mixedcos

Average Accuracy: 38.1% → 67.6%

Time: 17.2s

Precision: binary64

Cost: 27588

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

Math

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

↓

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

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

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 ((cos((2.0 * x)) / (pow(c, 2.0) * (x * (x * pow(s, 2.0))))) <= ((double) INFINITY)) {
		tmp = (((1.0 / x) / s) / (c / t_0)) / (c * (x * s));
	} else {
		tmp = (t_0 / t_1) / t_1;
	}
	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 = 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 = (((1.0 / x) / s) / (c / t_0)) / (c * (x * s));
	} else {
		tmp = (t_0 / t_1) / t_1;
	}
	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 (math.cos((2.0 * x)) / (math.pow(c, 2.0) * (x * (x * math.pow(s, 2.0))))) <= math.inf:
		tmp = (((1.0 / x) / s) / (c / t_0)) / (c * (x * s))
	else:
		tmp = (t_0 / t_1) / t_1
	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 (Float64(cos(Float64(2.0 * x)) / Float64((c ^ 2.0) * Float64(x * Float64(x * (s ^ 2.0))))) <= Inf)
		tmp = Float64(Float64(Float64(Float64(1.0 / x) / s) / Float64(c / t_0)) / Float64(c * Float64(x * s)));
	else
		tmp = Float64(Float64(t_0 / t_1) / t_1);
	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 ((cos((2.0 * x)) / ((c ^ 2.0) * (x * (x * (s ^ 2.0))))) <= Inf)
		tmp = (((1.0 / x) / s) / (c / t_0)) / (c * (x * s));
	else
		tmp = (t_0 / t_1) / t_1;
	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[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[(N[(N[(1.0 / x), $MachinePrecision] / s), $MachinePrecision] / N[(c / t$95$0), $MachinePrecision]), $MachinePrecision] / N[(c * N[(x * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 / t$95$1), $MachinePrecision] / t$95$1), $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 50.5%

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

   2. Simplified 50.7%

      \[\leadsto \color{blue}{\frac{\frac{\cos \left(2 \cdot x\right)}{c \cdot c}}{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}} \]
      Step-by-step derivation

      [Start] 50.5	\[ \frac{\cos \left(2 \cdot x\right)}{{c}^{2} \cdot \left(\left(x \cdot {s}^{2}\right) \cdot x\right)} \]
      associate-/r* [=>] 50.7	\[ \color{blue}{\frac{\frac{\cos \left(2 \cdot x\right)}{{c}^{2}}}{\left(x \cdot {s}^{2}\right) \cdot x}} \]
      unpow2 [=>] 50.7	\[ \frac{\frac{\cos \left(2 \cdot x\right)}{\color{blue}{c \cdot c}}}{\left(x \cdot {s}^{2}\right) \cdot x} \]
      *-commutative [=>] 50.7	\[ \frac{\frac{\cos \left(2 \cdot x\right)}{c \cdot c}}{\color{blue}{x \cdot \left(x \cdot {s}^{2}\right)}} \]
      unpow2 [=>] 50.7	\[ \frac{\frac{\cos \left(2 \cdot x\right)}{c \cdot c}}{x \cdot \left(x \cdot \color{blue}{\left(s \cdot s\right)}\right)} \]

