Linear.Quaternion:$csinh from linear-1.19.1.3

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 7

Speedup: 1.0×

• 50.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cosh x \leq 1.000000000002:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (cosh x) 1.000000000002) (/ (sin y) y) (cosh x)))

C

double code(double x, double y) {
	double tmp;
	if (cosh(x) <= 1.000000000002) {
		tmp = sin(y) / y;
	} else {
		tmp = cosh(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (cosh(x) <= 1.000000000002d0) then
        tmp = sin(y) / y
    else
        tmp = cosh(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.cosh(x) <= 1.000000000002) {
		tmp = Math.sin(y) / y;
	} else {
		tmp = Math.cosh(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.cosh(x) <= 1.000000000002:
		tmp = math.sin(y) / y
	else:
		tmp = math.cosh(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (cosh(x) <= 1.000000000002)
		tmp = Float64(sin(y) / y);
	else
		tmp = cosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (cosh(x) <= 1.000000000002)
		tmp = sin(y) / y;
	else
		tmp = cosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cosh[x], $MachinePrecision], 1.000000000002], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[Cosh[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cosh.f64 x) < 1.00000000000199996

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 99.7%

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

   if 1.00000000000199996 < (cosh.f64 x)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.7%

      \[\leadsto \cosh x \cdot \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \leq 1.000000000002:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 3: 71.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(\frac{1}{y} + 0.5 \cdot \frac{x \cdot x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.4e-6)
   (/ (sin y) y)
   (if (<= x 6.4e+151)
     (cosh x)
     (* (sin y) (+ (/ 1.0 y) (* 0.5 (/ (* x x) y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.4e-6) {
		tmp = sin(y) / y;
	} else if (x <= 6.4e+151) {
		tmp = cosh(x);
	} else {
		tmp = sin(y) * ((1.0 / y) + (0.5 * ((x * x) / 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 <= 2.4d-6) then
        tmp = sin(y) / y
    else if (x <= 6.4d+151) then
        tmp = cosh(x)
    else
        tmp = sin(y) * ((1.0d0 / y) + (0.5d0 * ((x * x) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.4e-6) {
		tmp = Math.sin(y) / y;
	} else if (x <= 6.4e+151) {
		tmp = Math.cosh(x);
	} else {
		tmp = Math.sin(y) * ((1.0 / y) + (0.5 * ((x * x) / y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.4e-6:
		tmp = math.sin(y) / y
	elif x <= 6.4e+151:
		tmp = math.cosh(x)
	else:
		tmp = math.sin(y) * ((1.0 / y) + (0.5 * ((x * x) / y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.4e-6)
		tmp = Float64(sin(y) / y);
	elseif (x <= 6.4e+151)
		tmp = cosh(x);
	else
		tmp = Float64(sin(y) * Float64(Float64(1.0 / y) + Float64(0.5 * Float64(Float64(x * x) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.4e-6)
		tmp = sin(y) / y;
	elseif (x <= 6.4e+151)
		tmp = cosh(x);
	else
		tmp = sin(y) * ((1.0 / y) + (0.5 * ((x * x) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.4e-6], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 6.4e+151], N[Cosh[x], $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] + N[(0.5 * N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.3999999999999999e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 68.0%

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

   if 2.3999999999999999e-6 < x < 6.39999999999999988e151

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.1%

      \[\leadsto \cosh x \cdot \color{blue}{1} \]

   if 6.39999999999999988e151 < x

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   3. Applied egg-rr 100.0%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 97.2%

      \[\leadsto \color{blue}{\left(\frac{1}{y} + 0.5 \cdot \frac{{x}^{2}}{y}\right)} \cdot \sin y \]
   7. Step-by-step derivation

      1. unpow2 97.2%

         \[\leadsto \left(\frac{1}{y} + 0.5 \cdot \frac{\color{blue}{x \cdot x}}{y}\right) \cdot \sin y \]

   8. Simplified 97.2%

      \[\leadsto \color{blue}{\left(\frac{1}{y} + 0.5 \cdot \frac{x \cdot x}{y}\right)} \cdot \sin y \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+151}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(\frac{1}{y} + 0.5 \cdot \frac{x \cdot x}{y}\right)\\ \end{array} \]

