Linear.Quaternion:$ccos from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 8.3s

Alternatives: 7

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 1.9205455380123404e+46
  2. y = 7.108964794200985e+198

• 49.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sinh y}{y}\\ \mathbf{if}\;t\_0 \leq 1:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;x \cdot t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sinh y) y))) (if (<= t_0 1.0) (sin x) (* x t_0))))

C

double code(double x, double y) {
	double t_0 = sinh(y) / y;
	double tmp;
	if (t_0 <= 1.0) {
		tmp = sin(x);
	} else {
		tmp = x * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sinh(y) / y
    if (t_0 <= 1.0d0) then
        tmp = sin(x)
    else
        tmp = x * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sinh(y) / y;
	double tmp;
	if (t_0 <= 1.0) {
		tmp = Math.sin(x);
	} else {
		tmp = x * t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sinh(y) / y
	tmp = 0
	if t_0 <= 1.0:
		tmp = math.sin(x)
	else:
		tmp = x * t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sinh(y) / y)
	tmp = 0.0
	if (t_0 <= 1.0)
		tmp = sin(x);
	else
		tmp = Float64(x * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sinh(y) / y;
	tmp = 0.0;
	if (t_0 <= 1.0)
		tmp = sin(x);
	else
		tmp = x * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, 1.0], N[Sin[x], $MachinePrecision], N[(x * t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (sinh.f64 y) y) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   if 1 < (/.f64 (sinh.f64 y) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.1%

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

Alternative 3: 55.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 33000000000:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{x \cdot \left(x \cdot y\right)}{y} \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 33000000000.0)
   (sin x)
   (* x (+ 1.0 (* (/ (* x (* x y)) y) -0.16666666666666666)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 33000000000.0) {
		tmp = sin(x);
	} else {
		tmp = x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 33000000000.0d0) then
        tmp = sin(x)
    else
        tmp = x * (1.0d0 + (((x * (x * y)) / y) * (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 33000000000.0) {
		tmp = Math.sin(x);
	} else {
		tmp = x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 33000000000.0:
		tmp = math.sin(x)
	else:
		tmp = x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 33000000000.0)
		tmp = sin(x);
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(Float64(x * Float64(x * y)) / y) * -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 33000000000.0)
		tmp = sin(x);
	else
		tmp = x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 33000000000.0], N[Sin[x], $MachinePrecision], N[(x * N[(1.0 + N[(N[(N[(x * N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.3e10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.7%

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

   if 3.3e10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 2.6%

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

   4. Taylor expanded in x around 0 18.1%

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

      1. *-commutative 18.1%

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

   6. Simplified 18.1%

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

      1. unpow2 18.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(x \cdot x\right)} \cdot -0.16666666666666666\right) \]

      2. *-un-lft-identity 18.1%

         \[\leadsto x \cdot \left(1 + \left(x \cdot \color{blue}{\left(1 \cdot x\right)}\right) \cdot -0.16666666666666666\right) \]

      3. associate-*r* 18.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(\left(x \cdot 1\right) \cdot x\right)} \cdot -0.16666666666666666\right) \]

      4. lft-mult-inverse 18.1%

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

      5. associate-*l* 18.1%

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

      6. div-inv 18.1%

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

      7. associate-*l/ 19.6%

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

      8. associate-*l/ 22.7%

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

   8. Applied egg-rr 22.7%

      \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\left(x \cdot y\right) \cdot x}{y}} \cdot -0.16666666666666666\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 33000000000:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{x \cdot \left(x \cdot y\right)}{y} \cdot -0.16666666666666666\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 35.6% accurate, 15.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 + \frac{x \cdot \left(x \cdot y\right)}{y} \cdot -0.16666666666666666\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* x (+ 1.0 (* (/ (* x (* x y)) y) -0.16666666666666666))))

C

double code(double x, double y) {
	return x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 + (((x * (x * y)) / y) * (-0.16666666666666666d0)))
end function

