mixedcos

Percentage Accurate: 66.6% → 99.1%

Time: 16.1s

Alternatives: 12

Speedup: 24.1×

• 31.4% 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: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(x \cdot s\right)\\ t_1 := \cos \left(2 \cdot x\right)\\ t_2 := x \cdot \left(c_m \cdot s\right)\\ \mathbf{if}\;\frac{t_1}{{c_m}^{2} \cdot \left(x \cdot \left(x \cdot {s}^{2}\right)\right)} \leq \infty:\\ \;\;\;\;\frac{1}{t_0} \cdot \frac{t_1}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_1}{t_2}}{t_2}\\ \end{array} \end{array} \]

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 (* x s))) (t_1 (cos (* 2.0 x))) (t_2 (* x (* c_m s))))
   (if (<= (/ t_1 (* (pow c_m 2.0) (* x (* x (pow s 2.0))))) INFINITY)
     (* (/ 1.0 t_0) (/ t_1 t_0))
     (/ (/ t_1 t_2) t_2))))

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 * (x * s);
	double t_1 = cos((2.0 * x));
	double t_2 = x * (c_m * s);
	double tmp;
	if ((t_1 / (pow(c_m, 2.0) * (x * (x * pow(s, 2.0))))) <= ((double) INFINITY)) {
		tmp = (1.0 / t_0) * (t_1 / t_0);
	} else {
		tmp = (t_1 / t_2) / t_2;
	}
	return tmp;
}

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 * (x * s);
	double t_1 = Math.cos((2.0 * x));
	double t_2 = x * (c_m * s);
	double tmp;
	if ((t_1 / (Math.pow(c_m, 2.0) * (x * (x * Math.pow(s, 2.0))))) <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / t_0) * (t_1 / t_0);
	} else {
		tmp = (t_1 / t_2) / t_2;
	}
	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 * (x * s)
	t_1 = math.cos((2.0 * x))
	t_2 = x * (c_m * s)
	tmp = 0
	if (t_1 / (math.pow(c_m, 2.0) * (x * (x * math.pow(s, 2.0))))) <= math.inf:
		tmp = (1.0 / t_0) * (t_1 / t_0)
	else:
		tmp = (t_1 / t_2) / t_2
	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(x * s))
	t_1 = cos(Float64(2.0 * x))
	t_2 = Float64(x * Float64(c_m * s))
	tmp = 0.0
	if (Float64(t_1 / Float64((c_m ^ 2.0) * Float64(x * Float64(x * (s ^ 2.0))))) <= Inf)
		tmp = Float64(Float64(1.0 / t_0) * Float64(t_1 / t_0));
	else
		tmp = Float64(Float64(t_1 / t_2) / t_2);
	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 * (x * s);
	t_1 = cos((2.0 * x));
	t_2 = x * (c_m * s);
	tmp = 0.0;
	if ((t_1 / ((c_m ^ 2.0) * (x * (x * (s ^ 2.0))))) <= Inf)
		tmp = (1.0 / t_0) * (t_1 / t_0);
	else
		tmp = (t_1 / t_2) / t_2;
	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[(x * s), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(c$95$m * s), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(N[Power[c$95$m, 2.0], $MachinePrecision] * N[(x * N[(x * N[Power[s, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(1.0 / t$95$0), $MachinePrecision] * N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 / t$95$2), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]

Derivation

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1. Add Preprocessing

Alternative 2: 86.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 3.4 \cdot 10^{-51}:\\ \;\;\;\;\frac{1}{c_m \cdot \left(\left(x \cdot s\right) \cdot \left(c_m \cdot \left(x \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\cos \left(2 \cdot x\right)}{s}}{\left(x \cdot \left(c_m \cdot s\right)\right) \cdot \left(x \cdot c_m\right)}\\ \end{array} \end{array} \]

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 3.4e-51)
   (/ 1.0 (* c_m (* (* x s) (* c_m (* x s)))))
   (/ (/ (cos (* 2.0 x)) s) (* (* x (* c_m s)) (* x c_m)))))