Alternative 4: 68.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+151}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.2e-6)
   (/ (sin y) y)
   (if (<= x 9e+151)
     (cosh x)
     (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.2e-6) {
		tmp = sin(y) / y;
	} else if (x <= 9e+151) {
		tmp = cosh(x);
	} else {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (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 <= 2.2d-6) then
        tmp = sin(y) / y
    else if (x <= 9d+151) then
        tmp = cosh(x)
    else
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.2e-6) {
		tmp = Math.sin(y) / y;
	} else if (x <= 9e+151) {
		tmp = Math.cosh(x);
	} else {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.2e-6:
		tmp = math.sin(y) / y
	elif x <= 9e+151:
		tmp = math.cosh(x)
	else:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.2e-6)
		tmp = Float64(sin(y) / y);
	elseif (x <= 9e+151)
		tmp = cosh(x);
	else
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.2e-6)
		tmp = sin(y) / y;
	elseif (x <= 9e+151)
		tmp = cosh(x);
	else
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.2e-6], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 9e+151], N[Cosh[x], $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.2000000000000001e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 68.0%

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

   if 2.2000000000000001e-6 < x < 8.9999999999999997e151

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.1%

      \[\leadsto \cosh x \cdot \color{blue}{1} \]

   if 8.9999999999999997e151 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.4%

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

      1. unpow2 91.4%

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

   4. Simplified 91.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{-6}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+151}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \end{array} \]

Alternative 5: 62.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 66.5%

   \[\leadsto \cosh x \cdot \color{blue}{1} \]

3. Final simplification 66.5%

   \[\leadsto \cosh x \]

Alternative 6: 32.4% accurate, 29.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.4%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\cosh x \cdot \frac{\sin y}{y}} \cdot \sqrt[3]{\cosh x \cdot \frac{\sin y}{y}}\right) \cdot \sqrt[3]{\cosh x \cdot \frac{\sin y}{y}}} \]

   2. pow3 99.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\cosh x \cdot \frac{\sin y}{y}}\right)}^{3}} \]

   3. *-commutative 99.4%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin y}{y} \cdot \cosh x}}\right)}^{3} \]

   4. associate-*l/ 99.4%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin y \cdot \cosh x}{y}}}\right)}^{3} \]

3. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\sin y \cdot \cosh x}{y}}\right)}^{3}} \]

4. Taylor expanded in x around 0 37.0%

   \[\leadsto {\color{blue}{\left({\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}\right)}}^{3} \]
5. Step-by-step derivation

   1. unpow1/3 49.5%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin y}{y}}\right)}}^{3} \]

6. Simplified 49.5%

   \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin y}{y}}\right)}}^{3} \]

7. Taylor expanded in y around 0 33.6%

   \[\leadsto \color{blue}{1 + -0.16666666666666666 \cdot {y}^{2}} \]
8. Step-by-step derivation

   1. *-commutative 33.6%

      \[\leadsto 1 + \color{blue}{{y}^{2} \cdot -0.16666666666666666} \]

   2. unpow2 33.6%

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

9. Simplified 33.6%

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

10. Taylor expanded in y around 0 33.6%

    \[\leadsto 1 + \color{blue}{-0.16666666666666666 \cdot {y}^{2}} \]
11. Step-by-step derivation

    1. *-commutative 33.6%

       \[\leadsto 1 + \color{blue}{{y}^{2} \cdot -0.16666666666666666} \]

    2. unpow2 33.6%

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

    3. associate-*r* 33.6%

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

12. Simplified 33.6%

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

13. Final simplification 33.6%

    \[\leadsto 1 + y \cdot \left(y \cdot -0.16666666666666666\right) \]

Alternative 7: 26.3% 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 99.9%

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

   1. add-cube-cbrt 99.4%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\cosh x \cdot \frac{\sin y}{y}} \cdot \sqrt[3]{\cosh x \cdot \frac{\sin y}{y}}\right) \cdot \sqrt[3]{\cosh x \cdot \frac{\sin y}{y}}} \]

   2. pow3 99.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\cosh x \cdot \frac{\sin y}{y}}\right)}^{3}} \]

   3. *-commutative 99.4%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin y}{y} \cdot \cosh x}}\right)}^{3} \]

   4. associate-*l/ 99.4%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin y \cdot \cosh x}{y}}}\right)}^{3} \]

3. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\sin y \cdot \cosh x}{y}}\right)}^{3}} \]

4. Taylor expanded in x around 0 37.0%

   \[\leadsto {\color{blue}{\left({\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}\right)}}^{3} \]
5. Step-by-step derivation

   1. unpow1/3 49.5%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin y}{y}}\right)}}^{3} \]

6. Simplified 49.5%

   \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin y}{y}}\right)}}^{3} \]

7. Taylor expanded in y around 0 28.6%

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

8. Final simplification 28.6%

   \[\leadsto 1 \]

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023199 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))