mixedcos

Average Error: 27.6 → 0.8

Time: 14.5s

Precision: binary64

Cost: 33924

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

Math

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

↓

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

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

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 = c * (x * s);
	double t_2 = x * (c * s);
	double tmp;
	if ((cos((2.0 * x)) / (pow(c, 2.0) * (x * (x * pow(s, 2.0))))) <= ((double) INFINITY)) {
		tmp = (t_0 / t_1) / t_1;
	} else {
		tmp = pow(((t_2 * t_2) / t_0), -1.0);
	}
	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 t_1 = c * (x * s);
	double t_2 = x * (c * s);
	double tmp;
	if ((Math.cos((2.0 * x)) / (Math.pow(c, 2.0) * (x * (x * Math.pow(s, 2.0))))) <= Double.POSITIVE_INFINITY) {
		tmp = (t_0 / t_1) / t_1;
	} else {
		tmp = Math.pow(((t_2 * t_2) / t_0), -1.0);
	}
	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 = c * (x * s)
	t_2 = x * (c * s)
	tmp = 0
	if (math.cos((2.0 * x)) / (math.pow(c, 2.0) * (x * (x * math.pow(s, 2.0))))) <= math.inf:
		tmp = (t_0 / t_1) / t_1
	else:
		tmp = math.pow(((t_2 * t_2) / t_0), -1.0)
	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(c * Float64(x * s))
	t_2 = Float64(x * Float64(c * s))
	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(t_0 / t_1) / t_1);
	else
		tmp = Float64(Float64(t_2 * t_2) / t_0) ^ -1.0;
	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 = c * (x * s);
	t_2 = x * (c * s);
	tmp = 0.0;
	if ((cos((2.0 * x)) / ((c ^ 2.0) * (x * (x * (s ^ 2.0))))) <= Inf)
		tmp = (t_0 / t_1) / t_1;
	else
		tmp = ((t_2 * t_2) / t_0) ^ -1.0;
	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[(c * N[(x * s), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(c * s), $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[(t$95$0 / t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision], N[Power[N[(N[(t$95$2 * t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision], -1.0], $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 17.7

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

   2. Simplified 15.8

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(c \cdot c\right) \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}} \]
      Proof
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 (*.f64 c c) (*.f64 x (*.f64 s s))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 (*.f64 c c) (*.f64 x (Rewrite<= unpow2_binary64 (pow.f64 s 2)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 c 2)) (*.f64 x (pow.f64 s 2))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (pow.f64 c 2) (*.f64 x (pow.f64 s 2))) x))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (Rewrite<= associate-*r*_binary64 (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x)))): 25 points increase in error, 9 points decrease in error

   3. Applied egg-rr 31.9

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

   4. Simplified 0.3

      \[\leadsto \color{blue}{\frac{\frac{\cos \left(x + x\right)}{c \cdot \left(s \cdot x\right)}}{c \cdot \left(s \cdot x\right)}} \]
      Proof
      (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c (*.f64 s x))) (*.f64 c (*.f64 s x))): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c (*.f64 s (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (*.f64 c (*.f64 s x))): 135 points increase in error, 10 points decrease in error
      (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 c (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 s (sqrt.f64 x)) (sqrt.f64 x))))) (*.f64 c (*.f64 s x))): 6 points increase in error, 10 points decrease in error
      (/.f64 (/.f64 (cos.f64 (+.f64 x x)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x)))) (*.f64 c (*.f64 s x))): 4 points increase in error, 11 points decrease in error
      (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x))))) (*.f64 c (*.f64 s x))): 0 points increase in error, 0 points decrease in error
      (/.f64 (*.f64 1 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x)))) (*.f64 c (*.f64 s (Rewrite<= rem-square-sqrt_binary64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)))))): 28 points increase in error, 1 points decrease in error
      (/.f64 (*.f64 1 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x)))) (*.f64 c (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 s (sqrt.f64 x)) (sqrt.f64 x))))): 6 points increase in error, 11 points decrease in error
      (/.f64 (*.f64 1 (/.f64 (cos.f64 (+.f64 x x)) (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x)))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x)))): 12 points increase in error, 7 points decrease in error
      (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x))) (/.f64 (cos.f64 (+.f64 x x)) (*.f64 (*.f64 c (*.f64 s (sqrt.f64 x))) (sqrt.f64 x))))): 11 points increase in error, 9 points decrease in error

   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 64.0

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

   2. Simplified 15.4

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}} \]
      Proof
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 x (*.f64 (*.f64 c s) (*.f64 c s))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 x (Rewrite<= unswap-sqr_binary64 (*.f64 (*.f64 c c) (*.f64 s s)))))): 66 points increase in error, 8 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 x (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 c 2)) (*.f64 s s))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 x (*.f64 (pow.f64 c 2) (Rewrite<= unpow2_binary64 (pow.f64 s 2)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (*.f64 x (Rewrite=> *-commutative_binary64 (*.f64 (pow.f64 s 2) (pow.f64 c 2)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (pow.f64 s 2)) (pow.f64 c 2))))): 12 points increase in error, 13 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (*.f64 x (Rewrite<= *-commutative_binary64 (*.f64 (pow.f64 c 2) (*.f64 x (pow.f64 s 2)))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (pow.f64 c 2) (*.f64 x (pow.f64 s 2))) x))): 0 points increase in error, 0 points decrease in error
      (/.f64 (cos.f64 (*.f64 2 x)) (Rewrite<= associate-*r*_binary64 (*.f64 (pow.f64 c 2) (*.f64 (*.f64 x (pow.f64 s 2)) x)))): 25 points increase in error, 9 points decrease in error

   3. Applied egg-rr 7.7

      \[\leadsto \color{blue}{{\left(\frac{{\left(\left(x \cdot c\right) \cdot s\right)}^{2}}{\cos \left(x + x\right)}\right)}^{-1}} \]