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 <= 3.4e-51) {
		tmp = 1.0 / (c_m * ((x * s) * (c_m * (x * s))));
	} else {
		tmp = (cos((2.0 * x)) / s) / ((x * (c_m * s)) * (x * c_m));
	}
	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 <= 3.4d-51) then
        tmp = 1.0d0 / (c_m * ((x * s) * (c_m * (x * s))))
    else
        tmp = (cos((2.0d0 * x)) / s) / ((x * (c_m * s)) * (x * c_m))
    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 <= 3.4e-51) {
		tmp = 1.0 / (c_m * ((x * s) * (c_m * (x * s))));
	} else {
		tmp = (Math.cos((2.0 * x)) / s) / ((x * (c_m * s)) * (x * c_m));
	}
	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 <= 3.4e-51:
		tmp = 1.0 / (c_m * ((x * s) * (c_m * (x * s))))
	else:
		tmp = (math.cos((2.0 * x)) / s) / ((x * (c_m * s)) * (x * c_m))
	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 <= 3.4e-51)
		tmp = Float64(1.0 / Float64(c_m * Float64(Float64(x * s) * Float64(c_m * Float64(x * s)))));
	else
		tmp = Float64(Float64(cos(Float64(2.0 * x)) / s) / Float64(Float64(x * Float64(c_m * s)) * Float64(x * c_m)));
	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 <= 3.4e-51)
		tmp = 1.0 / (c_m * ((x * s) * (c_m * (x * s))));
	else
		tmp = (cos((2.0 * x)) / s) / ((x * (c_m * s)) * (x * c_m));
	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, 3.4e-51], N[(1.0 / N[(c$95$m * N[(N[(x * s), $MachinePrecision] * N[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / s), $MachinePrecision] / N[(N[(x * N[(c$95$m * s), $MachinePrecision]), $MachinePrecision] * N[(x * c$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 3: 97.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} t_0 := x \cdot \left(c_m \cdot s\right)\\ \mathbf{if}\;c_m \leq 9.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{\cos \left(2 \cdot x\right)}{t_0}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;{\left(c_m \cdot \left(x \cdot s\right)\right)}^{-2}\\ \end{array} \end{array} \]

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 (* x (* c_m s))))
   (if (<= c_m 9.8e+23)
     (/ (/ (cos (* 2.0 x)) t_0) t_0)
     (pow (* c_m (* x s)) -2.0))))

C

c_m = fabs(c);
assert(x < c_m && c_m < s);
double code(double x, double c_m, double s) {
	double t_0 = x * (c_m * s);
	double tmp;
	if (c_m <= 9.8e+23) {
		tmp = (cos((2.0 * x)) / t_0) / t_0;
	} else {
		tmp = pow((c_m * (x * s)), -2.0);
	}
	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 = x * (c_m * s)
    if (c_m <= 9.8d+23) then
        tmp = (cos((2.0d0 * x)) / t_0) / t_0
    else
        tmp = (c_m * (x * s)) ** (-2.0d0)
    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 = x * (c_m * s);
	double tmp;
	if (c_m <= 9.8e+23) {
		tmp = (Math.cos((2.0 * x)) / t_0) / t_0;
	} else {
		tmp = Math.pow((c_m * (x * s)), -2.0);
	}
	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 = x * (c_m * s)
	tmp = 0
	if c_m <= 9.8e+23:
		tmp = (math.cos((2.0 * x)) / t_0) / t_0
	else:
		tmp = math.pow((c_m * (x * s)), -2.0)
	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(x * Float64(c_m * s))
	tmp = 0.0
	if (c_m <= 9.8e+23)
		tmp = Float64(Float64(cos(Float64(2.0 * x)) / t_0) / t_0);
	else
		tmp = Float64(c_m * Float64(x * s)) ^ -2.0;
	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 = x * (c_m * s);
	tmp = 0.0;
	if (c_m <= 9.8e+23)
		tmp = (cos((2.0 * x)) / t_0) / t_0;
	else
		tmp = (c_m * (x * s)) ^ -2.0;
	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[(x * N[(c$95$m * s), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c$95$m, 9.8e+23], N[(N[(N[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision], N[Power[N[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 97.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} t_0 := \cos \left(2 \cdot x\right)\\ t_1 := x \cdot \left(c_m \cdot s\right)\\ \mathbf{if}\;c_m \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{\frac{t_0}{t_1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{t_0}{c_m \cdot \left(x \cdot s\right)}}{x \cdot s}}{c_m}\\ \end{array} \end{array} \]

