Linear.Quaternion:$csinh from linear-1.19.1.3

Percentage Accurate: 99.9% → 99.8%

Time: 17.2s

Alternatives: 23

Speedup: 1.0×

• 48.4% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 2: 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. Add Preprocessing
3. Add Preprocessing

Alternative 3: 94.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\\ \mathbf{if}\;x \leq 500000:\\ \;\;\;\;\left(1 + x \cdot \left(x \cdot \left(0.5 + x \cdot \left(x \cdot t\_0\right)\right)\right)\right) \cdot \frac{\sin y}{y}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+48}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x \cdot x\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot t\_0\right)}{y} \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 0.041666666666666664 (* x (* x 0.001388888888888889)))))
   (if (<= x 500000.0)
     (* (+ 1.0 (* x (* x (+ 0.5 (* x (* x t_0)))))) (/ (sin y) y))
     (if (<= x 3.6e+48)
       (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
       (* (/ (+ 1.0 (* (* x x) (+ 0.5 (* (* x x) t_0)))) y) (sin y))))))

C

double code(double x, double y) {
	double t_0 = 0.041666666666666664 + (x * (x * 0.001388888888888889));
	double tmp;
	if (x <= 500000.0) {
		tmp = (1.0 + (x * (x * (0.5 + (x * (x * t_0)))))) * (sin(y) / y);
	} else if (x <= 3.6e+48) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * t_0)))) / y) * sin(y);
	}
	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 = 0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))
    if (x <= 500000.0d0) then
        tmp = (1.0d0 + (x * (x * (0.5d0 + (x * (x * t_0)))))) * (sin(y) / y)
    else if (x <= 3.6d+48) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = ((1.0d0 + ((x * x) * (0.5d0 + ((x * x) * t_0)))) / y) * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.041666666666666664 + (x * (x * 0.001388888888888889));
	double tmp;
	if (x <= 500000.0) {
		tmp = (1.0 + (x * (x * (0.5 + (x * (x * t_0)))))) * (Math.sin(y) / y);
	} else if (x <= 3.6e+48) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * t_0)))) / y) * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.041666666666666664 + (x * (x * 0.001388888888888889))
	tmp = 0
	if x <= 500000.0:
		tmp = (1.0 + (x * (x * (0.5 + (x * (x * t_0)))))) * (math.sin(y) / y)
	elif x <= 3.6e+48:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * t_0)))) / y) * math.sin(y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889)))
	tmp = 0.0
	if (x <= 500000.0)
		tmp = Float64(Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * Float64(x * t_0)))))) * Float64(sin(y) / y));
	elseif (x <= 3.6e+48)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(Float64(x * x) * t_0)))) / y) * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.041666666666666664 + (x * (x * 0.001388888888888889));
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = (1.0 + (x * (x * (0.5 + (x * (x * t_0)))))) * (sin(y) / y);
	elseif (x <= 3.6e+48)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * t_0)))) / y) * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 500000.0], N[(N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+48], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(N[(x * x), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < 5e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5e5 < x < 3.59999999999999983e48

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 3.59999999999999983e48 < x

   1. Initial program 100.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 94.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + x \cdot \left(x \cdot \left(0.5 + x \cdot \left(x \cdot \left(0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\right)\right)\right)\right)\right) \cdot \frac{\sin y}{y}\\ \mathbf{if}\;x \leq 500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+51}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0
         (*
          (+
           1.0
           (*
            x
            (*
             x
             (+
              0.5
              (*
               x
               (*
                x
                (+ 0.041666666666666664 (* x (* x 0.001388888888888889)))))))))
          (/ (sin y) y))))
   (if (<= x 500000.0)
     t_0
     (if (<= x 7.2e+51)
       (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
       t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 + (x * (x * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))))) * (sin(y) / y);
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 7.2e+51) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = 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 = (1.0d0 + (x * (x * (0.5d0 + (x * (x * (0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))))))))) * (sin(y) / y)
    if (x <= 500000.0d0) then
        tmp = t_0
    else if (x <= 7.2d+51) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 + (x * (x * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))))) * (Math.sin(y) / y);
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 7.2e+51) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 + (x * (x * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))))) * (math.sin(y) / y)
	tmp = 0
	if x <= 500000.0:
		tmp = t_0
	elif x <= 7.2e+51:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * Float64(x * Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889))))))))) * Float64(sin(y) / y))
	tmp = 0.0
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 7.2e+51)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 + (x * (x * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))))) * (sin(y) / y);
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 7.2e+51)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * N[(x * N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 500000.0], t$95$0, If[LessEqual[x, 7.2e+51], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < 5e5 or 7.20000000000000022e51 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5e5 < x < 7.20000000000000022e51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 91.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 500000:\\ \;\;\;\;\frac{\left(1 + \left(x \cdot x\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot 0.041666666666666664\right)\right) \cdot \sin y}{y}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin y}{y} \cdot \left(1 + x \cdot \left(x \cdot \left(0.5 + x \cdot \left(x \cdot 0.041666666666666664\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 500000.0)
   (/
    (* (+ 1.0 (* (* x x) (+ 0.5 (* (* x x) 0.041666666666666664)))) (sin y))
    y)
   (if (<= x 2.5e+77)
     (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
     (*
      (/ (sin y) y)
      (+ 1.0 (* x (* x (+ 0.5 (* x (* x 0.041666666666666664))))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * 0.041666666666666664)))) * sin(y)) / y;
	} else if (x <= 2.5e+77) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = (sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 500000.0d0) then
        tmp = ((1.0d0 + ((x * x) * (0.5d0 + ((x * x) * 0.041666666666666664d0)))) * sin(y)) / y
    else if (x <= 2.5d+77) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = (sin(y) / y) * (1.0d0 + (x * (x * (0.5d0 + (x * (x * 0.041666666666666664d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * 0.041666666666666664)))) * Math.sin(y)) / y;
	} else if (x <= 2.5e+77) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = (Math.sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 500000.0:
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * 0.041666666666666664)))) * math.sin(y)) / y
	elif x <= 2.5e+77:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = (math.sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 500000.0)
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(Float64(x * x) * 0.041666666666666664)))) * sin(y)) / y);
	elseif (x <= 2.5e+77)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(Float64(sin(y) / y) * Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * Float64(x * 0.041666666666666664)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * 0.041666666666666664)))) * sin(y)) / y;
	elseif (x <= 2.5e+77)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = (sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 500000.0], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(N[(x * x), $MachinePrecision] * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 2.5e+77], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 5e5

