Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.9% → 99.8%

Time: 8.8s

Alternatives: 5

Speedup: 1.0×

• 49.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 0.0005:\\ \;\;\;\;y \cdot \frac{\sin x}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 0.0005) (* y (/ (sin x) x)) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 0.0005) {
		tmp = y * (sin(x) / x);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= 0.0005d0) then
        tmp = y * (sin(x) / x)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 0.0005) {
		tmp = y * (Math.sin(x) / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 0.0005:
		tmp = y * (math.sin(x) / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 0.0005)
		tmp = Float64(y * Float64(sin(x) / x));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 0.0005)
		tmp = y * (sin(x) / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], N[(y * N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 5.0000000000000001e-4

   1. Initial program 85.4%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 52.7%

      \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.2%

         \[\leadsto \color{blue}{y \cdot \frac{\sin x}{x}} \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{y \cdot \frac{\sin x}{x}} \]

   if 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 77.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{2}{e^{y} - \frac{1}{e^{y}}}}} \]
   8. Step-by-step derivation

      1. metadata-eval 77.2%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot 2}}{e^{y} - \frac{1}{e^{y}}}} \]

      2. associate-*l/ 77.2%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{y} - \frac{1}{e^{y}}} \cdot 2}} \]

      3. associate-/r/ 77.2%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{e^{y} - \frac{1}{e^{y}}}{2}}}} \]

      4. rec-exp 77.2%

         \[\leadsto \frac{1}{\frac{1}{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}} \]

      5. sinh-def 77.2%

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

   9. Simplified 77.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\sinh y}}} \]
   10. Step-by-step derivation

       1. remove-double-div 77.2%

          \[\leadsto \color{blue}{\sinh y} \]

       2. sinh-def 77.2%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       3. div-sub 77.2%

          \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]

   11. Applied egg-rr 77.2%

       \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]
   12. Step-by-step derivation

       1. div-sub 77.2%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       2. sinh-def 77.2%

          \[\leadsto \color{blue}{\sinh y} \]

   13. Simplified 77.2%

       \[\leadsto \color{blue}{\sinh y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq 2 \cdot 10^{-26}:\\ \;\;\;\;\frac{1}{\frac{x}{y} \cdot \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) 2e-26) (/ 1.0 (* (/ x y) (/ 1.0 x))) (sinh y)))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= 2e-26) {
		tmp = 1.0 / ((x / y) * (1.0 / x));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= 2d-26) then
        tmp = 1.0d0 / ((x / y) * (1.0d0 / x))
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= 2e-26) {
		tmp = 1.0 / ((x / y) * (1.0 / x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= 2e-26:
		tmp = 1.0 / ((x / y) * (1.0 / x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= 2e-26)
		tmp = Float64(1.0 / Float64(Float64(x / y) * Float64(1.0 / x)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= 2e-26)
		tmp = 1.0 / ((x / y) * (1.0 / x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-26], N[(1.0 / N[(N[(x / y), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < 2.0000000000000001e-26

   1. Initial program 85.2%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 85.2%

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

      2. clear-num 84.1%

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

      3. *-commutative 84.1%

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

      4. associate-/r* 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in y around 0 50.9%

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

   8. Taylor expanded in x around 0 21.8%

      \[\leadsto \frac{1}{\frac{x}{\color{blue}{x \cdot y}}} \]
   9. Step-by-step derivation

      1. *-commutative 21.8%

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

   10. Simplified 21.8%

       \[\leadsto \frac{1}{\frac{x}{\color{blue}{y \cdot x}}} \]
   11. Step-by-step derivation

       1. associate-/r* 56.8%

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

       2. div-inv 56.8%

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

   12. Applied egg-rr 56.8%

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

   if 2.0000000000000001e-26 < (sinh.f64 y)

   1. Initial program 100.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 74.0%

      \[\leadsto \frac{1}{\color{blue}{\frac{2}{e^{y} - \frac{1}{e^{y}}}}} \]
   8. Step-by-step derivation

      1. metadata-eval 74.0%

         \[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot 2}}{e^{y} - \frac{1}{e^{y}}}} \]

      2. associate-*l/ 74.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{e^{y} - \frac{1}{e^{y}}} \cdot 2}} \]

      3. associate-/r/ 74.0%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{e^{y} - \frac{1}{e^{y}}}{2}}}} \]

      4. rec-exp 74.0%

         \[\leadsto \frac{1}{\frac{1}{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}} \]

      5. sinh-def 75.2%

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

   9. Simplified 75.2%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\sinh y}}} \]
   10. Step-by-step derivation

       1. remove-double-div 75.2%

          \[\leadsto \color{blue}{\sinh y} \]

       2. sinh-def 74.0%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       3. div-sub 74.0%

          \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]

   11. Applied egg-rr 74.0%

       \[\leadsto \color{blue}{\frac{e^{y}}{2} - \frac{e^{-y}}{2}} \]
   12. Step-by-step derivation

       1. div-sub 74.0%

          \[\leadsto \color{blue}{\frac{e^{y} - e^{-y}}{2}} \]

       2. sinh-def 75.2%

          \[\leadsto \color{blue}{\sinh y} \]

   13. Simplified 75.2%

       \[\leadsto \color{blue}{\sinh y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.0% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x * (y / x)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. associate-*r/ 88.7%

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

   2. clear-num 87.8%

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

   3. *-commutative 87.8%

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

   4. associate-/r* 98.9%

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

6. Applied egg-rr 98.9%

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

7. Taylor expanded in y around 0 41.2%

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

8. Taylor expanded in x around 0 21.3%

   \[\leadsto \frac{1}{\frac{x}{\color{blue}{x \cdot y}}} \]
9. Step-by-step derivation

   1. *-commutative 21.3%

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

10. Simplified 21.3%

    \[\leadsto \frac{1}{\frac{x}{\color{blue}{y \cdot x}}} \]
11. Step-by-step derivation

    1. associate-/r* 51.1%

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

    2. associate-/r/ 53.0%

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

    3. clear-num 52.0%

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

12. Applied egg-rr 52.0%

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

13. Final simplification 52.0%

    \[\leadsto x \cdot \frac{y}{x} \]
14. Add Preprocessing

Alternative 5: 27.8% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 88.7%

   \[\frac{\sin x \cdot \sinh y}{x} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 42.1%

   \[\leadsto \color{blue}{\frac{y \cdot \sin x}{x}} \]
6. Step-by-step derivation

   1. associate-/l* 53.3%

      \[\leadsto \color{blue}{y \cdot \frac{\sin x}{x}} \]

7. Simplified 53.3%

   \[\leadsto \color{blue}{y \cdot \frac{\sin x}{x}} \]

8. Taylor expanded in x around 0 27.9%

   \[\leadsto \color{blue}{y} \]
9. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024083 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :alt
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))