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 (cos (* 2.0 x))) (t_1 (* x (* c_m s))))
   (if (<= c_m 4.2e-48)
     (/ (/ t_0 t_1) t_1)
     (/ (/ (/ t_0 (* c_m (* x s))) (* x s)) c_m))))

C

c_m = fabs(c);
assert(x < c_m && c_m < s);
double code(double x, double c_m, double s) {
	double t_0 = cos((2.0 * x));
	double t_1 = x * (c_m * s);
	double tmp;
	if (c_m <= 4.2e-48) {
		tmp = (t_0 / t_1) / t_1;
	} else {
		tmp = ((t_0 / (c_m * (x * s))) / (x * s)) / c_m;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = cos((2.0d0 * x))
    t_1 = x * (c_m * s)
    if (c_m <= 4.2d-48) then
        tmp = (t_0 / t_1) / t_1
    else
        tmp = ((t_0 / (c_m * (x * s))) / (x * s)) / c_m
    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 = Math.cos((2.0 * x));
	double t_1 = x * (c_m * s);
	double tmp;
	if (c_m <= 4.2e-48) {
		tmp = (t_0 / t_1) / t_1;
	} else {
		tmp = ((t_0 / (c_m * (x * s))) / (x * s)) / c_m;
	}
	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 = math.cos((2.0 * x))
	t_1 = x * (c_m * s)
	tmp = 0
	if c_m <= 4.2e-48:
		tmp = (t_0 / t_1) / t_1
	else:
		tmp = ((t_0 / (c_m * (x * s))) / (x * s)) / c_m
	return tmp

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	t_0 = cos(Float64(2.0 * x))
	t_1 = Float64(x * Float64(c_m * s))
	tmp = 0.0
	if (c_m <= 4.2e-48)
		tmp = Float64(Float64(t_0 / t_1) / t_1);
	else
		tmp = Float64(Float64(Float64(t_0 / Float64(c_m * Float64(x * s))) / Float64(x * s)) / c_m);
	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 = cos((2.0 * x));
	t_1 = x * (c_m * s);
	tmp = 0.0;
	if (c_m <= 4.2e-48)
		tmp = (t_0 / t_1) / t_1;
	else
		tmp = ((t_0 / (c_m * (x * s))) / (x * s)) / c_m;
	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[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(c$95$m * s), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c$95$m, 4.2e-48], N[(N[(t$95$0 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision], N[(N[(N[(t$95$0 / N[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * s), $MachinePrecision]), $MachinePrecision] / c$95$m), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 93.9% accurate, 2.7× speedup

Math

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

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
 (/ (/ (cos (* 2.0 x)) c_m) (* (* x s) (* c_m (* x s)))))

C

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

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 = (cos((2.0d0 * x)) / c_m) / ((x * s) * (c_m * (x * s)))
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.cos((2.0 * x)) / c_m) / ((x * s) * (c_m * (x * s)));
}

Python

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

Julia

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

MATLAB

c_m = abs(c);
x, c_m, s = num2cell(sort([x, c_m, s])){:}
function tmp = code(x, c_m, s)
	tmp = (cos((2.0 * x)) / c_m) / ((x * s) * (c_m * (x * s)));
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[Cos[N[(2.0 * x), $MachinePrecision]], $MachinePrecision] / c$95$m), $MachinePrecision] / N[(N[(x * s), $MachinePrecision] * N[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 6: 78.9% accurate, 2.9× speedup

Math

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

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 (/ c_m (/ (/ 1.0 x) s)) -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((c_m / ((1.0 / x) / s)), -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 = (c_m / ((1.0d0 / x) / s)) ** (-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((c_m / ((1.0 / x) / s)), -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((c_m / ((1.0 / x) / s)), -2.0)

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	return Float64(c_m / Float64(Float64(1.0 / x) / s)) ^ -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 = (c_m / ((1.0 / x) / s)) ^ -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[(c$95$m / N[(N[(1.0 / x), $MachinePrecision] / s), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision]

