mixedcos

Average Accuracy: 55.7% → 97.0%

Time: 17.5s

Precision: binary64

Cost: 13704

\[ \begin{array}{c}[c, s] = \mathsf{sort}([c, s])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(x + x\right)\\ t_1 := x \cdot \left(c \cdot s\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;\frac{t_0}{t_1} \cdot \frac{1}{t_1}\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-205}:\\ \;\;\;\;\frac{t_0}{{\left(c \cdot \left(x \cdot s\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {\left(s \cdot \left(c \cdot x\right)\right)}^{-2}\\ \end{array} \]

FPCore

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

↓

(FPCore (x c s)
 :precision binary64
 (let* ((t_0 (cos (+ x x))) (t_1 (* x (* c s))))
   (if (<= c -5.2e+212)
     (* (/ t_0 t_1) (/ 1.0 t_1))
     (if (<= c -8e-205)
       (/ t_0 (pow (* c (* x s)) 2.0))
       (* t_0 (pow (* s (* c x)) -2.0))))))

C

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

↓

double code(double x, double c, double s) {
	double t_0 = cos((x + x));
	double t_1 = x * (c * s);
	double tmp;
	if (c <= -5.2e+212) {
		tmp = (t_0 / t_1) * (1.0 / t_1);
	} else if (c <= -8e-205) {
		tmp = t_0 / pow((c * (x * s)), 2.0);
	} else {
		tmp = t_0 * pow((s * (c * x)), -2.0);
	}
	return tmp;
}

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

↓

real(8) function code(x, c, s)
    real(8), intent (in) :: x
    real(8), intent (in) :: c
    real(8), intent (in) :: s
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = cos((x + x))
    t_1 = x * (c * s)
    if (c <= (-5.2d+212)) then
        tmp = (t_0 / t_1) * (1.0d0 / t_1)
    else if (c <= (-8d-205)) then
        tmp = t_0 / ((c * (x * s)) ** 2.0d0)
    else
        tmp = t_0 * ((s * (c * x)) ** (-2.0d0))
    end if
    code = tmp
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));
}

↓

public static double code(double x, double c, double s) {
	double t_0 = Math.cos((x + x));
	double t_1 = x * (c * s);
	double tmp;
	if (c <= -5.2e+212) {
		tmp = (t_0 / t_1) * (1.0 / t_1);
	} else if (c <= -8e-205) {
		tmp = t_0 / Math.pow((c * (x * s)), 2.0);
	} else {
		tmp = t_0 * Math.pow((s * (c * x)), -2.0);
	}
	return tmp;
}

Python

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

↓

def code(x, c, s):
	t_0 = math.cos((x + x))
	t_1 = x * (c * s)
	tmp = 0
	if c <= -5.2e+212:
		tmp = (t_0 / t_1) * (1.0 / t_1)
	elif c <= -8e-205:
		tmp = t_0 / math.pow((c * (x * s)), 2.0)
	else:
		tmp = t_0 * math.pow((s * (c * x)), -2.0)
	return tmp

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

↓

function code(x, c, s)
	t_0 = cos(Float64(x + x))
	t_1 = Float64(x * Float64(c * s))
	tmp = 0.0
	if (c <= -5.2e+212)
		tmp = Float64(Float64(t_0 / t_1) * Float64(1.0 / t_1));
	elseif (c <= -8e-205)
		tmp = Float64(t_0 / (Float64(c * Float64(x * s)) ^ 2.0));
	else
		tmp = Float64(t_0 * (Float64(s * Float64(c * x)) ^ -2.0));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, c, s)
	t_0 = cos((x + x));
	t_1 = x * (c * s);
	tmp = 0.0;
	if (c <= -5.2e+212)
		tmp = (t_0 / t_1) * (1.0 / t_1);
	elseif (c <= -8e-205)
		tmp = t_0 / ((c * (x * s)) ^ 2.0);
	else
		tmp = t_0 * ((s * (c * x)) ^ -2.0);
	end
	tmp_2 = tmp;
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]

