Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 7

Speedup: 1.0×

• 49.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \cos x \cdot \frac{\sinh y}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))

C

double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cos(x) * (sinh(y) / y)
end function

Java

public static double code(double x, double y) {
	return Math.cos(x) * (Math.sinh(y) / y);
}

Python

def code(x, y):
	return math.cos(x) * (math.sinh(y) / y)

Julia

function code(x, y)
	return Float64(cos(x) * Float64(sinh(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = cos(x) * (sinh(y) / y);
end

Wolfram

code[x_, y_] := N[(N[Cos[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot \frac{\sinh y}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))

C

double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cos(x) * (sinh(y) / y)
end function

Java

public static double code(double x, double y) {
	return Math.cos(x) * (Math.sinh(y) / y);
}

Python

def code(x, y):
	return math.cos(x) * (math.sinh(y) / y)

Julia

function code(x, y)
	return Float64(cos(x) * Float64(sinh(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = cos(x) * (sinh(y) / y);
end

Wolfram

code[x_, y_] := N[(N[Cos[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\cos x}{\frac{y}{\sinh y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (cos x) (/ y (sinh y))))

C

double code(double x, double y) {
	return cos(x) / (y / sinh(y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cos(x) / (y / sinh(y))
end function

Java

public static double code(double x, double y) {
	return Math.cos(x) / (y / Math.sinh(y));
}

Python

def code(x, y):
	return math.cos(x) / (y / math.sinh(y))

Julia

function code(x, y)
	return Float64(cos(x) / Float64(y / sinh(y)))
end

MATLAB

function tmp = code(x, y)
	tmp = cos(x) / (y / sinh(y));
end

Wolfram

code[x_, y_] := N[(N[Cos[x], $MachinePrecision] / N[(y / N[Sinh[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num 100.0%

      \[\leadsto \cos x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}} \]

   2. un-div-inv 100.0%

      \[\leadsto \color{blue}{\frac{\cos x}{\frac{y}{\sinh y}}} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{\cos x}{\frac{y}{\sinh y}}} \]

5. Final simplification 100.0%

   \[\leadsto \frac{\cos x}{\frac{y}{\sinh y}} \]
6. Add Preprocessing

Alternative 2: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{+24}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{y}^{6} \cdot 0.004629629629629629}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.18e+24) (cos x) (cbrt (* (pow y 6.0) 0.004629629629629629))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.18e+24) {
		tmp = cos(x);
	} else {
		tmp = cbrt((pow(y, 6.0) * 0.004629629629629629));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.18e+24) {
		tmp = Math.cos(x);
	} else {
		tmp = Math.cbrt((Math.pow(y, 6.0) * 0.004629629629629629));
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.18e+24)
		tmp = cos(x);
	else
		tmp = cbrt(Float64((y ^ 6.0) * 0.004629629629629629));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.18e+24], N[Cos[x], $MachinePrecision], N[Power[N[(N[Power[y, 6.0], $MachinePrecision] * 0.004629629629629629), $MachinePrecision], 1/3], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.17999999999999997e24

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\cos x} \]

   if 1.17999999999999997e24 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)}}{y} \]
   4. Step-by-step derivation

      1. distribute-rgt-in 74.9%

         \[\leadsto \cos x \cdot \frac{\color{blue}{1 \cdot y + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}}{y} \]

      2. *-lft-identity 74.9%

         \[\leadsto \cos x \cdot \frac{\color{blue}{y} + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}{y} \]

      3. associate-*l* 74.9%

         \[\leadsto \cos x \cdot \frac{y + \color{blue}{0.16666666666666666 \cdot \left({y}^{2} \cdot y\right)}}{y} \]

      4. unpow2 74.9%

         \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot y\right)}{y} \]

      5. unpow3 74.9%

         \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \color{blue}{{y}^{3}}}{y} \]

   5. Simplified 74.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y + 0.16666666666666666 \cdot {y}^{3}}}{y} \]

   6. Taylor expanded in x around 0 58.7%

      \[\leadsto \color{blue}{\frac{y + 0.16666666666666666 \cdot {y}^{3}}{y}} \]

   7. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot {y}^{2}} \]
   8. Step-by-step derivation

      1. add-cbrt-cube 68.7%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \left(0.16666666666666666 \cdot {y}^{2}\right)\right) \cdot \left(0.16666666666666666 \cdot {y}^{2}\right)}} \]

      2. pow1/3 68.7%

         \[\leadsto \color{blue}{{\left(\left(\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \left(0.16666666666666666 \cdot {y}^{2}\right)\right) \cdot \left(0.16666666666666666 \cdot {y}^{2}\right)\right)}^{0.3333333333333333}} \]