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 5e5 < x < 2.50000000000000002e77

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 2.50000000000000002e77 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 91.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{y} \cdot \left(1 + x \cdot \left(x \cdot \left(0.5 + x \cdot \left(x \cdot 0.041666666666666664\right)\right)\right)\right)\\ \mathbf{if}\;x \leq 500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0
         (*
          (/ (sin y) y)
          (+ 1.0 (* x (* x (+ 0.5 (* x (* x 0.041666666666666664)))))))))
   (if (<= x 500000.0)
     t_0
     (if (<= x 2.5e+77)
       (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
       t_0))))

C

double code(double x, double y) {
	double t_0 = (sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 2.5e+77) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = 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 = (sin(y) / y) * (1.0d0 + (x * (x * (0.5d0 + (x * (x * 0.041666666666666664d0))))))
    if (x <= 500000.0d0) then
        tmp = t_0
    else if (x <= 2.5d+77) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (Math.sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 2.5e+77) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (math.sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))))
	tmp = 0
	if x <= 500000.0:
		tmp = t_0
	elif x <= 2.5e+77:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(sin(y) / y) * Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * Float64(x * 0.041666666666666664)))))))
	tmp = 0.0
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 2.5e+77)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (sin(y) / y) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 2.5e+77)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision] * N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 500000.0], t$95$0, If[LessEqual[x, 2.5e+77], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < 5e5 or 2.50000000000000002e77 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5e5 < x < 2.50000000000000002e77

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 86.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sin y}{\frac{y}{1 + x \cdot \left(x \cdot 0.5\right)}}\\ \mathbf{if}\;x \leq 500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+141}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sin y) (/ y (+ 1.0 (* x (* x 0.5)))))))
   (if (<= x 500000.0)
     t_0
     (if (<= x 3.5e+141)
       (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
       t_0))))

C

double code(double x, double y) {
	double t_0 = sin(y) / (y / (1.0 + (x * (x * 0.5))));
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 3.5e+141) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = 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 = sin(y) / (y / (1.0d0 + (x * (x * 0.5d0))))
    if (x <= 500000.0d0) then
        tmp = t_0
    else if (x <= 3.5d+141) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sin(y) / (y / (1.0 + (x * (x * 0.5))));
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 3.5e+141) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sin(y) / (y / (1.0 + (x * (x * 0.5))))
	tmp = 0
	if x <= 500000.0:
		tmp = t_0
	elif x <= 3.5e+141:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sin(y) / Float64(y / Float64(1.0 + Float64(x * Float64(x * 0.5)))))
	tmp = 0.0
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 3.5e+141)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sin(y) / (y / (1.0 + (x * (x * 0.5))));
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 3.5e+141)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] / N[(y / N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 500000.0], t$95$0, If[LessEqual[x, 3.5e+141], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < 5e5 or 3.5e141 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 5e5 < x < 3.5e141

