Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 18.7s

Alternatives: 22

Speedup: 1.0×

• 49.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 80.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot y\right) \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq 8.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{\left(1 - 0.027777777777777776 \cdot t\_0\right) \cdot \cos x}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+51}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot y\right) \cdot t\_0\right) \cdot \left(0.0001984126984126984 \cdot \cos x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (* y y) (* y y))))
   (if (<= y 8.6e-5)
     (/
      (* (- 1.0 (* 0.027777777777777776 t_0)) (cos x))
      (+ 1.0 (* -0.16666666666666666 (* y y))))
     (if (<= y 2.4e+51)
       (/ (sinh y) y)
       (* (* (* y y) t_0) (* 0.0001984126984126984 (cos x)))))))

C

double code(double x, double y) {
	double t_0 = (y * y) * (y * y);
	double tmp;
	if (y <= 8.6e-5) {
		tmp = ((1.0 - (0.027777777777777776 * t_0)) * cos(x)) / (1.0 + (-0.16666666666666666 * (y * y)));
	} else if (y <= 2.4e+51) {
		tmp = sinh(y) / y;
	} else {
		tmp = ((y * y) * t_0) * (0.0001984126984126984 * cos(x));
	}
	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 = (y * y) * (y * y)
    if (y <= 8.6d-5) then
        tmp = ((1.0d0 - (0.027777777777777776d0 * t_0)) * cos(x)) / (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else if (y <= 2.4d+51) then
        tmp = sinh(y) / y
    else
        tmp = ((y * y) * t_0) * (0.0001984126984126984d0 * cos(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * y) * (y * y);
	double tmp;
	if (y <= 8.6e-5) {
		tmp = ((1.0 - (0.027777777777777776 * t_0)) * Math.cos(x)) / (1.0 + (-0.16666666666666666 * (y * y)));
	} else if (y <= 2.4e+51) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = ((y * y) * t_0) * (0.0001984126984126984 * Math.cos(x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * y) * (y * y)
	tmp = 0
	if y <= 8.6e-5:
		tmp = ((1.0 - (0.027777777777777776 * t_0)) * math.cos(x)) / (1.0 + (-0.16666666666666666 * (y * y)))
	elif y <= 2.4e+51:
		tmp = math.sinh(y) / y
	else:
		tmp = ((y * y) * t_0) * (0.0001984126984126984 * math.cos(x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * y) * Float64(y * y))
	tmp = 0.0
	if (y <= 8.6e-5)
		tmp = Float64(Float64(Float64(1.0 - Float64(0.027777777777777776 * t_0)) * cos(x)) / Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	elseif (y <= 2.4e+51)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(Float64(Float64(y * y) * t_0) * Float64(0.0001984126984126984 * cos(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * y) * (y * y);
	tmp = 0.0;
	if (y <= 8.6e-5)
		tmp = ((1.0 - (0.027777777777777776 * t_0)) * cos(x)) / (1.0 + (-0.16666666666666666 * (y * y)));
	elseif (y <= 2.4e+51)
		tmp = sinh(y) / y;
	else
		tmp = ((y * y) * t_0) * (0.0001984126984126984 * cos(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 8.6e-5], N[(N[(N[(1.0 - N[(0.027777777777777776 * t$95$0), $MachinePrecision]), $MachinePrecision] * N[Cos[x], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+51], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(y * y), $MachinePrecision] * t$95$0), $MachinePrecision] * N[(0.0001984126984126984 * N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.6000000000000003e-5

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 8.6000000000000003e-5 < y < 2.3999999999999999e51

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 2.3999999999999999e51 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