      3. pow3 68.7%

         \[\leadsto {\color{blue}{\left({\left(0.16666666666666666 \cdot {y}^{2}\right)}^{3}\right)}}^{0.3333333333333333} \]

      4. *-commutative 68.7%

         \[\leadsto {\left({\color{blue}{\left({y}^{2} \cdot 0.16666666666666666\right)}}^{3}\right)}^{0.3333333333333333} \]

      5. unpow-prod-down 68.7%

         \[\leadsto {\color{blue}{\left({\left({y}^{2}\right)}^{3} \cdot {0.16666666666666666}^{3}\right)}}^{0.3333333333333333} \]

      6. pow-pow 68.7%

         \[\leadsto {\left(\color{blue}{{y}^{\left(2 \cdot 3\right)}} \cdot {0.16666666666666666}^{3}\right)}^{0.3333333333333333} \]

      7. metadata-eval 68.7%

         \[\leadsto {\left({y}^{\color{blue}{6}} \cdot {0.16666666666666666}^{3}\right)}^{0.3333333333333333} \]

      8. metadata-eval 68.7%

         \[\leadsto {\left({y}^{6} \cdot \color{blue}{0.004629629629629629}\right)}^{0.3333333333333333} \]

   9. Applied egg-rr 68.7%

      \[\leadsto \color{blue}{{\left({y}^{6} \cdot 0.004629629629629629\right)}^{0.3333333333333333}} \]
   10. Step-by-step derivation

       1. unpow1/3 68.7%

          \[\leadsto \color{blue}{\sqrt[3]{{y}^{6} \cdot 0.004629629629629629}} \]

   11. Simplified 68.7%

       \[\leadsto \color{blue}{\sqrt[3]{{y}^{6} \cdot 0.004629629629629629}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.18 \cdot 10^{+24}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{y}^{6} \cdot 0.004629629629629629}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \cos x \cdot \frac{\sinh y}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))

C

double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cos(x) * (sinh(y) / y)
end function

Java

public static double code(double x, double y) {
	return Math.cos(x) * (Math.sinh(y) / y);
}

Python

def code(x, y):
	return math.cos(x) * (math.sinh(y) / y)

Julia

function code(x, y)
	return Float64(cos(x) * Float64(sinh(y) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = cos(x) * (sinh(y) / y);
end

Wolfram

code[x_, y_] := N[(N[Cos[x], $MachinePrecision] * N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \cos x \cdot \frac{\sinh y}{y} \]
4. Add Preprocessing

Alternative 4: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+23}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{y + 0.16666666666666666 \cdot {y}^{3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 5.5e+23) (cos x) (/ (+ y (* 0.16666666666666666 (pow y 3.0))) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5.5e+23) {
		tmp = cos(x);
	} else {
		tmp = (y + (0.16666666666666666 * pow(y, 3.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 5.5d+23) then
        tmp = cos(x)
    else
        tmp = (y + (0.16666666666666666d0 * (y ** 3.0d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 5.5e+23) {
		tmp = Math.cos(x);
	} else {
		tmp = (y + (0.16666666666666666 * Math.pow(y, 3.0))) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5.5e+23:
		tmp = math.cos(x)
	else:
		tmp = (y + (0.16666666666666666 * math.pow(y, 3.0))) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5.5e+23)
		tmp = cos(x);
	else
		tmp = Float64(Float64(y + Float64(0.16666666666666666 * (y ^ 3.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.5e+23)
		tmp = cos(x);
	else
		tmp = (y + (0.16666666666666666 * (y ^ 3.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5.5e+23], N[Cos[x], $MachinePrecision], N[(N[(y + N[(0.16666666666666666 * N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.50000000000000004e23

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\cos x} \]

   if 5.50000000000000004e23 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)}}{y} \]
   4. Step-by-step derivation

      1. distribute-rgt-in 74.9%

         \[\leadsto \cos x \cdot \frac{\color{blue}{1 \cdot y + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}}{y} \]

      2. *-lft-identity 74.9%

         \[\leadsto \cos x \cdot \frac{\color{blue}{y} + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}{y} \]

      3. associate-*l* 74.9%

         \[\leadsto \cos x \cdot \frac{y + \color{blue}{0.16666666666666666 \cdot \left({y}^{2} \cdot y\right)}}{y} \]

      4. unpow2 74.9%

         \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot y\right)}{y} \]

      5. unpow3 74.9%

         \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \color{blue}{{y}^{3}}}{y} \]