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 84.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + x \cdot \left(0.5 \cdot x\right)\right) \cdot \frac{\sin y}{y}\\ \mathbf{if}\;x \leq 500000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+154}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (+ 1.0 (* x (* 0.5 x))) (/ (sin y) y))))
   (if (<= x 500000.0)
     t_0
     (if (<= x 1.85e+154)
       (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
       t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 + (x * (0.5 * x))) * (sin(y) / y);
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 1.85e+154) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = 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 = (1.0d0 + (x * (0.5d0 * x))) * (sin(y) / y)
    if (x <= 500000.0d0) then
        tmp = t_0
    else if (x <= 1.85d+154) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 + (x * (0.5 * x))) * (Math.sin(y) / y);
	double tmp;
	if (x <= 500000.0) {
		tmp = t_0;
	} else if (x <= 1.85e+154) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 + (x * (0.5 * x))) * (math.sin(y) / y)
	tmp = 0
	if x <= 500000.0:
		tmp = t_0
	elif x <= 1.85e+154:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 + Float64(x * Float64(0.5 * x))) * Float64(sin(y) / y))
	tmp = 0.0
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 1.85e+154)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 + (x * (0.5 * x))) * (sin(y) / y);
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = t_0;
	elseif (x <= 1.85e+154)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 + N[(x * N[(0.5 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 500000.0], t$95$0, If[LessEqual[x, 1.85e+154], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < 5e5 or 1.84999999999999997e154 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5e5 < x < 1.84999999999999997e154

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 68.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 500000:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 500000.0)
   (/ (sin y) y)
   (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = sin(y) / y;
	} 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 <= 500000.0d0) then
        tmp = sin(y) / y
    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 <= 500000.0) {
		tmp = Math.sin(y) / y;
	} else {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 500000.0:
		tmp = math.sin(y) / y
	else:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 500000.0)
		tmp = Float64(sin(y) / y);
	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 <= 500000.0)
		tmp = sin(y) / y;
	else
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 500000.0], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 5e5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 69.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.34:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+44}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x \cdot x\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\right)\right)}{y} \cdot \left(y \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.34)
   (/ (sin y) y)
   (if (<= x 6e+44)
     (cosh x)
     (*
      (/
       (+
        1.0
        (*
         (* x x)
         (+
          0.5
          (*
           (* x x)
           (+ 0.041666666666666664 (* x (* x 0.001388888888888889)))))))
       y)
      (* y (+ 1.0 (* (* y y) -0.16666666666666666)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.34) {
		tmp = sin(y) / y;
	} else if (x <= 6e+44) {
		tmp = cosh(x);
	} else {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((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 (x <= 0.34d0) then
        tmp = sin(y) / y
    else if (x <= 6d+44) then
        tmp = cosh(x)
    else
        tmp = ((1.0d0 + ((x * x) * (0.5d0 + ((x * x) * (0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))))))) / y) * (y * (1.0d0 + ((y * y) * (-0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.34) {
		tmp = Math.sin(y) / y;
	} else if (x <= 6e+44) {
		tmp = Math.cosh(x);
	} else {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.34:
		tmp = math.sin(y) / y
	elif x <= 6e+44:
		tmp = math.cosh(x)
	else:
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.34)
		tmp = Float64(sin(y) / y);
	elseif (x <= 6e+44)
		tmp = cosh(x);
	else
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(Float64(x * x) * Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889))))))) / y) * Float64(y * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.34)
		tmp = sin(y) / y;
	elseif (x <= 6e+44)
		tmp = cosh(x);
	else
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.34], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 6e+44], N[Cosh[x], $MachinePrecision], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(N[(x * x), $MachinePrecision] * N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * N[(y * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 0.340000000000000024

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 0.340000000000000024 < x < 5.99999999999999974e44

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 5.99999999999999974e44 < x

   1. Initial program 100.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 62.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6 \cdot 10^{+42}:\\ \;\;\;\;\cosh x\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x \cdot x\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\right)\right)}{y} \cdot \left(y \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.6e+42)
   (cosh x)
   (*
    (/
     (+
      1.0
      (*
       (* x x)
       (+
        0.5
        (*
         (* x x)
         (+ 0.041666666666666664 (* x (* x 0.001388888888888889)))))))
     y)
    (* y (+ 1.0 (* (* y y) -0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.6e+42) {
		tmp = cosh(x);
	} else {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((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 (x <= 2.6d+42) then
        tmp = cosh(x)
    else
        tmp = ((1.0d0 + ((x * x) * (0.5d0 + ((x * x) * (0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))))))) / y) * (y * (1.0d0 + ((y * y) * (-0.16666666666666666d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.6e+42) {
		tmp = Math.cosh(x);
	} else {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.6e+42:
		tmp = math.cosh(x)
	else:
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.6e+42)
		tmp = cosh(x);
	else
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(Float64(x * x) * Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889))))))) / y) * Float64(y * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.6e+42)
		tmp = cosh(x);
	else
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.6e+42], N[Cosh[x], $MachinePrecision], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(N[(x * x), $MachinePrecision] * N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * N[(y * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.5999999999999999e42