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

Alternative 3: 86.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.6 \cdot 10^{-5}:\\ \;\;\;\;\cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+51}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left(0.0001984126984126984 \cdot \cos x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8.6e-5)
   (* (cos x) (+ 1.0 (* 0.16666666666666666 (* y y))))
   (if (<= y 2e+51)
     (/ (sinh y) y)
     (* (* (* y y) (* (* y y) (* y y))) (* 0.0001984126984126984 (cos x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.6e-5) {
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else if (y <= 2e+51) {
		tmp = sinh(y) / y;
	} else {
		tmp = ((y * y) * ((y * y) * (y * y))) * (0.0001984126984126984 * cos(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 <= 8.6d-5) then
        tmp = cos(x) * (1.0d0 + (0.16666666666666666d0 * (y * y)))
    else if (y <= 2d+51) then
        tmp = sinh(y) / y
    else
        tmp = ((y * y) * ((y * y) * (y * y))) * (0.0001984126984126984d0 * cos(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 8.6e-5) {
		tmp = Math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else if (y <= 2e+51) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = ((y * y) * ((y * y) * (y * y))) * (0.0001984126984126984 * Math.cos(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.6e-5:
		tmp = math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)))
	elif y <= 2e+51:
		tmp = math.sinh(y) / y
	else:
		tmp = ((y * y) * ((y * y) * (y * y))) * (0.0001984126984126984 * math.cos(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.6e-5)
		tmp = Float64(cos(x) * Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))));
	elseif (y <= 2e+51)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(Float64(Float64(y * y) * Float64(Float64(y * y) * Float64(y * y))) * Float64(0.0001984126984126984 * cos(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8.6e-5)
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	elseif (y <= 2e+51)
		tmp = sinh(y) / y;
	else
		tmp = ((y * y) * ((y * y) * (y * y))) * (0.0001984126984126984 * cos(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.6e-5], N[(N[Cos[x], $MachinePrecision] * N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+51], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.0001984126984126984 * N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.6000000000000003e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 8.6000000000000003e-5 < y < 2e51

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 2e51 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

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

Alternative 4: 86.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.6 \cdot 10^{-5}:\\ \;\;\;\;\cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{\left(1 + \left(x \cdot x\right) \cdot -0.5\right) \cdot \sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(1 + y \cdot \left(y \cdot \left(0.16666666666666666 + \left(y \cdot y\right) \cdot 0.008333333333333333\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8.6e-5)
   (* (cos x) (+ 1.0 (* 0.16666666666666666 (* y y))))
   (if (<= y 3.8e+77)
     (/ (* (+ 1.0 (* (* x x) -0.5)) (sinh y)) y)
     (*
      (cos x)
      (+
       1.0
       (*
        y
        (* y (+ 0.16666666666666666 (* (* y y) 0.008333333333333333)))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.6e-5) {
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else if (y <= 3.8e+77) {
		tmp = ((1.0 + ((x * x) * -0.5)) * sinh(y)) / y;
	} else {
		tmp = cos(x) * (1.0 + (y * (y * (0.16666666666666666 + ((y * y) * 0.008333333333333333)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 8.6d-5) then
        tmp = cos(x) * (1.0d0 + (0.16666666666666666d0 * (y * y)))
    else if (y <= 3.8d+77) then
        tmp = ((1.0d0 + ((x * x) * (-0.5d0))) * sinh(y)) / y
    else
        tmp = cos(x) * (1.0d0 + (y * (y * (0.16666666666666666d0 + ((y * y) * 0.008333333333333333d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 8.6e-5) {
		tmp = Math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else if (y <= 3.8e+77) {
		tmp = ((1.0 + ((x * x) * -0.5)) * Math.sinh(y)) / y;
	} else {
		tmp = Math.cos(x) * (1.0 + (y * (y * (0.16666666666666666 + ((y * y) * 0.008333333333333333)))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.6e-5:
		tmp = math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)))
	elif y <= 3.8e+77:
		tmp = ((1.0 + ((x * x) * -0.5)) * math.sinh(y)) / y
	else:
		tmp = math.cos(x) * (1.0 + (y * (y * (0.16666666666666666 + ((y * y) * 0.008333333333333333)))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.6e-5)
		tmp = Float64(cos(x) * Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))));
	elseif (y <= 3.8e+77)
		tmp = Float64(Float64(Float64(1.0 + Float64(Float64(x * x) * -0.5)) * sinh(y)) / y);
	else
		tmp = Float64(cos(x) * Float64(1.0 + Float64(y * Float64(y * Float64(0.16666666666666666 + Float64(Float64(y * y) * 0.008333333333333333))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8.6e-5)
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	elseif (y <= 3.8e+77)
		tmp = ((1.0 + ((x * x) * -0.5)) * sinh(y)) / y;
	else
		tmp = cos(x) * (1.0 + (y * (y * (0.16666666666666666 + ((y * y) * 0.008333333333333333)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.6e-5], N[(N[Cos[x], $MachinePrecision] * N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+77], N[(N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[Cos[x], $MachinePrecision] * N[(1.0 + N[(y * N[(y * N[(0.16666666666666666 + N[(N[(y * y), $MachinePrecision] * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.6000000000000003e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 8.6000000000000003e-5 < y < 3.8000000000000001e77