↓

code[x_, c_, s_] := Block[{t$95$0 = N[Cos[N[(x + x), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(c * s), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+212], N[(N[(t$95$0 / t$95$1), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -8e-205], N[(t$95$0 / N[Power[N[(c * N[(x * s), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[Power[N[(s * N[(c * x), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -5.1999999999999997e212

   1. Initial program 58.1%

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

   2. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}} \]
      Proof

      [Start] 58.1	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
      *-commutative [=>] 58.1	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\color{blue}{\left({s}^{2} \cdot x\right)} \cdot x\right)} \]
      associate-*l* [=>] 52.5	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \color{blue}{\left({s}^{2} \cdot \left(x \cdot x\right)\right)}} \]
      associate-*r* [=>] 52.6	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left({c}^{2} \cdot {s}^{2}\right) \cdot \left(x \cdot x\right)}} \]
      *-commutative [=>] 52.6	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(x \cdot x\right) \cdot \left({c}^{2} \cdot {s}^{2}\right)}} \]
      unpow2 [=>] 52.6	\[ \frac{\cos \left(2 \cdot x\right)}{\left(x \cdot x\right) \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot {s}^{2}\right)} \]
      unpow2 [=>] 52.6	\[ \frac{\cos \left(2 \cdot x\right)}{\left(x \cdot x\right) \cdot \left(\left(c \cdot c\right) \cdot \color{blue}{\left(s \cdot s\right)}\right)} \]
      unswap-sqr [=>] 76.0	\[ \frac{\cos \left(2 \cdot x\right)}{\left(x \cdot x\right) \cdot \color{blue}{\left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)}} \]
      unswap-sqr [=>] 96.0	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}} \]

   3. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{\frac{\cos \left(x + x\right)}{x \cdot \left(c \cdot s\right)} \cdot \frac{1}{x \cdot \left(c \cdot s\right)}} \]

   if -5.1999999999999997e212 < c < -8e-205

   1. Initial program 60.2%

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

   2. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}} \]
      Proof

      [Start] 60.2	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
      associate-*r* [=>] 64.2	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left({c}^{2} \cdot \left(x \cdot {s}^{2}\right)\right) \cdot x}} \]
      *-commutative [=>] 64.2	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{x \cdot \left({c}^{2} \cdot \left(x \cdot {s}^{2}\right)\right)}} \]
      *-commutative [=>] 64.2	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left({c}^{2} \cdot \color{blue}{\left({s}^{2} \cdot x\right)}\right)} \]
      associate-*r* [=>] 60.3	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \color{blue}{\left(\left({c}^{2} \cdot {s}^{2}\right) \cdot x\right)}} \]
      *-commutative [=>] 60.3	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \color{blue}{\left(x \cdot \left({c}^{2} \cdot {s}^{2}\right)\right)}} \]
      unpow2 [=>] 60.3	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot {s}^{2}\right)\right)} \]
      unpow2 [=>] 60.3	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot c\right) \cdot \color{blue}{\left(s \cdot s\right)}\right)\right)} \]
      unswap-sqr [=>] 77.6	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \color{blue}{\left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)}\right)} \]

   3. Taylor expanded in x around inf 54.7%

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{{s}^{2} \cdot \left({c}^{2} \cdot {x}^{2}\right)}} \]

   4. Simplified 98.3%

      \[\leadsto \color{blue}{\frac{\cos \left(x + x\right)}{{\left(c \cdot \left(s \cdot x\right)\right)}^{2}}} \]
      Proof