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 2.5999999999999999e42 < x

   1. Initial program 100.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 56.1% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 60:\\ \;\;\;\;\frac{\frac{1 + \left(x \cdot x\right) \cdot \left(0.5 + x \cdot \left(x \cdot 0.041666666666666664\right)\right)}{y}}{\frac{1 + \left(y \cdot y\right) \cdot 0.16666666666666666}{y}}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{-1}{0 - \frac{1}{1 + x \cdot \left(x \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + 0.001388888888888889 \cdot \left(x \cdot x\right)\right)\right)\right)}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+100}:\\ \;\;\;\;\left(1 + x \cdot \left(0.5 \cdot x\right)\right) \cdot \left(1 + \left(y \cdot y\right) \cdot \left(-0.16666666666666666 + \left(y \cdot y\right) \cdot 0.008333333333333333\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right) \cdot \left(1 + 0.5 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 60.0)
   (/
    (/ (+ 1.0 (* (* x x) (+ 0.5 (* x (* x 0.041666666666666664))))) y)
    (/ (+ 1.0 (* (* y y) 0.16666666666666666)) y))
   (if (<= y 3.2e+50)
     (/
      -1.0
      (-
       0.0
       (/
        1.0
        (+
         1.0
         (*
          x
          (*
           x
           (+
            0.5
            (*
             (* x x)
             (+ 0.041666666666666664 (* 0.001388888888888889 (* x x)))))))))))
     (if (<= y 3.3e+100)
       (*
        (+ 1.0 (* x (* 0.5 x)))
        (+
         1.0
         (*
          (* y y)
          (+ -0.16666666666666666 (* (* y y) 0.008333333333333333)))))
       (* (+ 1.0 (* (* y y) -0.16666666666666666)) (+ 1.0 (* 0.5 (* x x))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 60.0) {
		tmp = ((1.0 + ((x * x) * (0.5 + (x * (x * 0.041666666666666664))))) / y) / ((1.0 + ((y * y) * 0.16666666666666666)) / y);
	} else if (y <= 3.2e+50) {
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x))))))))));
	} else if (y <= 3.3e+100) {
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 60.0d0) then
        tmp = ((1.0d0 + ((x * x) * (0.5d0 + (x * (x * 0.041666666666666664d0))))) / y) / ((1.0d0 + ((y * y) * 0.16666666666666666d0)) / y)
    else if (y <= 3.2d+50) then
        tmp = (-1.0d0) / (0.0d0 - (1.0d0 / (1.0d0 + (x * (x * (0.5d0 + ((x * x) * (0.041666666666666664d0 + (0.001388888888888889d0 * (x * x))))))))))
    else if (y <= 3.3d+100) then
        tmp = (1.0d0 + (x * (0.5d0 * x))) * (1.0d0 + ((y * y) * ((-0.16666666666666666d0) + ((y * y) * 0.008333333333333333d0))))
    else
        tmp = (1.0d0 + ((y * y) * (-0.16666666666666666d0))) * (1.0d0 + (0.5d0 * (x * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 60.0) {
		tmp = ((1.0 + ((x * x) * (0.5 + (x * (x * 0.041666666666666664))))) / y) / ((1.0 + ((y * y) * 0.16666666666666666)) / y);
	} else if (y <= 3.2e+50) {
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x))))))))));
	} else if (y <= 3.3e+100) {
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 60.0:
		tmp = ((1.0 + ((x * x) * (0.5 + (x * (x * 0.041666666666666664))))) / y) / ((1.0 + ((y * y) * 0.16666666666666666)) / y)
	elif y <= 3.2e+50:
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x))))))))))
	elif y <= 3.3e+100:
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))))
	else:
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 60.0)
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(x * Float64(x * 0.041666666666666664))))) / y) / Float64(Float64(1.0 + Float64(Float64(y * y) * 0.16666666666666666)) / y));
	elseif (y <= 3.2e+50)
		tmp = Float64(-1.0 / Float64(0.0 - Float64(1.0 / Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(Float64(x * x) * Float64(0.041666666666666664 + Float64(0.001388888888888889 * Float64(x * x)))))))))));
	elseif (y <= 3.3e+100)
		tmp = Float64(Float64(1.0 + Float64(x * Float64(0.5 * x))) * Float64(1.0 + Float64(Float64(y * y) * Float64(-0.16666666666666666 + Float64(Float64(y * y) * 0.008333333333333333)))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)) * Float64(1.0 + Float64(0.5 * Float64(x * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 60.0)
		tmp = ((1.0 + ((x * x) * (0.5 + (x * (x * 0.041666666666666664))))) / y) / ((1.0 + ((y * y) * 0.16666666666666666)) / y);
	elseif (y <= 3.2e+50)
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x))))))))));
	elseif (y <= 3.3e+100)
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))));
	else
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 60.0], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(x * N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / N[(N[(1.0 + N[(N[(y * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+50], N[(-1.0 / N[(0.0 - N[(1.0 / N[(1.0 + N[(x * N[(x * N[(0.5 + N[(N[(x * x), $MachinePrecision] * N[(0.041666666666666664 + N[(0.001388888888888889 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+100], N[(N[(1.0 + N[(x * N[(0.5 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(y * y), $MachinePrecision] * N[(-0.16666666666666666 + N[(N[(y * y), $MachinePrecision] * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 60

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 60 < y < 3.19999999999999983e50

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 3.19999999999999983e50 < y < 3.3000000000000001e100