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 3.8000000000000001e77 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

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

Alternative 5: 84.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{if}\;y \leq 8.6 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+153}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (cos x) (+ 1.0 (* 0.16666666666666666 (* y y))))))
   (if (<= y 8.6e-5) t_0 (if (<= y 7e+153) (/ (sinh y) y) t_0))))

C

double code(double x, double y) {
	double t_0 = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	double tmp;
	if (y <= 8.6e-5) {
		tmp = t_0;
	} else if (y <= 7e+153) {
		tmp = sinh(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 = cos(x) * (1.0d0 + (0.16666666666666666d0 * (y * y)))
    if (y <= 8.6d-5) then
        tmp = t_0
    else if (y <= 7d+153) then
        tmp = sinh(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.cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	double tmp;
	if (y <= 8.6e-5) {
		tmp = t_0;
	} else if (y <= 7e+153) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)))
	tmp = 0
	if y <= 8.6e-5:
		tmp = t_0
	elif y <= 7e+153:
		tmp = math.sinh(y) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(cos(x) * Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))))
	tmp = 0.0
	if (y <= 8.6e-5)
		tmp = t_0;
	elseif (y <= 7e+153)
		tmp = Float64(sinh(y) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	tmp = 0.0;
	if (y <= 8.6e-5)
		tmp = t_0;
	elseif (y <= 7e+153)
		tmp = sinh(y) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Cos[x], $MachinePrecision] * N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 8.6e-5], t$95$0, If[LessEqual[y, 7e+153], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < 8.6000000000000003e-5 or 6.9999999999999998e153 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 8.6000000000000003e-5 < y < 6.9999999999999998e153

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

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

Alternative 6: 72.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-5}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 7.8e-5)
   (cos x)
   (if (<= y 3.3e+154)
     (/ (sinh y) y)
     (* (cos x) (* y (* y 0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.8e-5) {
		tmp = cos(x);
	} else if (y <= 3.3e+154) {
		tmp = sinh(y) / y;
	} else {
		tmp = cos(x) * (y * (y * 0.16666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 7.8d-5) then
        tmp = cos(x)
    else if (y <= 3.3d+154) then
        tmp = sinh(y) / y
    else
        tmp = cos(x) * (y * (y * 0.16666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 7.8e-5) {
		tmp = Math.cos(x);
	} else if (y <= 3.3e+154) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = Math.cos(x) * (y * (y * 0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.8e-5:
		tmp = math.cos(x)
	elif y <= 3.3e+154:
		tmp = math.sinh(y) / y
	else:
		tmp = math.cos(x) * (y * (y * 0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.8e-5)
		tmp = cos(x);
	elseif (y <= 3.3e+154)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(cos(x) * Float64(y * Float64(y * 0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7.8e-5)
		tmp = cos(x);
	elseif (y <= 3.3e+154)
		tmp = sinh(y) / y;
	else
		tmp = cos(x) * (y * (y * 0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.8e-5], N[Cos[x], $MachinePrecision], If[LessEqual[y, 3.3e+154], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(N[Cos[x], $MachinePrecision] * N[(y * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.7999999999999999e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 7.7999999999999999e-5 < y < 3.3e154

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 3.3e154 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around inf 0

      \[\leadsto expr\]

   8. Simplified 0

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

Alternative 7: 69.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot \left(0.008333333333333333 + \left(x \cdot x\right) \cdot -0.004166666666666667\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.1e-5)
   (cos x)
   (if (<= y 1.5e+151)
     (/ (sinh y) y)
     (*
      (* y y)
      (*
       (* y y)
       (+ 0.008333333333333333 (* (* x x) -0.004166666666666667)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.1e-5) {
		tmp = cos(x);
	} else if (y <= 1.5e+151) {
		tmp = sinh(y) / y;
	} else {
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.1d-5) then
        tmp = cos(x)
    else if (y <= 1.5d+151) then
        tmp = sinh(y) / y
    else
        tmp = (y * y) * ((y * y) * (0.008333333333333333d0 + ((x * x) * (-0.004166666666666667d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.1e-5) {
		tmp = Math.cos(x);
	} else if (y <= 1.5e+151) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.1e-5:
		tmp = math.cos(x)
	elif y <= 1.5e+151:
		tmp = math.sinh(y) / y
	else:
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.1e-5)
		tmp = cos(x);
	elseif (y <= 1.5e+151)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(Float64(y * y) * Float64(Float64(y * y) * Float64(0.008333333333333333 + Float64(Float64(x * x) * -0.004166666666666667))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.1e-5)
		tmp = cos(x);
	elseif (y <= 1.5e+151)
		tmp = sinh(y) / y;
	else
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.1e-5], N[Cos[x], $MachinePrecision], If[LessEqual[y, 1.5e+151], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] * N[(0.008333333333333333 + N[(N[(x * x), $MachinePrecision] * -0.004166666666666667), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.1e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.1e-5 < y < 1.5e151

