mixedcos

Average Accuracy: 56.9% → 97.5%

Time: 18.5s

Precision: binary64

Cost: 33540

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

Math

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

↓

\[\begin{array}{l} t_0 := \cos \left(x + x\right)\\ \mathbf{if}\;\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(x \cdot \left(x \cdot {s}^{2}\right)\right)} \leq \infty:\\ \;\;\;\;{\left(s \cdot \left(x \cdot c\right)\right)}^{-2} \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{{\left(x \cdot \left(c \cdot s\right)\right)}^{2}}\\ \end{array} \]

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))))
   (if (<=
        (/ (cos (* 2.0 x)) (* (pow c 2.0) (* x (* x (pow s 2.0)))))
        INFINITY)
     (* (pow (* s (* x c)) -2.0) t_0)
     (/ t_0 (pow (* x (* c s)) 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 tmp;
	if ((cos((2.0 * x)) / (pow(c, 2.0) * (x * (x * pow(s, 2.0))))) <= ((double) INFINITY)) {
		tmp = pow((s * (x * c)), -2.0) * t_0;
	} else {
		tmp = t_0 / pow((x * (c * s)), 2.0);
	}
	return tmp;
}

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x))) < +inf.0

   1. Initial program 71.9%

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

   2. Simplified 97.6%

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

      [Start] 71.9	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
      *-commutative [=>] 71.9	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \color{blue}{\left(x \cdot \left(x \cdot {s}^{2}\right)\right)}} \]
      associate-*r* [=>] 64.9	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \color{blue}{\left(\left(x \cdot x\right) \cdot {s}^{2}\right)}} \]
      associate-*r* [=>] 64.8	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left({c}^{2} \cdot \left(x \cdot x\right)\right) \cdot {s}^{2}}} \]
      unpow2 [=>] 64.8	\[ \frac{\cos \left(2 \cdot x\right)}{\left(\color{blue}{\left(c \cdot c\right)} \cdot \left(x \cdot x\right)\right) \cdot {s}^{2}} \]
      unswap-sqr [=>] 76.0	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(\left(c \cdot x\right) \cdot \left(c \cdot x\right)\right)} \cdot {s}^{2}} \]
      unpow2 [=>] 76.0	\[ \frac{\cos \left(2 \cdot x\right)}{\left(\left(c \cdot x\right) \cdot \left(c \cdot x\right)\right) \cdot \color{blue}{\left(s \cdot s\right)}} \]
      swap-sqr [<=] 97.6	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(\left(c \cdot x\right) \cdot s\right) \cdot \left(\left(c \cdot x\right) \cdot s\right)}} \]
      *-commutative [<=] 97.6	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left(s \cdot \left(c \cdot x\right)\right)} \cdot \left(\left(c \cdot x\right) \cdot s\right)} \]
      *-commutative [<=] 97.6	\[ \frac{\cos \left(2 \cdot x\right)}{\left(s \cdot \left(c \cdot x\right)\right) \cdot \color{blue}{\left(s \cdot \left(c \cdot x\right)\right)}} \]
      *-commutative [=>] 97.6	\[ \frac{\cos \left(2 \cdot x\right)}{\left(s \cdot \color{blue}{\left(x \cdot c\right)}\right) \cdot \left(s \cdot \left(c \cdot x\right)\right)} \]
      *-commutative [=>] 97.6	\[ \frac{\cos \left(2 \cdot x\right)}{\left(s \cdot \left(x \cdot c\right)\right) \cdot \left(s \cdot \color{blue}{\left(x \cdot c\right)}\right)} \]

   3. Applied egg-rr 98.1%

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

      [Start] 97.6	\[ \frac{\cos \left(2 \cdot x\right)}{\left(s \cdot \left(x \cdot c\right)\right) \cdot \left(s \cdot \left(x \cdot c\right)\right)} \]
      clear-num [=>] 97.6	\[ \color{blue}{\frac{1}{\frac{\left(s \cdot \left(x \cdot c\right)\right) \cdot \left(s \cdot \left(x \cdot c\right)\right)}{\cos \left(2 \cdot x\right)}}} \]
      associate-/r/ [=>] 97.6	\[ \color{blue}{\frac{1}{\left(s \cdot \left(x \cdot c\right)\right) \cdot \left(s \cdot \left(x \cdot c\right)\right)} \cdot \cos \left(2 \cdot x\right)} \]
      pow2 [=>] 97.6	\[ \frac{1}{\color{blue}{{\left(s \cdot \left(x \cdot c\right)\right)}^{2}}} \cdot \cos \left(2 \cdot x\right) \]
      pow-flip [=>] 98.1	\[ \color{blue}{{\left(s \cdot \left(x \cdot c\right)\right)}^{\left(-2\right)}} \cdot \cos \left(2 \cdot x\right) \]
      metadata-eval [=>] 98.1	\[ {\left(s \cdot \left(x \cdot c\right)\right)}^{\color{blue}{-2}} \cdot \cos \left(2 \cdot x\right) \]
      cos-2 [=>] 97.9	\[ {\left(s \cdot \left(x \cdot c\right)\right)}^{-2} \cdot \color{blue}{\left(\cos x \cdot \cos x - \sin x \cdot \sin x\right)} \]
      cos-sum [<=] 98.1	\[ {\left(s \cdot \left(x \cdot c\right)\right)}^{-2} \cdot \color{blue}{\cos \left(x + x\right)} \]

   if +inf.0 < (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x)))