Java

public static double code(double x, double y) {
	return x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666));
}

Python

def code(x, y):
	return x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 + Float64(Float64(Float64(x * Float64(x * y)) / y) * -0.16666666666666666)))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (1.0 + (((x * (x * y)) / y) * -0.16666666666666666));
end

Wolfram

code[x_, y_] := N[(x * N[(1.0 + N[(N[(N[(x * N[(x * y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 55.7%

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

4. Taylor expanded in x around 0 37.5%

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

   1. *-commutative 37.5%

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

6. Simplified 37.5%

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

   1. unpow2 37.5%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(x \cdot x\right)} \cdot -0.16666666666666666\right) \]

   2. *-un-lft-identity 37.5%

      \[\leadsto x \cdot \left(1 + \left(x \cdot \color{blue}{\left(1 \cdot x\right)}\right) \cdot -0.16666666666666666\right) \]

   3. associate-*r* 37.5%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(\left(x \cdot 1\right) \cdot x\right)} \cdot -0.16666666666666666\right) \]

   4. lft-mult-inverse 37.5%

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

   5. associate-*l* 37.5%

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

   6. div-inv 37.5%

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

   7. associate-*l/ 38.2%

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

   8. associate-*l/ 39.0%

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

8. Applied egg-rr 39.0%

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

9. Final simplification 39.0%

   \[\leadsto x \cdot \left(1 + \frac{x \cdot \left(x \cdot y\right)}{y} \cdot -0.16666666666666666\right) \]
10. Add Preprocessing

Alternative 5: 29.5% accurate, 20.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{+77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 8.5e+77) x (/ (* x y) y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 8.5e+77) {
		tmp = x;
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 8.5d+77) then
        tmp = x
    else
        tmp = (x * y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 8.5e+77) {
		tmp = x;
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 8.5e+77:
		tmp = x
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 8.5e+77)
		tmp = x;
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 8.5e+77)
		tmp = x;
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 8.5e+77], x, N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.50000000000000018e77

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.9%

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

   4. Taylor expanded in y around 0 37.8%

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

   if 8.50000000000000018e77 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 18.7%

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

      1. clear-num 18.7%

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

      2. un-div-inv 18.7%

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

   5. Applied egg-rr 18.7%

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

      1. associate-/r/ 18.6%

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

   7. Simplified 18.6%

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

   8. Taylor expanded in y around 0 2.5%

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

      1. associate-*l/ 9.5%

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

   10. Applied egg-rr 9.5%

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

Alternative 6: 34.3% accurate, 22.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* x (+ 1.0 (* -0.16666666666666666 (* x x)))))

C

double code(double x, double y) {
	return x * (1.0 + (-0.16666666666666666 * (x * x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (1.0d0 + ((-0.16666666666666666d0) * (x * x)))
end function

Java

public static double code(double x, double y) {
	return x * (1.0 + (-0.16666666666666666 * (x * x)));
}

Python

def code(x, y):
	return x * (1.0 + (-0.16666666666666666 * (x * x)))

Julia

function code(x, y)
	return Float64(x * Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))))
end

MATLAB

function tmp = code(x, y)
	tmp = x * (1.0 + (-0.16666666666666666 * (x * x)));
end

Wolfram

code[x_, y_] := N[(x * N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 55.7%

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

4. Taylor expanded in x around 0 37.5%

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

   1. *-commutative 37.5%

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

6. Simplified 37.5%

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

   1. unpow2 37.5%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(x \cdot x\right)} \cdot -0.16666666666666666\right) \]

8. Applied egg-rr 37.5%

   \[\leadsto x \cdot \left(1 + \color{blue}{\left(x \cdot x\right)} \cdot -0.16666666666666666\right) \]

9. Final simplification 37.5%

   \[\leadsto x \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \]
10. Add Preprocessing

Alternative 7: 26.6% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 65.0%

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

4. Taylor expanded in y around 0 32.1%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024191 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))