mixedcos

Percentage Accurate: 66.8% → 99.1%

Time: 13.6s

Alternatives: 8

Speedup: 24.1×

• 31.7% 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: 66.8% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 93.6% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 3: 94.9% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 4: 97.1% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 5: 79.8% accurate, 20.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 6: 76.5% accurate, 24.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 7: 79.8% accurate, 24.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 8: 79.9% accurate, 24.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2024008 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))