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.3000000000000001e100 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 58.9% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{-157}:\\ \;\;\;\;\frac{1 + \left(x \cdot x\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\right)\right)}{y} \cdot y\\ \mathbf{elif}\;y \leq 200000000000:\\ \;\;\;\;\left(-0.16666666666666666 \cdot \left(y \cdot y\right) + 1\right) \cdot \left(1 + x \cdot \left(x \cdot \left(0.5 + x \cdot \left(x \cdot 0.041666666666666664\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+100}:\\ \;\;\;\;\left(1 + x \cdot \left(0.5 \cdot x\right)\right) \cdot \left(1 + \left(y \cdot y\right) \cdot \left(-0.16666666666666666 + \left(y \cdot y\right) \cdot 0.008333333333333333\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right) \cdot \left(1 + 0.5 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1e-157)
   (*
    (/
     (+
      1.0
      (*
       (* x x)
       (+
        0.5
        (*
         (* x x)
         (+ 0.041666666666666664 (* x (* x 0.001388888888888889)))))))
     y)
    y)
   (if (<= y 200000000000.0)
     (*
      (+ (* -0.16666666666666666 (* y y)) 1.0)
      (+ 1.0 (* x (* x (+ 0.5 (* x (* x 0.041666666666666664)))))))
     (if (<= y 3.3e+100)
       (*
        (+ 1.0 (* x (* 0.5 x)))
        (+
         1.0
         (*
          (* y y)
          (+ -0.16666666666666666 (* (* y y) 0.008333333333333333)))))
       (* (+ 1.0 (* (* y y) -0.16666666666666666)) (+ 1.0 (* 0.5 (* x x))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1e-157) {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * y;
	} else if (y <= 200000000000.0) {
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	} else if (y <= 3.3e+100) {
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	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-157) then
        tmp = ((1.0d0 + ((x * x) * (0.5d0 + ((x * x) * (0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))))))) / y) * y
    else if (y <= 200000000000.0d0) then
        tmp = (((-0.16666666666666666d0) * (y * y)) + 1.0d0) * (1.0d0 + (x * (x * (0.5d0 + (x * (x * 0.041666666666666664d0))))))
    else if (y <= 3.3d+100) then
        tmp = (1.0d0 + (x * (0.5d0 * x))) * (1.0d0 + ((y * y) * ((-0.16666666666666666d0) + ((y * y) * 0.008333333333333333d0))))
    else
        tmp = (1.0d0 + ((y * y) * (-0.16666666666666666d0))) * (1.0d0 + (0.5d0 * (x * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1e-157) {
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * y;
	} else if (y <= 200000000000.0) {
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	} else if (y <= 3.3e+100) {
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1e-157:
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * y
	elif y <= 200000000000.0:
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))))
	elif y <= 3.3e+100:
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))))
	else:
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1e-157)
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(Float64(x * x) * Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889))))))) / y) * y);
	elseif (y <= 200000000000.0)
		tmp = Float64(Float64(Float64(-0.16666666666666666 * Float64(y * y)) + 1.0) * Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * Float64(x * 0.041666666666666664)))))));
	elseif (y <= 3.3e+100)
		tmp = Float64(Float64(1.0 + Float64(x * Float64(0.5 * x))) * Float64(1.0 + Float64(Float64(y * y) * Float64(-0.16666666666666666 + Float64(Float64(y * y) * 0.008333333333333333)))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)) * Float64(1.0 + Float64(0.5 * Float64(x * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1e-157)
		tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * y;
	elseif (y <= 200000000000.0)
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	elseif (y <= 3.3e+100)
		tmp = (1.0 + (x * (0.5 * x))) * (1.0 + ((y * y) * (-0.16666666666666666 + ((y * y) * 0.008333333333333333))));
	else
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1e-157], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(N[(x * x), $MachinePrecision] * N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 200000000000.0], N[(N[(N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] * N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+100], N[(N[(1.0 + N[(x * N[(0.5 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(y * y), $MachinePrecision] * N[(-0.16666666666666666 + N[(N[(y * y), $MachinePrecision] * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 9.99999999999999943e-158

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 9.99999999999999943e-158 < y < 2e11