   1. Initial program 0.0%

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

   2. Simplified 0.6%

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

      [Start] 0.0	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
      associate-*r* [=>] 0.4	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{\left({c}^{2} \cdot \left(x \cdot {s}^{2}\right)\right) \cdot x}} \]
      *-commutative [=>] 0.4	\[ \frac{\cos \left(2 \cdot x\right)}{\color{blue}{x \cdot \left({c}^{2} \cdot \left(x \cdot {s}^{2}\right)\right)}} \]
      associate-*r* [=>] 0.6	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \color{blue}{\left(\left({c}^{2} \cdot x\right) \cdot {s}^{2}\right)}} \]
      unpow2 [=>] 0.6	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot x\right) \cdot {s}^{2}\right)} \]
      unpow2 [=>] 0.6	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \color{blue}{\left(s \cdot s\right)}\right)} \]

   3. Taylor expanded in x around inf 0.2%

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

   4. Simplified 95.5%

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

      [Start] 0.2	\[ \frac{\cos \left(2 \cdot x\right)}{{s}^{2} \cdot \left({c}^{2} \cdot {x}^{2}\right)} \]
      count-2 [<=] 0.2	\[ \frac{\cos \color{blue}{\left(x + x\right)}}{{s}^{2} \cdot \left({c}^{2} \cdot {x}^{2}\right)} \]
      associate-*r* [=>] 0.2	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left({s}^{2} \cdot {c}^{2}\right) \cdot {x}^{2}}} \]
      unpow2 [=>] 0.2	\[ \frac{\cos \left(x + x\right)}{\left(\color{blue}{\left(s \cdot s\right)} \cdot {c}^{2}\right) \cdot {x}^{2}} \]
      unpow2 [=>] 0.2	\[ \frac{\cos \left(x + x\right)}{\left(\left(s \cdot s\right) \cdot \color{blue}{\left(c \cdot c\right)}\right) \cdot {x}^{2}} \]
      unswap-sqr [=>] 62.8	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left(\left(s \cdot c\right) \cdot \left(s \cdot c\right)\right)} \cdot {x}^{2}} \]
      unpow2 [=>] 62.8	\[ \frac{\cos \left(x + x\right)}{\left(\left(s \cdot c\right) \cdot \left(s \cdot c\right)\right) \cdot \color{blue}{\left(x \cdot x\right)}} \]
      swap-sqr [<=] 95.5	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left(\left(s \cdot c\right) \cdot x\right) \cdot \left(\left(s \cdot c\right) \cdot x\right)}} \]
      rem-square-sqrt [<=] 48.3	\[ \frac{\cos \left(x + x\right)}{\left(\left(s \cdot c\right) \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \cdot \left(\left(s \cdot c\right) \cdot x\right)} \]
      associate-*l* [<=] 48.3	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\left(\left(\left(s \cdot c\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}\right)} \cdot \left(\left(s \cdot c\right) \cdot x\right)} \]
      associate-*r* [<=] 46.8	\[ \frac{\cos \left(x + x\right)}{\left(\color{blue}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right)} \cdot \sqrt{x}\right) \cdot \left(\left(s \cdot c\right) \cdot x\right)} \]
      rem-square-sqrt [<=] 46.6	\[ \frac{\cos \left(x + x\right)}{\left(\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}\right) \cdot \left(\left(s \cdot c\right) \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right)} \]
      associate-*l* [<=] 46.6	\[ \frac{\cos \left(x + x\right)}{\left(\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\left(\left(s \cdot c\right) \cdot \sqrt{x}\right) \cdot \sqrt{x}\right)}} \]
      associate-*r* [<=] 48.2	\[ \frac{\cos \left(x + x\right)}{\left(\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right)} \cdot \sqrt{x}\right)} \]
      unpow2 [<=] 48.2	\[ \frac{\cos \left(x + x\right)}{\color{blue}{{\left(\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}\right)}^{2}}} \]
      associate-*r* [=>] 48.1	\[ \frac{\cos \left(x + x\right)}{{\left(\color{blue}{\left(\left(s \cdot c\right) \cdot \sqrt{x}\right)} \cdot \sqrt{x}\right)}^{2}} \]
      associate-*l* [=>] 48.1	\[ \frac{\cos \left(x + x\right)}{{\color{blue}{\left(\left(s \cdot c\right) \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)\right)}}^{2}} \]
      rem-square-sqrt [=>] 95.5	\[ \frac{\cos \left(x + x\right)}{{\left(\left(s \cdot c\right) \cdot \color{blue}{x}\right)}^{2}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(x \cdot \left(x \cdot {s}^{2}\right)\right)} \leq \infty:\\ \;\;\;\;{\left(s \cdot \left(x \cdot c\right)\right)}^{-2} \cdot \cos \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos \left(x + x\right)}{{\left(x \cdot \left(c \cdot s\right)\right)}^{2}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	79.4%
Cost	7888