Derivation

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

Alternative 7: 79.0% accurate, 3.0× speedup

Math

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

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 (* c_m (* x s)) -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((c_m * (x * s)), -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 = (c_m * (x * s)) ** (-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((c_m * (x * s)), -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((c_m * (x * s)), -2.0)

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	return Float64(c_m * Float64(x * s)) ^ -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 = (c_m * (x * s)) ^ -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[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision]

Derivation

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

Alternative 8: 76.8% accurate, 20.8× speedup

Math

\[\begin{array}{l} c_m = \left|c\right| \\ [x, c_m, s] = \mathsf{sort}([x, c_m, s])\\ \\ \begin{array}{l} t_0 := c_m \cdot \left(x \cdot s\right)\\ \mathbf{if}\;s \leq 2.9 \cdot 10^{+207}:\\ \;\;\;\;\frac{1}{\left(x \cdot c_m\right) \cdot \left(s \cdot t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(c_m \cdot s\right) \cdot \left(x \cdot t_0\right)}\\ \end{array} \end{array} \]

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 (* x s))))
   (if (<= s 2.9e+207)
     (/ 1.0 (* (* x c_m) (* 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 * (x * s);
	double tmp;
	if (s <= 2.9e+207) {
		tmp = 1.0 / ((x * c_m) * (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 * (x * s)
    if (s <= 2.9d+207) then
        tmp = 1.0d0 / ((x * c_m) * (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 * (x * s);
	double tmp;
	if (s <= 2.9e+207) {
		tmp = 1.0 / ((x * c_m) * (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 * (x * s)
	tmp = 0
	if s <= 2.9e+207:
		tmp = 1.0 / ((x * c_m) * (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(x * s))
	tmp = 0.0
	if (s <= 2.9e+207)
		tmp = Float64(1.0 / Float64(Float64(x * c_m) * 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 * (x * s);
	tmp = 0.0;
	if (s <= 2.9e+207)
		tmp = 1.0 / ((x * c_m) * (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[(x * s), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[s, 2.9e+207], N[(1.0 / N[(N[(x * c$95$m), $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

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

Alternative 9: 79.0% accurate, 20.9× speedup

Math

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

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 (* x s))) (/ (/ 1.0 c_m) (* x s))))

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 * (x * s))) * ((1.0 / c_m) / (x * s));
}

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 * (x * s))) * ((1.0d0 / c_m) / (x * s))
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 * (x * s))) * ((1.0 / c_m) / (x * s));
}

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 * (x * s))) * ((1.0 / c_m) / (x * s))

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	return Float64(Float64(1.0 / Float64(c_m * Float64(x * s))) * Float64(Float64(1.0 / c_m) / Float64(x * s)))
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 * (x * s))) * ((1.0 / c_m) / (x * s));
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[(1.0 / N[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(1.0 / c$95$m), $MachinePrecision] / N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 78.9% accurate, 20.9× speedup

Math

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

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 (* x s))) (/ (/ (/ 1.0 s) x) c_m)))

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 * (x * s))) * (((1.0 / s) / x) / c_m);
}

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 * (x * s))) * (((1.0d0 / s) / x) / c_m)
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 * (x * s))) * (((1.0 / s) / x) / c_m);
}

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 * (x * s))) * (((1.0 / s) / x) / c_m)

Julia

c_m = abs(c)
x, c_m, s = sort([x, c_m, s])
function code(x, c_m, s)
	return Float64(Float64(1.0 / Float64(c_m * Float64(x * s))) * Float64(Float64(Float64(1.0 / s) / x) / c_m))
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 * (x * s))) * (((1.0 / s) / x) / c_m);
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[(1.0 / N[(c$95$m * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(1.0 / s), $MachinePrecision] / x), $MachinePrecision] / c$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 75.8% accurate, 24.1× speedup

Math

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

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 (* x s))))))

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 * (x * s))));
}

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 * (x * s))))
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 * (x * s))));
}

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 * (x * s))))

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(x * s)))))
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 * (x * s))));
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[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 78.8% accurate, 24.1× speedup

Math

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

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 (* x s)))) (/ 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 * (x * s);
	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 * (x * s)
    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 * (x * s);
	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 * (x * s)
	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(x * s))
	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 * (x * s);
	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[(x * s), $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 2024006 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))