   1. Initial program 99.9%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 2e11 < y < 3.3000000000000001e100

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 3.3000000000000001e100 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 14: 51.4% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 500000:\\ \;\;\;\;\frac{1 + x \cdot \left(x \cdot 0.5\right)}{1 + \left(y \cdot y\right) \cdot 0.16666666666666666}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{51.42857142857143 + \left(x \cdot x\right) \cdot 25.714285714285715}{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+177}:\\ \;\;\;\;1 + x \cdot \left(x \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + 0.001388888888888889 \cdot \left(x \cdot x\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right) \cdot \left(1 + 0.5 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 500000.0)
   (/ (+ 1.0 (* x (* x 0.5))) (+ 1.0 (* (* y y) 0.16666666666666666)))
   (if (<= x 7.2e+69)
     (/
      (+ 51.42857142857143 (* (* x x) 25.714285714285715))
      (* (* y y) (* y y)))
     (if (<= x 2e+177)
       (+
        1.0
        (*
         x
         (*
          x
          (+
           0.5
           (*
            (* x x)
            (+ 0.041666666666666664 (* 0.001388888888888889 (* x x))))))))
       (* (+ 1.0 (* (* y y) -0.16666666666666666)) (+ 1.0 (* 0.5 (* x x))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666));
	} else if (x <= 7.2e+69) {
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y));
	} else if (x <= 2e+177) {
		tmp = 1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x)))))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 500000.0d0) then
        tmp = (1.0d0 + (x * (x * 0.5d0))) / (1.0d0 + ((y * y) * 0.16666666666666666d0))
    else if (x <= 7.2d+69) then
        tmp = (51.42857142857143d0 + ((x * x) * 25.714285714285715d0)) / ((y * y) * (y * y))
    else if (x <= 2d+177) then
        tmp = 1.0d0 + (x * (x * (0.5d0 + ((x * x) * (0.041666666666666664d0 + (0.001388888888888889d0 * (x * x)))))))
    else
        tmp = (1.0d0 + ((y * y) * (-0.16666666666666666d0))) * (1.0d0 + (0.5d0 * (x * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666));
	} else if (x <= 7.2e+69) {
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y));
	} else if (x <= 2e+177) {
		tmp = 1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x)))))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 500000.0:
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666))
	elif x <= 7.2e+69:
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y))
	elif x <= 2e+177:
		tmp = 1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x)))))))
	else:
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 500000.0)
		tmp = Float64(Float64(1.0 + Float64(x * Float64(x * 0.5))) / Float64(1.0 + Float64(Float64(y * y) * 0.16666666666666666)));
	elseif (x <= 7.2e+69)
		tmp = Float64(Float64(51.42857142857143 + Float64(Float64(x * x) * 25.714285714285715)) / Float64(Float64(y * y) * Float64(y * y)));
	elseif (x <= 2e+177)
		tmp = Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(Float64(x * x) * Float64(0.041666666666666664 + Float64(0.001388888888888889 * Float64(x * x))))))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)) * Float64(1.0 + Float64(0.5 * Float64(x * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666));
	elseif (x <= 7.2e+69)
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y));
	elseif (x <= 2e+177)
		tmp = 1.0 + (x * (x * (0.5 + ((x * x) * (0.041666666666666664 + (0.001388888888888889 * (x * x)))))));
	else
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 500000.0], N[(N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e+69], N[(N[(51.42857142857143 + N[(N[(x * x), $MachinePrecision] * 25.714285714285715), $MachinePrecision]), $MachinePrecision] / N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+177], N[(1.0 + N[(x * N[(x * N[(0.5 + N[(N[(x * x), $MachinePrecision] * N[(0.041666666666666664 + N[(0.001388888888888889 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 5e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 5e5 < x < 7.2000000000000005e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 7.2000000000000005e69 < x < 2e177

   1. Initial program 100.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 2e177 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 15: 50.7% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 500000:\\ \;\;\;\;\frac{1 + x \cdot \left(x \cdot 0.5\right)}{1 + \left(y \cdot y\right) \cdot 0.16666666666666666}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+58}:\\ \;\;\;\;\frac{51.42857142857143 + \left(x \cdot x\right) \cdot 25.714285714285715}{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(-0.16666666666666666 \cdot \left(y \cdot y\right) + 1\right) \cdot \left(1 + x \cdot \left(x \cdot \left(0.5 + x \cdot \left(x \cdot 0.041666666666666664\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 500000.0)
   (/ (+ 1.0 (* x (* x 0.5))) (+ 1.0 (* (* y y) 0.16666666666666666)))
   (if (<= x 3.3e+58)
     (/
      (+ 51.42857142857143 (* (* x x) 25.714285714285715))
      (* (* y y) (* y y)))
     (*
      (+ (* -0.16666666666666666 (* y y)) 1.0)
      (+ 1.0 (* x (* x (+ 0.5 (* x (* x 0.041666666666666664))))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666));
	} else if (x <= 3.3e+58) {
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y));
	} else {
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 500000.0d0) then
        tmp = (1.0d0 + (x * (x * 0.5d0))) / (1.0d0 + ((y * y) * 0.16666666666666666d0))
    else if (x <= 3.3d+58) then
        tmp = (51.42857142857143d0 + ((x * x) * 25.714285714285715d0)) / ((y * y) * (y * y))
    else
        tmp = (((-0.16666666666666666d0) * (y * y)) + 1.0d0) * (1.0d0 + (x * (x * (0.5d0 + (x * (x * 0.041666666666666664d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 500000.0) {
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666));
	} else if (x <= 3.3e+58) {
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y));
	} else {
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 500000.0:
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666))
	elif x <= 3.3e+58:
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y))
	else:
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 500000.0)
		tmp = Float64(Float64(1.0 + Float64(x * Float64(x * 0.5))) / Float64(1.0 + Float64(Float64(y * y) * 0.16666666666666666)));
	elseif (x <= 3.3e+58)
		tmp = Float64(Float64(51.42857142857143 + Float64(Float64(x * x) * 25.714285714285715)) / Float64(Float64(y * y) * Float64(y * y)));
	else
		tmp = Float64(Float64(Float64(-0.16666666666666666 * Float64(y * y)) + 1.0) * Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(x * Float64(x * 0.041666666666666664)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 500000.0)
		tmp = (1.0 + (x * (x * 0.5))) / (1.0 + ((y * y) * 0.16666666666666666));
	elseif (x <= 3.3e+58)
		tmp = (51.42857142857143 + ((x * x) * 25.714285714285715)) / ((y * y) * (y * y));
	else
		tmp = ((-0.16666666666666666 * (y * y)) + 1.0) * (1.0 + (x * (x * (0.5 + (x * (x * 0.041666666666666664))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 500000.0], N[(N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+58], N[(N[(51.42857142857143 + N[(N[(x * x), $MachinePrecision] * 25.714285714285715), $MachinePrecision]), $MachinePrecision] / N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] * N[(1.0 + N[(x * N[(x * N[(0.5 + N[(x * N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 5e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 5e5 < x < 3.29999999999999983e58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 3.29999999999999983e58 < x