   5. Simplified 74.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y + 0.16666666666666666 \cdot {y}^{3}}}{y} \]

   6. Taylor expanded in x around 0 58.7%

      \[\leadsto \color{blue}{\frac{y + 0.16666666666666666 \cdot {y}^{3}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{+23}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{y + 0.16666666666666666 \cdot {y}^{3}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+24}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot {y}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.35e+24) (cos x) (* 0.16666666666666666 (pow y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.35e+24) {
		tmp = cos(x);
	} else {
		tmp = 0.16666666666666666 * pow(y, 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.35d+24) then
        tmp = cos(x)
    else
        tmp = 0.16666666666666666d0 * (y ** 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.35e+24) {
		tmp = Math.cos(x);
	} else {
		tmp = 0.16666666666666666 * Math.pow(y, 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.35e+24:
		tmp = math.cos(x)
	else:
		tmp = 0.16666666666666666 * math.pow(y, 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.35e+24)
		tmp = cos(x);
	else
		tmp = Float64(0.16666666666666666 * (y ^ 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.35e+24)
		tmp = cos(x);
	else
		tmp = 0.16666666666666666 * (y ^ 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.35e+24], N[Cos[x], $MachinePrecision], N[(0.16666666666666666 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.35e24

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\cos x} \]

   if 1.35e24 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)}}{y} \]
   4. Step-by-step derivation

      1. distribute-rgt-in 74.9%

         \[\leadsto \cos x \cdot \frac{\color{blue}{1 \cdot y + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}}{y} \]

      2. *-lft-identity 74.9%

         \[\leadsto \cos x \cdot \frac{\color{blue}{y} + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}{y} \]

      3. associate-*l* 74.9%

         \[\leadsto \cos x \cdot \frac{y + \color{blue}{0.16666666666666666 \cdot \left({y}^{2} \cdot y\right)}}{y} \]

      4. unpow2 74.9%

         \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot y\right)}{y} \]

      5. unpow3 74.9%

         \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \color{blue}{{y}^{3}}}{y} \]

   5. Simplified 74.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y + 0.16666666666666666 \cdot {y}^{3}}}{y} \]

   6. Taylor expanded in x around 0 58.7%

      \[\leadsto \color{blue}{\frac{y + 0.16666666666666666 \cdot {y}^{3}}{y}} \]

   7. Taylor expanded in y around inf 44.2%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot {y}^{2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+24}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot {y}^{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \cos x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (cos x))

C

double code(double x, double y) {
	return cos(x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = cos(x)
end function

Java

public static double code(double x, double y) {
	return Math.cos(x);
}

Python

def code(x, y):
	return math.cos(x)

Julia

function code(x, y)
	return cos(x)
end

MATLAB

function tmp = code(x, y)
	tmp = cos(x);
end

Wolfram

code[x_, y_] := N[Cos[x], $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 50.1%

   \[\leadsto \color{blue}{\cos x} \]

4. Final simplification 50.1%

   \[\leadsto \cos x \]
5. Add Preprocessing

Alternative 7: 29.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 82.4%

   \[\leadsto \cos x \cdot \frac{\color{blue}{y \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)}}{y} \]
4. Step-by-step derivation

   1. distribute-rgt-in 82.4%

      \[\leadsto \cos x \cdot \frac{\color{blue}{1 \cdot y + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}}{y} \]

   2. *-lft-identity 82.4%

      \[\leadsto \cos x \cdot \frac{\color{blue}{y} + \left(0.16666666666666666 \cdot {y}^{2}\right) \cdot y}{y} \]

   3. associate-*l* 82.4%

      \[\leadsto \cos x \cdot \frac{y + \color{blue}{0.16666666666666666 \cdot \left({y}^{2} \cdot y\right)}}{y} \]

   4. unpow2 82.4%

      \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot y\right)}{y} \]

   5. unpow3 82.4%

      \[\leadsto \cos x \cdot \frac{y + 0.16666666666666666 \cdot \color{blue}{{y}^{3}}}{y} \]

5. Simplified 82.4%

   \[\leadsto \cos x \cdot \frac{\color{blue}{y + 0.16666666666666666 \cdot {y}^{3}}}{y} \]

6. Taylor expanded in x around 0 51.8%

   \[\leadsto \color{blue}{\frac{y + 0.16666666666666666 \cdot {y}^{3}}{y}} \]

7. Taylor expanded in y around 0 27.5%

   \[\leadsto \color{blue}{1} \]

8. Final simplification 27.5%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))