      [Start] 54.7	\[ \frac{\cos \left(2 \cdot x\right)}{{s}^{2} \cdot \left({c}^{2} \cdot {x}^{2}\right)} \]
      count-2 [<=] 54.7	\[ \frac{\cos \color{blue}{\left(x + x\right)}}{{s}^{2} \cdot \left({c}^{2} \cdot {x}^{2}\right)} \]
      associate-*r* [=>] 54.1	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left({s}^{2} \cdot {c}^{2}\right) \cdot {x}^{2}}} \]
      associate-/r* [=>] 54.0	\[ \color{blue}{\frac{\frac{\cos \left(x + x\right)}{{s}^{2} \cdot {c}^{2}}}{{x}^{2}}} \]
      *-commutative [<=] 54.0	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{{c}^{2} \cdot {s}^{2}}}}{{x}^{2}} \]
      unpow2 [=>] 54.0	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(c \cdot c\right)} \cdot {s}^{2}}}{{x}^{2}} \]
      unpow2 [=>] 54.0	\[ \frac{\frac{\cos \left(x + x\right)}{\left(c \cdot c\right) \cdot \color{blue}{\left(s \cdot s\right)}}}{{x}^{2}} \]
      swap-sqr [<=] 67.4	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(c \cdot s\right) \cdot \left(c \cdot s\right)}}}{{x}^{2}} \]
      unpow2 [<=] 67.4	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{{\left(c \cdot s\right)}^{2}}}}{{x}^{2}} \]
      associate-/l/ [=>] 67.6	\[ \color{blue}{\frac{\cos \left(x + x\right)}{{x}^{2} \cdot {\left(c \cdot s\right)}^{2}}} \]
      unpow2 [=>] 67.6	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left(x \cdot x\right)} \cdot {\left(c \cdot s\right)}^{2}} \]
      unpow2 [=>] 67.6	\[ \frac{\cos \left(x + x\right)}{\left(x \cdot x\right) \cdot \color{blue}{\left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)}} \]
      swap-sqr [<=] 96.1	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}} \]
      unpow2 [<=] 96.1	\[ \frac{\cos \left(x + x\right)}{\color{blue}{{\left(x \cdot \left(c \cdot s\right)\right)}^{2}}} \]
      *-commutative [=>] 96.1	\[ \frac{\cos \left(x + x\right)}{{\color{blue}{\left(\left(c \cdot s\right) \cdot x\right)}}^{2}} \]
      associate-*l* [=>] 98.3	\[ \frac{\cos \left(x + x\right)}{{\color{blue}{\left(c \cdot \left(s \cdot x\right)\right)}}^{2}} \]

   if -8e-205 < c

   1. Initial program 46.0%

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

   2. Simplified 94.9%

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}} \]
      Proof

      [Start] 46.0	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
      *-commutative [=>] 46.0	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\color{blue}{\left({s}^{2} \cdot x\right)} \cdot x\right)} \]
      associate-*l* [=>] 41.5	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \color{blue}{\left({s}^{2} \cdot \left(x \cdot x\right)\right)}} \]
      associate-*r* [=>] 41.8	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left({c}^{2} \cdot {s}^{2}\right) \cdot \left(x \cdot x\right)}} \]
      *-commutative [=>] 41.8	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(x \cdot x\right) \cdot \left({c}^{2} \cdot {s}^{2}\right)}} \]
      unpow2 [=>] 41.8	\[ \frac{\cos \left(2 \cdot x\right)}{\left(x \cdot x\right) \cdot \left(\color{blue}{\left(c \cdot c\right)} \cdot {s}^{2}\right)} \]
      unpow2 [=>] 41.8	\[ \frac{\cos \left(2 \cdot x\right)}{\left(x \cdot x\right) \cdot \left(\left(c \cdot c\right) \cdot \color{blue}{\left(s \cdot s\right)}\right)} \]
      unswap-sqr [=>] 66.5	\[ \frac{\cos \left(2 \cdot x\right)}{\left(x \cdot x\right) \cdot \color{blue}{\left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)}} \]
      unswap-sqr [=>] 94.9	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}} \]

   3. Taylor expanded in x around inf 41.5%

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left({s}^{2} \cdot {x}^{2}\right)}} \]

   4. Simplified 95.1%

      \[\leadsto \color{blue}{\cos \left(x + x\right) \cdot {\left(s \cdot \left(c \cdot x\right)\right)}^{-2}} \]
      Proof