   1. Initial program 100.0%

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

   4. Applied egg-rr 0

      \[\leadsto expr\]

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 60.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \frac{1 + \left(x \cdot x\right) \cdot \left(0.5 + \left(x \cdot x\right) \cdot \left(0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\right)\right)}{y} \cdot \left(y \cdot \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (*
  (/
   (+
    1.0
    (*
     (* x x)
     (+
      0.5
      (* (* x x) (+ 0.041666666666666664 (* x (* x 0.001388888888888889)))))))
   y)
  (* y (+ 1.0 (* (* y y) -0.16666666666666666)))))

C

double code(double x, double y) {
	return ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (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 + ((x * x) * (0.5d0 + ((x * x) * (0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))))))) / y) * (y * (1.0d0 + ((y * y) * (-0.16666666666666666d0))))
end function

Java

public static double code(double x, double y) {
	return ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)));
}

Python

def code(x, y):
	return ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)))

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(Float64(x * x) * Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889))))))) / y) * Float64(y * Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666))))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 + ((x * x) * (0.5 + ((x * x) * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))) / y) * (y * (1.0 + ((y * y) * -0.16666666666666666)));
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(N[(x * x), $MachinePrecision] * N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] * N[(y * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

5. Taylor expanded in x around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]
11. Add Preprocessing

Alternative 17: 58.5% accurate, 7.6× speedup

Math

\[\begin{array}{l} \\ \left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right) \cdot \left(1 + \left(x \cdot x\right) \cdot \left(0.5 + x \cdot \left(x \cdot \left(0.041666666666666664 + x \cdot \left(x \cdot 0.001388888888888889\right)\right)\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (*
  (+ 1.0 (* (* y y) -0.16666666666666666))
  (+
   1.0
   (*
    (* x x)
    (+
     0.5
     (* x (* x (+ 0.041666666666666664 (* x (* x 0.001388888888888889))))))))))

C

double code(double x, double y) {
	return (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + ((x * x) * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + ((y * y) * (-0.16666666666666666d0))) * (1.0d0 + ((x * x) * (0.5d0 + (x * (x * (0.041666666666666664d0 + (x * (x * 0.001388888888888889d0))))))))
end function

Java

public static double code(double x, double y) {
	return (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + ((x * x) * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))));
}

Python

def code(x, y):
	return (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + ((x * x) * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))))

Julia

function code(x, y)
	return Float64(Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)) * Float64(1.0 + Float64(Float64(x * x) * Float64(0.5 + Float64(x * Float64(x * Float64(0.041666666666666664 + Float64(x * Float64(x * 0.001388888888888889)))))))))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + ((x * x) * (0.5 + (x * (x * (0.041666666666666664 + (x * (x * 0.001388888888888889))))))));
end

Wolfram

code[x_, y_] := N[(N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(0.5 + N[(x * N[(x * N[(0.041666666666666664 + N[(x * N[(x * 0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

4. Applied egg-rr 0

   \[\leadsto expr\]

5. Taylor expanded in x around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]

8. Taylor expanded in y around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]
11. Add Preprocessing

Alternative 18: 54.9% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.9 \cdot 10^{+96}:\\ \;\;\;\;1 + x \cdot \left(x \cdot \left(0.5 + \left(0.041666666666666664 \cdot x\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(y \cdot y\right) \cdot -0.16666666666666666\right) \cdot \left(1 + 0.5 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.9e+96)
   (+ 1.0 (* x (* x (+ 0.5 (* (* 0.041666666666666664 x) x)))))
   (* (+ 1.0 (* (* y y) -0.16666666666666666)) (+ 1.0 (* 0.5 (* x x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.9e+96) {
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4.9d+96) then
        tmp = 1.0d0 + (x * (x * (0.5d0 + ((0.041666666666666664d0 * x) * x))))
    else
        tmp = (1.0d0 + ((y * y) * (-0.16666666666666666d0))) * (1.0d0 + (0.5d0 * (x * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.9e+96) {
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
	} else {
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.9e+96:
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))))
	else:
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.9e+96)
		tmp = Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(Float64(0.041666666666666664 * x) * x)))));
	else
		tmp = Float64(Float64(1.0 + Float64(Float64(y * y) * -0.16666666666666666)) * Float64(1.0 + Float64(0.5 * Float64(x * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.9e+96)
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
	else
		tmp = (1.0 + ((y * y) * -0.16666666666666666)) * (1.0 + (0.5 * (x * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.9e+96], N[(1.0 + N[(x * N[(x * N[(0.5 + N[(N[(0.041666666666666664 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.8999999999999996e96

