Linear.Quaternion:$ccos from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 6

Speedup: 1.0×

• 48.9% 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. Final simplification 100.0%

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

Alternative 2: 87.4% 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. 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. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 75.8%

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

   5. Applied egg-rr 75.8%

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

   6. Taylor expanded in x around 0 48.4%

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

   7. Taylor expanded in x around 0 72.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot \left(e^{y} - \frac{1}{e^{y}}\right)}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{\frac{x \cdot \left(e^{y} - \frac{1}{e^{y}}\right)}{y} \cdot 0.5} \]

      2. *-commutative 72.2%

         \[\leadsto \frac{\color{blue}{\left(e^{y} - \frac{1}{e^{y}}\right) \cdot x}}{y} \cdot 0.5 \]

      3. associate-/l* 44.8%

         \[\leadsto \color{blue}{\frac{e^{y} - \frac{1}{e^{y}}}{\frac{y}{x}}} \cdot 0.5 \]

      4. associate-/r/ 44.8%

         \[\leadsto \color{blue}{\frac{e^{y} - \frac{1}{e^{y}}}{\frac{\frac{y}{x}}{0.5}}} \]

      5. metadata-eval 44.8%

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

      6. associate-/l* 44.8%

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

      7. *-commutative 44.8%

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

      8. /-rgt-identity 44.8%

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

      9. associate-/r* 44.8%

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

      10. rec-exp 44.8%

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

      11. sinh-def 45.2%

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

      12. associate-/r/ 72.6%

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

      13. *-commutative 72.6%

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

   9. Simplified 72.6%

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

4. Final simplification 86.7%

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

Alternative 3: 54.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 920000000:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot {x}^{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 920000000.0) (sin x) (* -0.16666666666666666 (pow x 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 920000000.0) {
		tmp = sin(x);
	} else {
		tmp = -0.16666666666666666 * pow(x, 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 920000000.0d0) then
        tmp = sin(x)
    else
        tmp = (-0.16666666666666666d0) * (x ** 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 920000000.0) {
		tmp = Math.sin(x);
	} else {
		tmp = -0.16666666666666666 * Math.pow(x, 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 920000000.0:
		tmp = math.sin(x)
	else:
		tmp = -0.16666666666666666 * math.pow(x, 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 920000000.0)
		tmp = sin(x);
	else
		tmp = Float64(-0.16666666666666666 * (x ^ 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 920000000.0)
		tmp = sin(x);
	else
		tmp = -0.16666666666666666 * (x ^ 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 920000000.0], N[Sin[x], $MachinePrecision], N[(-0.16666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.2e8

   1. Initial program 100.0%

      \[\sin x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in y around 0 68.4%

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

   if 9.2e8 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 64.9%

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

   5. Applied egg-rr 64.9%

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

   6. Taylor expanded in y around 0 2.4%

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

   7. Taylor expanded in x around 0 24.1%

      \[\leadsto \color{blue}{\left(-0.16666666666666666 \cdot \frac{{x}^{3}}{y} + \frac{x}{y}\right)} \cdot y \]

   8. Taylor expanded in x around inf 23.9%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 920000000:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot {x}^{3}\\ \end{array} \]

Alternative 4: 54.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{+109}:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1e+109) (sin x) (/ (* x y) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1e+109) {
		tmp = sin(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 (y <= 1d+109) then
        tmp = sin(x)
    else
        tmp = (x * y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1e+109) {
		tmp = Math.sin(x);
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1e+109:
		tmp = math.sin(x)
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1e+109)
		tmp = sin(x);
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1e+109)
		tmp = sin(x);
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1e+109], N[Sin[x], $MachinePrecision], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.99999999999999982e108

   1. Initial program 100.0%

      \[\sin x \cdot \frac{\sinh y}{y} \]

   2. Taylor expanded in y around 0 61.6%

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

   if 9.99999999999999982e108 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 52.9%

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

   5. Applied egg-rr 52.9%

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

   6. Taylor expanded in y around 0 2.3%

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

      1. *-commutative 2.3%

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

      2. associate-*r/ 2.5%

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

   8. Applied egg-rr 2.5%

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

   9. Taylor expanded in x around 0 7.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 10^{+109}:\\ \;\;\;\;\sin x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \]

Alternative 5: 29.1% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.53 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.53e+100) x (/ (* x y) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.53e+100) {
		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 (y <= 1.53d+100) 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 (y <= 1.53e+100) {
		tmp = x;
	} else {
		tmp = (x * y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.53e+100:
		tmp = x
	else:
		tmp = (x * y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.53e+100)
		tmp = x;
	else
		tmp = Float64(Float64(x * y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.53e+100)
		tmp = x;
	else
		tmp = (x * y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.53e+100], x, N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.53e100

   1. Initial program 100.0%

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

      1. associate-*r/ 88.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   6. Taylor expanded in x around 0 52.2%

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

   7. Taylor expanded in y around 0 31.1%

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

   if 1.53e100 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. associate-/r/ 52.8%

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

   5. Applied egg-rr 52.8%

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

   6. Taylor expanded in y around 0 2.3%

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

      1. *-commutative 2.3%

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

      2. associate-*r/ 2.5%

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

   8. Applied egg-rr 2.5%

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

   9. Taylor expanded in x around 0 7.1%

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

4. Final simplification 27.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.53 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \end{array} \]

Alternative 6: 26.8% 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. Step-by-step derivation

   1. associate-*r/ 89.7%

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

   2. associate-/l* 100.0%

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

3. Simplified 100.0%

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

   1. associate-/r/ 88.2%

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

5. Applied egg-rr 88.2%

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

6. Taylor expanded in x around 0 48.4%

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

7. Taylor expanded in y around 0 27.0%

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

8. Final simplification 27.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023302 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))