\[\begin{array}{l} t_0 := \frac{\frac{1}{x \cdot s}}{c}\\ t_1 := \frac{\cos \left(2 \cdot x\right)}{s \cdot \left(\left(x \cdot x\right) \cdot \left(s \cdot \left(c \cdot c\right)\right)\right)}\\ t_2 := s \cdot \left(x \cdot c\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+157}:\\ \;\;\;\;\frac{\left|\frac{\frac{1}{s}}{x \cdot c}\right|}{x \cdot \left(c \cdot s\right)}\\ \mathbf{elif}\;x \leq -0.0175:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.16:\\ \;\;\;\;t_0 \cdot t_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_2 \cdot t_2}\\ \end{array} \]

Alternative 2
Accuracy	84.5%
Cost	7625

\[\begin{array}{l} t_0 := \frac{\frac{1}{x \cdot s}}{c}\\ \mathbf{if}\;x \leq -0.0175 \lor \neg \left(x \leq 0.16\right):\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(s \cdot \left(s \cdot \left(c \cdot \left(x \cdot c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot t_0\\ \end{array} \]

Alternative 3
Accuracy	93.9%
Cost	7625

\[\begin{array}{l} t_0 := \frac{\frac{1}{x \cdot s}}{c}\\ \mathbf{if}\;x \leq -2 \cdot 10^{-8} \lor \neg \left(x \leq 10^{-32}\right):\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{\left(s \cdot \left(x \cdot c\right)\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot t_0\\ \end{array} \]

Alternative 4
Accuracy	96.9%
Cost	7625

\[\begin{array}{l} t_0 := x \cdot \left(c \cdot s\right)\\ \mathbf{if}\;x \leq -8.4 \cdot 10^{-203} \lor \neg \left(x \leq 3.5 \cdot 10^{-176}\right):\\ \;\;\;\;\frac{\frac{\cos \left(x + x\right)}{t_0}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{{\left(c \cdot \left(x \cdot s\right)\right)}^{2}}\\ \end{array} \]

Alternative 5
Accuracy	95.1%
Cost	7492

\[\begin{array}{l} t_0 := \frac{\frac{1}{x \cdot s}}{c}\\ t_1 := s \cdot \left(x \cdot c\right)\\ \mathbf{if}\;s \leq 1.2 \cdot 10^{+162}:\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{t_1 \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot t_0\\ \end{array} \]

Alternative 6
Accuracy	73.8%
Cost	1097

\[\begin{array}{l} t_0 := s \cdot \left(x \cdot c\right)\\ \mathbf{if}\;c \leq -5.4 \cdot 10^{-223} \lor \neg \left(c \leq 4.8 \cdot 10^{-239}\right):\\ \;\;\;\;\frac{1}{t_0 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(c \cdot s\right) \cdot \left(c \cdot \left(s \cdot \left(x \cdot x\right)\right)\right)}\\ \end{array} \]

Alternative 7
Accuracy	74.1%
Cost	1096

\[\begin{array}{l} t_0 := s \cdot \left(x \cdot c\right)\\ \mathbf{if}\;c \leq -2.65 \cdot 10^{-231}:\\ \;\;\;\;\frac{1}{t_0 \cdot t_0}\\ \mathbf{elif}\;c \leq 1.22 \cdot 10^{-202}:\\ \;\;\;\;\frac{1}{\left(c \cdot s\right) \cdot \left(\left(x \cdot x\right) \cdot \left(c \cdot s\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\left(x \cdot s\right) \cdot \left(c \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 8
Accuracy	74.6%
Cost	964

\[\begin{array}{l} t_0 := s \cdot \left(x \cdot c\right)\\ \mathbf{if}\;s \leq 4.4 \cdot 10^{+89}:\\ \;\;\;\;\frac{1}{t_0 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \left(\left(x \cdot s\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 9
Accuracy	73.9%
Cost	964

\[\begin{array}{l} t_0 := x \cdot \left(c \cdot s\right)\\ \mathbf{if}\;s \leq 2.7 \cdot 10^{+131}:\\ \;\;\;\;\frac{\frac{1}{t_0}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \left(\left(x \cdot s\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 10
Accuracy	74.6%
Cost	964

\[\begin{array}{l} \mathbf{if}\;c \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{\frac{1}{s}}{x \cdot c}}{s \cdot \left(x \cdot c\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \left(\left(x \cdot s\right) \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 11
Accuracy	73.4%
Cost	960

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

Alternative 12
Accuracy	73.1%
Cost	960

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

Alternative 13
Accuracy	46.0%
Cost	832

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

Alternative 14
Accuracy	59.0%
Cost	832

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

Alternative 15
Accuracy	68.8%
Cost	832

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

Reproduce

herbie shell --seed 2023151 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))