      [Start] 41.5	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left({s}^{2} \cdot {x}^{2}\right)} \]
      count-2 [<=] 41.5	\[ \frac{\cos \color{blue}{\left(x + x\right)}}{{c}^{2} \cdot \left({s}^{2} \cdot {x}^{2}\right)} \]
      associate-*r* [=>] 41.8	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left({c}^{2} \cdot {s}^{2}\right) \cdot {x}^{2}}} \]
      associate-/r* [=>] 42.0	\[ \color{blue}{\frac{\frac{\cos \left(x + x\right)}{{c}^{2} \cdot {s}^{2}}}{{x}^{2}}} \]
      unpow2 [=>] 42.0	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(c \cdot c\right)} \cdot {s}^{2}}}{{x}^{2}} \]
      unpow2 [=>] 42.0	\[ \frac{\frac{\cos \left(x + x\right)}{\left(c \cdot c\right) \cdot \color{blue}{\left(s \cdot s\right)}}}{{x}^{2}} \]
      swap-sqr [<=] 66.3	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(c \cdot s\right) \cdot \left(c \cdot s\right)}}}{{x}^{2}} \]
      *-lft-identity [<=] 66.3	\[ \frac{\frac{\color{blue}{1 \cdot \cos \left(x + x\right)}}{\left(c \cdot s\right) \cdot \left(c \cdot s\right)}}{{x}^{2}} \]
      times-frac [=>] 66.4	\[ \frac{\color{blue}{\frac{1}{c \cdot s} \cdot \frac{\cos \left(x + x\right)}{c \cdot s}}}{{x}^{2}} \]
      associate-*l/ [<=] 72.8	\[ \color{blue}{\frac{\frac{1}{c \cdot s}}{{x}^{2}} \cdot \frac{\cos \left(x + x\right)}{c \cdot s}} \]
      unpow2 [=>] 72.8	\[ \frac{\frac{1}{c \cdot s}}{\color{blue}{x \cdot x}} \cdot \frac{\cos \left(x + x\right)}{c \cdot s} \]
      associate-/r* [<=] 72.8	\[ \color{blue}{\frac{1}{\left(c \cdot s\right) \cdot \left(x \cdot x\right)}} \cdot \frac{\cos \left(x + x\right)}{c \cdot s} \]
      associate-*r* [=>] 87.3	\[ \frac{1}{\color{blue}{\left(\left(c \cdot s\right) \cdot x\right) \cdot x}} \cdot \frac{\cos \left(x + x\right)}{c \cdot s} \]
      *-commutative [<=] 87.3	\[ \frac{1}{\color{blue}{\left(x \cdot \left(c \cdot s\right)\right)} \cdot x} \cdot \frac{\cos \left(x + x\right)}{c \cdot s} \]
      associate-/r* [=>] 87.7	\[ \color{blue}{\frac{\frac{1}{x \cdot \left(c \cdot s\right)}}{x}} \cdot \frac{\cos \left(x + x\right)}{c \cdot s} \]

3. Recombined 3 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+212}:\\ \;\;\;\;\frac{\cos \left(x + x\right)}{x \cdot \left(c \cdot s\right)} \cdot \frac{1}{x \cdot \left(c \cdot s\right)}\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-205}:\\ \;\;\;\;\frac{\cos \left(x + x\right)}{{\left(c \cdot \left(x \cdot s\right)\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(x + x\right) \cdot {\left(s \cdot \left(c \cdot x\right)\right)}^{-2}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	95.9%
Cost	13440

\[\cos \left(x + x\right) \cdot {\left(s \cdot \left(c \cdot x\right)\right)}^{-2} \]

Alternative 2
Accuracy	95.3%
Cost	7880

\[\begin{array}{l} t_0 := \cos \left(x + x\right)\\ t_1 := \frac{\frac{1}{x}}{c \cdot s}\\ t_2 := x \cdot \left(c \cdot s\right)\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{t_0}{t_2} \cdot \frac{1}{t_2}\\ \mathbf{elif}\;c \leq -4.6 \cdot 10^{-234}:\\ \;\;\;\;\frac{t_0}{c \cdot \left(\left(x \cdot s\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(t_1 \cdot t_1\right)\\ \end{array} \]