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if 1.5e151 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

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

Alternative 8: 68.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.008333333333333333 + \left(y \cdot y\right) \cdot 0.0001984126984126984\\ t_1 := y \cdot \left(y \cdot y\right)\\ t_2 := \left(y \cdot y\right) \cdot \left(y \cdot 0.008333333333333333\right)\\ t_3 := \left(y \cdot y\right) \cdot t\_0\\ t_4 := \left(y \cdot y\right) \cdot \left(y \cdot y\right)\\ t_5 := \left(y \cdot y\right) \cdot t\_4\\ \mathbf{if}\;y \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 10^{+34}:\\ \;\;\;\;\left(1 + \left(x \cdot x\right) \cdot \left(-0.5 + x \cdot \left(x \cdot \left(0.041666666666666664 + \left(x \cdot x\right) \cdot -0.001388888888888889\right)\right)\right)\right) \cdot \left(1 + \frac{\left(0.004629629629629629 + t\_3 \cdot \left(\left(t\_4 \cdot t\_0\right) \cdot t\_0\right)\right) \cdot \left(y \cdot y\right)}{0.027777777777777776 + t\_3 \cdot \left(t\_3 - 0.16666666666666666\right)}\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \frac{\left(5.787037037037037 \cdot 10^{-7} \cdot t\_5\right) \cdot t\_1 + 0.004629629629629629 \cdot t\_1}{t\_2 \cdot t\_2 + \left(\left(y \cdot 0.16666666666666666\right) \cdot \left(y \cdot 0.16666666666666666\right) - t\_2 \cdot \left(y \cdot 0.16666666666666666\right)\right)} + 1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+79}:\\ \;\;\;\;t\_5 \cdot \left(0.0001984126984126984 + \left(-0.5 + \left(x \cdot x\right) \cdot \left(x \cdot \left(x \cdot -0.001388888888888889\right) + 0.041666666666666664\right)\right) \cdot \left(\left(x \cdot x\right) \cdot 0.0001984126984126984\right)\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(y \cdot y\right) \cdot \left(0.16666666666666666 + y \cdot \left(y \cdot \left(0.0001984126984126984 \cdot \left(y \cdot y\right) + 0.008333333333333333\right)\right)\right) + 1\right) \cdot \left(1 + \left(x \cdot x\right) \cdot \left(-0.5 + \left(x \cdot x\right) \cdot 0.041666666666666664\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot \left(0.008333333333333333 + \left(x \cdot x\right) \cdot -0.004166666666666667\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 0.008333333333333333 (* (* y y) 0.0001984126984126984)))
        (t_1 (* y (* y y)))
        (t_2 (* (* y y) (* y 0.008333333333333333)))
        (t_3 (* (* y y) t_0))
        (t_4 (* (* y y) (* y y)))
        (t_5 (* (* y y) t_4)))
   (if (<= y 1.6e-5)
     (cos x)
     (if (<= y 1e+34)
       (*
        (+
         1.0
         (*
          (* x x)
          (+
           -0.5
           (*
            x
            (*
             x
             (+ 0.041666666666666664 (* (* x x) -0.001388888888888889)))))))
        (+
         1.0
         (/
          (* (+ 0.004629629629629629 (* t_3 (* (* t_4 t_0) t_0))) (* y y))
          (+ 0.027777777777777776 (* t_3 (- t_3 0.16666666666666666))))))
       (if (<= y 6e+51)
         (+
          (*
           y
           (/
            (+
             (* (* 5.787037037037037e-7 t_5) t_1)
             (* 0.004629629629629629 t_1))
            (+
             (* t_2 t_2)
             (-
              (* (* y 0.16666666666666666) (* y 0.16666666666666666))
              (* t_2 (* y 0.16666666666666666))))))
          1.0)
         (if (<= y 4e+79)
           (*
            t_5
            (+
             0.0001984126984126984
             (*
              (+
               -0.5
               (*
                (* x x)
                (+ (* x (* x -0.001388888888888889)) 0.041666666666666664)))
              (* (* x x) 0.0001984126984126984))))
           (if (<= y 3.6e+151)
             (*
              (+
               (*
                (* y y)
                (+
                 0.16666666666666666
                 (*
                  y
                  (*
                   y
                   (+
                    (* 0.0001984126984126984 (* y y))
                    0.008333333333333333)))))
               1.0)
              (+ 1.0 (* (* x x) (+ -0.5 (* (* x x) 0.041666666666666664)))))
             (*
              (* y y)
              (*
               (* y y)
               (+
                0.008333333333333333
                (* (* x x) -0.004166666666666667)))))))))))