   3. Applied egg-rr 60.8%

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

      [Start] 50.7	\[ \frac{\frac{\cos \left(2 \cdot x\right)}{c \cdot c}}{x \cdot \left(x \cdot \left(s \cdot s\right)\right)} \]
      associate-/l/ [=>] 50.5	\[ \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right) \cdot \left(c \cdot c\right)}} \]
      div-inv [=>] 50.5	\[ \color{blue}{\cos \left(2 \cdot x\right) \cdot \frac{1}{\left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right) \cdot \left(c \cdot c\right)}} \]
      cos-2 [=>] 50.5	\[ \color{blue}{\left(\cos x \cdot \cos x - \sin x \cdot \sin x\right)} \cdot \frac{1}{\left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right) \cdot \left(c \cdot c\right)} \]
      cos-sum [<=] 50.5	\[ \color{blue}{\cos \left(x + x\right)} \cdot \frac{1}{\left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right) \cdot \left(c \cdot c\right)} \]
      *-commutative [=>] 50.5	\[ \cos \left(x + x\right) \cdot \frac{1}{\color{blue}{\left(c \cdot c\right) \cdot \left(x \cdot \left(x \cdot \left(s \cdot s\right)\right)\right)}} \]
      add-sqr-sqrt [=>] 50.5	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot \color{blue}{\left(\sqrt{x \cdot \left(x \cdot \left(s \cdot s\right)\right)} \cdot \sqrt{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\right)}} \]
      pow2 [=>] 50.5	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot \color{blue}{{\left(\sqrt{x \cdot \left(x \cdot \left(s \cdot s\right)\right)}\right)}^{2}}} \]
      associate-*r* [=>] 45.4	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\left(\sqrt{\color{blue}{\left(x \cdot x\right) \cdot \left(s \cdot s\right)}}\right)}^{2}} \]
      sqrt-prod [=>] 45.5	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\color{blue}{\left(\sqrt{x \cdot x} \cdot \sqrt{s \cdot s}\right)}}^{2}} \]
      sqrt-unprod [<=] 24.5	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\left(\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \sqrt{s \cdot s}\right)}^{2}} \]
      sqrt-prod [=>] 14.8	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\left(\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\sqrt{s} \cdot \sqrt{s}\right)}\right)}^{2}} \]
      add-sqr-sqrt [<=] 29.1	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\left(\color{blue}{x} \cdot \left(\sqrt{s} \cdot \sqrt{s}\right)\right)}^{2}} \]
      add-sqr-sqrt [<=] 60.8	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\left(x \cdot \color{blue}{s}\right)}^{2}} \]

   4. Applied egg-rr 72.4%

      \[\leadsto \color{blue}{\frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{c \cdot \left(x \cdot s\right)}} \]
      Step-by-step derivation

      [Start] 60.8	\[ \cos \left(x + x\right) \cdot \frac{1}{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}} \]
      un-div-inv [=>] 60.8	\[ \color{blue}{\frac{\cos \left(x + x\right)}{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      add-sqr-sqrt [=>] 60.7	\[ \frac{\cos \left(x + x\right)}{\color{blue}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}} \cdot \sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}}} \]
      associate-/r* [=>] 60.7	\[ \color{blue}{\frac{\frac{\cos \left(x + x\right)}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}}} \]
      sqrt-prod [=>] 60.8	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\sqrt{c \cdot c} \cdot \sqrt{{\left(x \cdot s\right)}^{2}}}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      sqrt-prod [=>] 36.7	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(\sqrt{c} \cdot \sqrt{c}\right)} \cdot \sqrt{{\left(x \cdot s\right)}^{2}}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      add-sqr-sqrt [<=] 52.9	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{c} \cdot \sqrt{{\left(x \cdot s\right)}^{2}}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      unpow2 [=>] 52.9	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \sqrt{\color{blue}{\left(x \cdot s\right) \cdot \left(x \cdot s\right)}}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      sqrt-prod [=>] 27.0	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \color{blue}{\left(\sqrt{x \cdot s} \cdot \sqrt{x \cdot s}\right)}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      add-sqr-sqrt [<=] 52.7	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \color{blue}{\left(x \cdot s\right)}}}{\sqrt{\left(c \cdot c\right) \cdot {\left(x \cdot s\right)}^{2}}} \]
      sqrt-prod [=>] 52.8	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{\color{blue}{\sqrt{c \cdot c} \cdot \sqrt{{\left(x \cdot s\right)}^{2}}}} \]
      sqrt-prod [=>] 33.3	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{\color{blue}{\left(\sqrt{c} \cdot \sqrt{c}\right)} \cdot \sqrt{{\left(x \cdot s\right)}^{2}}} \]
      add-sqr-sqrt [<=] 52.3	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{\color{blue}{c} \cdot \sqrt{{\left(x \cdot s\right)}^{2}}} \]
      unpow2 [=>] 52.3	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{c \cdot \sqrt{\color{blue}{\left(x \cdot s\right) \cdot \left(x \cdot s\right)}}} \]
      sqrt-prod [=>] 34.5	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{c \cdot \color{blue}{\left(\sqrt{x \cdot s} \cdot \sqrt{x \cdot s}\right)}} \]
      add-sqr-sqrt [<=] 72.4	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{c \cdot \color{blue}{\left(x \cdot s\right)}} \]

   5. Applied egg-rr 72.4%

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

      [Start] 72.4	\[ \frac{\frac{\cos \left(x + x\right)}{c \cdot \left(x \cdot s\right)}}{c \cdot \left(x \cdot s\right)} \]
      associate-/r* [=>] 72.4	\[ \frac{\color{blue}{\frac{\frac{\cos \left(x + x\right)}{c}}{x \cdot s}}}{c \cdot \left(x \cdot s\right)} \]
      div-inv [=>] 72.4	\[ \frac{\color{blue}{\frac{\cos \left(x + x\right)}{c} \cdot \frac{1}{x \cdot s}}}{c \cdot \left(x \cdot s\right)} \]