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 4.8999999999999996e96 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 53.3% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.9 \cdot 10^{+96}:\\ \;\;\;\;1 + x \cdot \left(x \cdot \left(0.5 + \left(0.041666666666666664 \cdot x\right) \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{0 - \frac{1}{1 + x \cdot \left(x \cdot 0.5\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.9e+96)
   (+ 1.0 (* x (* x (+ 0.5 (* (* 0.041666666666666664 x) x)))))
   (/ -1.0 (- 0.0 (/ 1.0 (+ 1.0 (* x (* x 0.5))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.9e+96) {
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
	} else {
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 4.9d+96) then
        tmp = 1.0d0 + (x * (x * (0.5d0 + ((0.041666666666666664d0 * x) * x))))
    else
        tmp = (-1.0d0) / (0.0d0 - (1.0d0 / (1.0d0 + (x * (x * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.9e+96) {
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
	} else {
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.9e+96:
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))))
	else:
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * 0.5)))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.9e+96)
		tmp = Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(Float64(0.041666666666666664 * x) * x)))));
	else
		tmp = Float64(-1.0 / Float64(0.0 - Float64(1.0 / Float64(1.0 + Float64(x * Float64(x * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.9e+96)
		tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
	else
		tmp = -1.0 / (0.0 - (1.0 / (1.0 + (x * (x * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.9e+96], N[(1.0 + N[(x * N[(x * N[(0.5 + N[(N[(0.041666666666666664 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(0.0 - N[(1.0 / N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.8999999999999996e96

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if 4.8999999999999996e96 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 54.3% accurate, 15.8× speedup

Math

\[\begin{array}{l} \\ 1 + x \cdot \left(x \cdot \left(0.5 + \left(0.041666666666666664 \cdot x\right) \cdot x\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (+ 1.0 (* x (* x (+ 0.5 (* (* 0.041666666666666664 x) x))))))

C

double code(double x, double y) {
	return 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 + (x * (x * (0.5d0 + ((0.041666666666666664d0 * x) * x))))
end function

Java

public static double code(double x, double y) {
	return 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
}

Python

def code(x, y):
	return 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))))

Julia

function code(x, y)
	return Float64(1.0 + Float64(x * Float64(x * Float64(0.5 + Float64(Float64(0.041666666666666664 * x) * x)))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 + (x * (x * (0.5 + ((0.041666666666666664 * x) * x))));
end

Wolfram

code[x_, y_] := N[(1.0 + N[(x * N[(x * N[(0.5 + N[(N[(0.041666666666666664 * x), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

7. Applied egg-rr 0

   \[\leadsto expr\]

8. Taylor expanded in x around 0 0

   \[\leadsto expr\]

10. Simplified 0

    \[\leadsto expr\]
11. Add Preprocessing

Alternative 21: 36.3% accurate, 20.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00022:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 0.00022) 1.0 (* x (* x 0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00022) {
		tmp = 1.0;
	} else {
		tmp = x * (x * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00022d0) then
        tmp = 1.0d0
    else
        tmp = x * (x * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00022) {
		tmp = 1.0;
	} else {
		tmp = x * (x * 0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00022:
		tmp = 1.0
	else:
		tmp = x * (x * 0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00022)
		tmp = 1.0;
	else
		tmp = Float64(x * Float64(x * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00022)
		tmp = 1.0;
	else
		tmp = x * (x * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00022], 1.0, N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.20000000000000008e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   if 2.20000000000000008e-4 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   9. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 45.8% accurate, 29.3× speedup

Math

\[\begin{array}{l} \\ 1 + 0.5 \cdot \left(x \cdot x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ 1.0 (* 0.5 (* x x))))

C

double code(double x, double y) {
	return 1.0 + (0.5 * (x * x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 + (0.5d0 * (x * x))
end function

Java

public static double code(double x, double y) {
	return 1.0 + (0.5 * (x * x));
}

Python

def code(x, y):
	return 1.0 + (0.5 * (x * x))

Julia

function code(x, y)
	return Float64(1.0 + Float64(0.5 * Float64(x * x)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 + (0.5 * (x * x));
end

Wolfram

code[x_, y_] := N[(1.0 + N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in x around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 23: 27.5% 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. Add Preprocessing

3. Taylor expanded in y around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]

6. Taylor expanded in x around 0 0

   \[\leadsto expr\]

8. Simplified 0

   \[\leadsto expr\]
9. Add Preprocessing

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 2024110 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

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

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