   4. Applied egg-rr 2.4

      \[\leadsto {\left(\frac{\color{blue}{\left(x \cdot \left(c \cdot s\right)\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)}}{\cos \left(x + x\right)}\right)}^{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.8

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

Alternatives

Alternative 1
Error	8.0
Cost	7888

\[\begin{array}{l} t_0 := \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ t_1 := \cos \left(x + x\right)\\ t_2 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;s \leq -9.5 \cdot 10^{-105}:\\ \;\;\;\;\frac{t_1}{s \cdot \left(s \cdot \left(c \cdot \left(x \cdot \left(x \cdot c\right)\right)\right)\right)}\\ \mathbf{elif}\;s \leq 2.2 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;s \leq 1.95 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{t_1}{x \cdot c}}{c \cdot \left(s \cdot \left(x \cdot s\right)\right)}\\ \mathbf{elif}\;s \leq 1.35 \cdot 10^{+204}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t_2}}{t_2}\\ \end{array} \]

Alternative 2
Error	7.2
Cost	7756

\[\begin{array}{l} t_0 := \cos \left(2 \cdot x\right)\\ t_1 := \frac{t_0}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ t_2 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{1}{t_2}}{t_2}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{c \cdot \left(c \cdot \left(x \cdot \left(s \cdot \left(x \cdot s\right)\right)\right)\right)}\\ \end{array} \]

Alternative 3
Error	6.6
Cost	7756

\[\begin{array}{l} t_0 := \cos \left(2 \cdot x\right)\\ t_1 := \frac{t_0}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ t_2 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{1}{t_2}}{t_2}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0}{\left(s \cdot \left(x \cdot s\right)\right) \cdot \left(c \cdot \left(x \cdot c\right)\right)}\\ \end{array} \]

Alternative 4
Error	7.3
Cost	7756

\[\begin{array}{l} t_0 := \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ t_1 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{1}{t_1}}{t_1}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+112}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos \left(x + x\right)}{s \cdot \left(s \cdot \left(c \cdot \left(x \cdot \left(x \cdot c\right)\right)\right)\right)}\\ \end{array} \]

Alternative 5
Error	4.5
Cost	7756

\[\begin{array}{l} t_0 := c \cdot \left(x \cdot s\right)\\ t_1 := \frac{\frac{\cos \left(x + x\right)}{x \cdot c}}{s \cdot t_0}\\ \mathbf{if}\;s \leq -3.5 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;s \leq 5.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ \mathbf{elif}\;s \leq 2 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t_0}}{t_0}\\ \end{array} \]

Alternative 6
Error	3.6
Cost	7756

\[\begin{array}{l} t_0 := c \cdot \left(x \cdot s\right)\\ t_1 := \frac{\frac{\cos \left(x + x\right)}{x \cdot c}}{s \cdot \left(s \cdot \left(x \cdot c\right)\right)}\\ \mathbf{if}\;s \leq -4.2 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;s \leq 5.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(x \cdot \left(\left(c \cdot s\right) \cdot \left(c \cdot s\right)\right)\right)}\\ \mathbf{elif}\;s \leq 5 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t_0}}{t_0}\\ \end{array} \]

Alternative 7
Error	10.2
Cost	7624

\[\begin{array}{l} t_0 := \frac{\cos \left(2 \cdot x\right)}{c \cdot \left(c \cdot \left(x \cdot \left(s \cdot \left(x \cdot s\right)\right)\right)\right)}\\ t_1 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;x \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.00018:\\ \;\;\;\;\frac{\frac{1}{t_1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	2.7
Cost	7360

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

Alternative 9
Error	17.2
Cost	1228

\[\begin{array}{l} t_0 := x \cdot \left(c \cdot s\right)\\ t_1 := \frac{1}{\left(c \cdot s\right) \cdot \left(x \cdot t_0\right)}\\ \mathbf{if}\;x \leq -5 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-308}:\\ \;\;\;\;\frac{1}{\left(x \cdot c\right) \cdot \left(s \cdot t_0\right)}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-222}:\\ \;\;\;\;\frac{1}{\left(x \cdot c\right) \cdot \left(c \cdot \left(s \cdot \left(x \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.0
Cost	964

\[\begin{array}{l} \mathbf{if}\;s \leq 5 \cdot 10^{+113}:\\ \;\;\;\;\frac{1}{\left(x \cdot c\right) \cdot \left(c \cdot \left(s \cdot \left(x \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \left(c \cdot \left(\left(x \cdot s\right) \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 11
Error	17.9
Cost	964

\[\begin{array}{l} \mathbf{if}\;s \leq 5 \cdot 10^{+176}:\\ \;\;\;\;\frac{1}{\left(x \cdot c\right) \cdot \left(s \cdot \left(c \cdot \left(x \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \left(c \cdot \left(\left(x \cdot s\right) \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 12
Error	17.6
Cost	964

\[\begin{array}{l} \mathbf{if}\;s \leq 1.1 \cdot 10^{+178}:\\ \;\;\;\;\frac{1}{\left(x \cdot c\right) \cdot \left(s \cdot \left(x \cdot \left(c \cdot s\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \left(c \cdot \left(\left(x \cdot s\right) \cdot \left(x \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 13
Error	17.4
Cost	964

\[\begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{1}{x \cdot c}}{s \cdot \left(s \cdot \left(x \cdot c\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(\left(c \cdot s\right) \cdot \left(x \cdot \left(c \cdot s\right)\right)\right)}\\ \end{array} \]

Alternative 14
Error	22.0
Cost	832

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

Alternative 15
Error	16.2
Cost	832

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

Reproduce

herbie shell --seed 2022329 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))