   6. Applied egg-rr 72.5%

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

      [Start] 72.4	\[ \frac{\frac{\cos \left(x + x\right)}{c} \cdot \frac{1}{x \cdot s}}{c \cdot \left(x \cdot s\right)} \]
      *-commutative [=>] 72.4	\[ \frac{\color{blue}{\frac{1}{x \cdot s} \cdot \frac{\cos \left(x + x\right)}{c}}}{c \cdot \left(x \cdot s\right)} \]
      clear-num [=>] 72.4	\[ \frac{\frac{1}{x \cdot s} \cdot \color{blue}{\frac{1}{\frac{c}{\cos \left(x + x\right)}}}}{c \cdot \left(x \cdot s\right)} \]
      un-div-inv [=>] 72.4	\[ \frac{\color{blue}{\frac{\frac{1}{x \cdot s}}{\frac{c}{\cos \left(x + x\right)}}}}{c \cdot \left(x \cdot s\right)} \]
      associate-/r* [=>] 72.5	\[ \frac{\frac{\color{blue}{\frac{\frac{1}{x}}{s}}}{\frac{c}{\cos \left(x + x\right)}}}{c \cdot \left(x \cdot s\right)} \]

   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 0.5%

      \[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      Step-by-step derivation

      [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* [=>] 0.5	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \color{blue}{\left(\left({c}^{2} \cdot x\right) \cdot {s}^{2}\right)}} \]
      unpow2 [=>] 0.5	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(\color{blue}{\left(c \cdot c\right)} \cdot x\right) \cdot {s}^{2}\right)} \]
      unpow2 [=>] 0.5	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \color{blue}{\left(s \cdot s\right)}\right)} \]

   3. Applied egg-rr 37.2%

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

      [Start] 0.5	\[ \frac{\cos \left(2 \cdot x\right)}{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)} \]
      *-un-lft-identity [=>] 0.5	\[ \frac{\color{blue}{1 \cdot \cos \left(2 \cdot x\right)}}{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)} \]
      add-sqr-sqrt [=>] 0.5	\[ \frac{1 \cdot \cos \left(2 \cdot x\right)}{\color{blue}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)} \cdot \sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}}} \]
      times-frac [=>] 0.5	\[ \color{blue}{\frac{1}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}}} \]
      *-commutative [=>] 0.5	\[ \frac{1}{\sqrt{\color{blue}{\left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right) \cdot x}}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      sqrt-prod [=>] 0.2	\[ \frac{1}{\color{blue}{\sqrt{\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)} \cdot \sqrt{x}}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      *-commutative [=>] 0.2	\[ \frac{1}{\sqrt{\color{blue}{\left(s \cdot s\right) \cdot \left(\left(c \cdot c\right) \cdot x\right)}} \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      sqrt-prod [=>] 0.2	\[ \frac{1}{\color{blue}{\left(\sqrt{s \cdot s} \cdot \sqrt{\left(c \cdot c\right) \cdot x}\right)} \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      sqrt-prod [=>] 0.2	\[ \frac{1}{\left(\color{blue}{\left(\sqrt{s} \cdot \sqrt{s}\right)} \cdot \sqrt{\left(c \cdot c\right) \cdot x}\right) \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      add-sqr-sqrt [<=] 0.2	\[ \frac{1}{\left(\color{blue}{s} \cdot \sqrt{\left(c \cdot c\right) \cdot x}\right) \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      sqrt-prod [=>] 0.2	\[ \frac{1}{\left(s \cdot \color{blue}{\left(\sqrt{c \cdot c} \cdot \sqrt{x}\right)}\right) \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      sqrt-prod [=>] 0.0	\[ \frac{1}{\left(s \cdot \left(\color{blue}{\left(\sqrt{c} \cdot \sqrt{c}\right)} \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]
      add-sqr-sqrt [<=] 0.2	\[ \frac{1}{\left(s \cdot \left(\color{blue}{c} \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \cdot \frac{\cos \left(2 \cdot x\right)}{\sqrt{x \cdot \left(\left(\left(c \cdot c\right) \cdot x\right) \cdot \left(s \cdot s\right)\right)}} \]