Alternative 3
Accuracy	95.3%
Cost	7753

\[\begin{array}{l} t_0 := x \cdot \left(c \cdot s\right)\\ t_1 := \cos \left(x + x\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+49} \lor \neg \left(c \leq -1.4 \cdot 10^{-234}\right):\\ \;\;\;\;\frac{t_1}{t_0} \cdot \frac{1}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{c \cdot \left(\left(x \cdot s\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	84.9%
Cost	7625

\[\begin{array}{l} t_0 := \frac{\frac{1}{c \cdot s}}{x}\\ \mathbf{if}\;x \leq -0.0071 \lor \neg \left(x \leq 0.00165\right):\\ \;\;\;\;\frac{\cos \left(x \cdot 2\right)}{x \cdot \left(c \cdot \left(c \cdot \left(s \cdot \left(x \cdot s\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot t_0\\ \end{array} \]

Alternative 5
Accuracy	89.6%
Cost	7625

\[\begin{array}{l} t_0 := \frac{\frac{1}{c \cdot s}}{x}\\ \mathbf{if}\;x \leq -7 \cdot 10^{-38} \lor \neg \left(x \leq 8.5 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{\cos \left(x \cdot 2\right)}{x \cdot \left(c \cdot \left(s \cdot \left(s \cdot \left(c \cdot x\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot t_0\\ \end{array} \]

Alternative 6
Accuracy	93.8%
Cost	7625

\[\begin{array}{l} t_0 := \frac{\frac{1}{c \cdot s}}{x}\\ \mathbf{if}\;x \leq -5 \cdot 10^{-54} \lor \neg \left(x \leq 1.05 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{\cos \left(x \cdot 2\right)}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot t_0\\ \end{array} \]

Alternative 7
Accuracy	95.0%
Cost	7625

\[\begin{array}{l} t_0 := x \cdot \left(c \cdot s\right)\\ \mathbf{if}\;c \leq -1 \cdot 10^{+52} \lor \neg \left(c \leq -3.5 \cdot 10^{-234}\right):\\ \;\;\;\;\frac{\cos \left(x \cdot 2\right)}{t_0 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos \left(x + x\right)}{c \cdot \left(\left(x \cdot s\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 8
Accuracy	88.0%
Cost	7624

\[\begin{array}{l} t_0 := \frac{\frac{1}{c \cdot s}}{x}\\ t_1 := \cos \left(x \cdot 2\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-37}:\\ \;\;\;\;\frac{t_1}{x \cdot \left(c \cdot \left(s \cdot \left(s \cdot \left(c \cdot x\right)\right)\right)\right)}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-59}:\\ \;\;\;\;t_0 \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 9
Accuracy	95.7%
Cost	7360

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

Alternative 10
Accuracy	73.2%
Cost	6912

\[{\left(\frac{\frac{1}{s}}{c \cdot x}\right)}^{2} \]

Alternative 11
Accuracy	73.3%
Cost	6784

\[{\left(s \cdot \left(c \cdot x\right)\right)}^{-2} \]

Alternative 12
Accuracy	72.1%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{-122} \lor \neg \left(c \leq 4.8 \cdot 10^{-134}\right):\\ \;\;\;\;\frac{1}{s \cdot \left(\left(c \cdot x\right) \cdot \left(s \cdot \left(c \cdot x\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 13
Accuracy	71.3%
Cost	964

\[\begin{array}{l} \mathbf{if}\;s \leq 1.08 \cdot 10^{+189}:\\ \;\;\;\;\frac{1}{s \cdot \left(\left(c \cdot x\right) \cdot \left(s \cdot \left(c \cdot x\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(\left(c \cdot s\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 14
Accuracy	73.3%
Cost	964

\[\begin{array}{l} t_0 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+212}:\\ \;\;\;\;\frac{1}{x \cdot \left(\left(c \cdot s\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_0 \cdot t_0}\\ \end{array} \]

Alternative 15
Accuracy	73.9%
Cost	964

\[\begin{array}{l} t_0 := c \cdot \left(x \cdot s\right)\\ t_1 := x \cdot \left(c \cdot s\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+212}:\\ \;\;\;\;\frac{1}{t_1 \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_0 \cdot t_0}\\ \end{array} \]

Alternative 16
Accuracy	70.4%
Cost	832

\[\frac{1}{s \cdot \left(\left(c \cdot x\right) \cdot \left(s \cdot \left(c \cdot x\right)\right)\right)} \]

Alternative 17
Accuracy	73.2%
Cost	832

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

Reproduce

herbie shell --seed 2023122 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))