fabs(c);
assert(x < c_m && c_m < s);
double code(double x, double c_m, double s) {
	double t_0 = c_m * (s * x);
	return (1.0 / t_0) * (cos((x * 2.0)) / t_0);
}

Fortran

c_m = abs(c)
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s
    real(8) :: t_0
    t_0 = c_m * (s * x)
    code = (1.0d0 / t_0) * (cos((x * 2.0d0)) / t_0)
end function

Java

c_m = Math.abs(c);
assert x < c_m && c_m < s;
public static double code(double x, double c_m, double s) {
	double t_0 = c_m * (s * x);
	return (1.0 / t_0) * (Math.cos((x * 2.0)) / t_0);
}

Python

c_m = math.fabs(c)
[x, c_m, s] = sort([x, c_m, s])
def code(x, c_m, s):
	t_0 = c_m * (s * x)
	return (1.0 / t_0) * (math.cos((x * 2.0)) / t_0)

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	t_0 = Float64(c_m * Float64(s * x))
	return Float64(Float64(1.0 / t_0) * Float64(cos(Float64(x * 2.0)) / t_0))
end

MATLAB

c_m = abs(c);
x, c_m, s = num2cell(sort([x, c_m, s])){:}
function tmp = code(x, c_m, s)
	t_0 = c_m * (s * x);
	tmp = (1.0 / t_0) * (cos((x * 2.0)) / t_0);
end

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 4: 79.2% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 5: 76.5% accurate, 20.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(s \cdot x\right)\\ \mathbf{if}\;s \leq 9.4 \cdot 10^{+253}:\\ \;\;\;\;\frac{1}{\left(c_m \cdot x\right) \cdot \left(s \cdot t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(c_m \cdot s\right) \cdot \left(x \cdot t_0\right)}\\ \end{array} \end{array} \]

FPCore

c_m = (fabs.f64 c)
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
(FPCore (x c_m s)
 :precision binary64
 (let* ((t_0 (* c_m (* s x))))
   (if (<= s 9.4e+253)
     (/ 1.0 (* (* c_m x) (* s t_0)))
     (/ 1.0 (* (* c_m s) (* x t_0))))))

C

c_m = fabs(c);
assert(x < c_m && c_m < s);
double code(double x, double c_m, double s) {
	double t_0 = c_m * (s * x);
	double tmp;
	if (s <= 9.4e+253) {
		tmp = 1.0 / ((c_m * x) * (s * t_0));
	} else {
		tmp = 1.0 / ((c_m * s) * (x * t_0));
	}
	return tmp;
}

Fortran

c_m = abs(c)
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
real(8) function code(x, c_m, s)
    real(8), intent (in) :: x
    real(8), intent (in) :: c_m
    real(8), intent (in) :: s
    real(8) :: t_0
    real(8) :: tmp
    t_0 = c_m * (s * x)
    if (s <= 9.4d+253) then
        tmp = 1.0d0 / ((c_m * x) * (s * t_0))
    else
        tmp = 1.0d0 / ((c_m * s) * (x * t_0))
    end if
    code = tmp
end function

Java

c_m = Math.abs(c);
assert x < c_m && c_m < s;
public static double code(double x, double c_m, double s) {
	double t_0 = c_m * (s * x);
	double tmp;
	if (s <= 9.4e+253) {
		tmp = 1.0 / ((c_m * x) * (s * t_0));
	} else {
		tmp = 1.0 / ((c_m * s) * (x * t_0));
	}
	return tmp;
}

Python

c_m = math.fabs(c)
[x, c_m, s] = sort([x, c_m, s])
def code(x, c_m, s):
	t_0 = c_m * (s * x)
	tmp = 0
	if s <= 9.4e+253:
		tmp = 1.0 / ((c_m * x) * (s * t_0))
	else:
		tmp = 1.0 / ((c_m * s) * (x * t_0))
	return tmp

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	t_0 = Float64(c_m * Float64(s * x))
	tmp = 0.0
	if (s <= 9.4e+253)
		tmp = Float64(1.0 / Float64(Float64(c_m * x) * Float64(s * t_0)));
	else
		tmp = Float64(1.0 / Float64(Float64(c_m * s) * Float64(x * t_0)));
	end
	return tmp
end

MATLAB

c_m = abs(c);
x, c_m, s = num2cell(sort([x, c_m, s])){:}
function tmp_2 = code(x, c_m, s)
	t_0 = c_m * (s * x);
	tmp = 0.0;
	if (s <= 9.4e+253)
		tmp = 1.0 / ((c_m * x) * (s * t_0));
	else
		tmp = 1.0 / ((c_m * s) * (x * t_0));
	end
	tmp_2 = tmp;
end

Wolfram

c_m = N[Abs[c], $MachinePrecision]
NOTE: x, c_m, and s should be sorted in increasing order before calling this function.
code[x_, c$95$m_, s_] := Block[{t$95$0 = N[(c$95$m * N[(s * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[s, 9.4e+253], N[(1.0 / N[(N[(c$95$m * x), $MachinePrecision] * N[(s * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(c$95$m * s), $MachinePrecision] * N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 79.2% accurate, 20.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 7: 76.1% accurate, 24.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 8: 79.1% accurate, 24.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))