   4. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{\frac{\cos \left(x + x\right)}{\left(s \cdot c\right) \cdot x}}{\left(s \cdot c\right) \cdot x}} \]
      Step-by-step derivation

      [Start] 37.2	\[ \frac{1}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \cdot \frac{\cos \left(x + x\right)}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \]
      associate-*l/ [=>] 37.2	\[ \color{blue}{\frac{1 \cdot \frac{\cos \left(x + x\right)}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}}}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}}} \]
      *-lft-identity [=>] 37.2	\[ \frac{\color{blue}{\frac{\cos \left(x + x\right)}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}}}}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \]
      associate-*r* [=>] 33.5	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(\left(s \cdot c\right) \cdot \sqrt{x}\right)} \cdot \sqrt{x}}}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \]
      associate-*l* [=>] 33.6	\[ \frac{\frac{\cos \left(x + x\right)}{\color{blue}{\left(s \cdot c\right) \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)}}}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \]
      rem-square-sqrt [=>] 33.7	\[ \frac{\frac{\cos \left(x + x\right)}{\left(s \cdot c\right) \cdot \color{blue}{x}}}{\left(s \cdot \left(c \cdot \sqrt{x}\right)\right) \cdot \sqrt{x}} \]
      associate-*r* [=>] 40.5	\[ \frac{\frac{\cos \left(x + x\right)}{\left(s \cdot c\right) \cdot x}}{\color{blue}{\left(\left(s \cdot c\right) \cdot \sqrt{x}\right)} \cdot \sqrt{x}} \]
      associate-*l* [=>] 40.4	\[ \frac{\frac{\cos \left(x + x\right)}{\left(s \cdot c\right) \cdot x}}{\color{blue}{\left(s \cdot c\right) \cdot \left(\sqrt{x} \cdot \sqrt{x}\right)}} \]
      rem-square-sqrt [=>] 77.2	\[ \frac{\frac{\cos \left(x + x\right)}{\left(s \cdot c\right) \cdot x}}{\left(s \cdot c\right) \cdot \color{blue}{x}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 73.5%

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

Alternatives

Alternative 1
Accuracy	52.6%
Cost	7756

\[\begin{array}{l} t_0 := s \cdot \left(x \cdot c\right)\\ t_1 := \frac{\cos \left(2 \cdot x\right)}{s \cdot \left(\left(x \cdot x\right) \cdot \left(s \cdot \left(c \cdot c\right)\right)\right)}\\ \mathbf{if}\;x \leq -0.00055:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-11}:\\ \;\;\;\;{t_0}^{-2}\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t_0}}{t_0}\\ \end{array} \]

Alternative 2
Accuracy	57.3%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-5} \lor \neg \left(x \leq 1.08 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{x \cdot \left(s \cdot \left(s \cdot \left(c \cdot \left(x \cdot c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;{\left(s \cdot \left(x \cdot c\right)\right)}^{-2}\\ \end{array} \]

Alternative 3
Accuracy	65.3%
Cost	7492

\[\begin{array}{l} t_0 := s \cdot \left(x \cdot c\right)\\ t_1 := c \cdot \left(x \cdot s\right)\\ \mathbf{if}\;s \leq 2.7 \cdot 10^{+262}:\\ \;\;\;\;\frac{\frac{\cos \left(x + x\right)}{t_1}}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{t_0 \cdot t_0}\\ \end{array} \]

Alternative 4
Accuracy	65.1%
Cost	7492

\[\begin{array}{l} t_0 := s \cdot \left(x \cdot c\right)\\ \mathbf{if}\;s \leq 2.8 \cdot 10^{+262}:\\ \;\;\;\;\frac{\frac{\frac{\cos \left(x + x\right)}{x \cdot s}}{c}}{c \cdot \left(x \cdot s\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\cos \left(2 \cdot x\right)}{t_0 \cdot t_0}\\ \end{array} \]

Alternative 5
Accuracy	63.1%
Cost	7360

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

Alternative 6
Accuracy	65.3%
Cost	7360

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

Alternative 7
Accuracy	49.8%
Cost	6784

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

Alternative 8
Accuracy	43.5%
Cost	832

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

Alternative 9
Accuracy	47.7%
Cost	832

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

Alternative 10
Accuracy	48.1%
Cost	832

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

Alternative 11
Accuracy	48.8%
Cost	832

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

Alternative 12
Accuracy	49.8%
Cost	832

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

Reproduce

herbie shell --seed 2023157 
(FPCore (x c s)
  :name "mixedcos"
  :precision binary64
  (/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x))))