C

double code(double x, double y) {
	double t_0 = 0.008333333333333333 + ((y * y) * 0.0001984126984126984);
	double t_1 = y * (y * y);
	double t_2 = (y * y) * (y * 0.008333333333333333);
	double t_3 = (y * y) * t_0;
	double t_4 = (y * y) * (y * y);
	double t_5 = (y * y) * t_4;
	double tmp;
	if (y <= 1.6e-5) {
		tmp = cos(x);
	} else if (y <= 1e+34) {
		tmp = (1.0 + ((x * x) * (-0.5 + (x * (x * (0.041666666666666664 + ((x * x) * -0.001388888888888889))))))) * (1.0 + (((0.004629629629629629 + (t_3 * ((t_4 * t_0) * t_0))) * (y * y)) / (0.027777777777777776 + (t_3 * (t_3 - 0.16666666666666666)))));
	} else if (y <= 6e+51) {
		tmp = (y * ((((5.787037037037037e-7 * t_5) * t_1) + (0.004629629629629629 * t_1)) / ((t_2 * t_2) + (((y * 0.16666666666666666) * (y * 0.16666666666666666)) - (t_2 * (y * 0.16666666666666666)))))) + 1.0;
	} else if (y <= 4e+79) {
		tmp = t_5 * (0.0001984126984126984 + ((-0.5 + ((x * x) * ((x * (x * -0.001388888888888889)) + 0.041666666666666664))) * ((x * x) * 0.0001984126984126984)));
	} else if (y <= 3.6e+151) {
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))));
	} else {
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)));
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 0.008333333333333333d0 + ((y * y) * 0.0001984126984126984d0)
    t_1 = y * (y * y)
    t_2 = (y * y) * (y * 0.008333333333333333d0)
    t_3 = (y * y) * t_0
    t_4 = (y * y) * (y * y)
    t_5 = (y * y) * t_4
    if (y <= 1.6d-5) then
        tmp = cos(x)
    else if (y <= 1d+34) then
        tmp = (1.0d0 + ((x * x) * ((-0.5d0) + (x * (x * (0.041666666666666664d0 + ((x * x) * (-0.001388888888888889d0)))))))) * (1.0d0 + (((0.004629629629629629d0 + (t_3 * ((t_4 * t_0) * t_0))) * (y * y)) / (0.027777777777777776d0 + (t_3 * (t_3 - 0.16666666666666666d0)))))
    else if (y <= 6d+51) then
        tmp = (y * ((((5.787037037037037d-7 * t_5) * t_1) + (0.004629629629629629d0 * t_1)) / ((t_2 * t_2) + (((y * 0.16666666666666666d0) * (y * 0.16666666666666666d0)) - (t_2 * (y * 0.16666666666666666d0)))))) + 1.0d0
    else if (y <= 4d+79) then
        tmp = t_5 * (0.0001984126984126984d0 + (((-0.5d0) + ((x * x) * ((x * (x * (-0.001388888888888889d0))) + 0.041666666666666664d0))) * ((x * x) * 0.0001984126984126984d0)))
    else if (y <= 3.6d+151) then
        tmp = (((y * y) * (0.16666666666666666d0 + (y * (y * ((0.0001984126984126984d0 * (y * y)) + 0.008333333333333333d0))))) + 1.0d0) * (1.0d0 + ((x * x) * ((-0.5d0) + ((x * x) * 0.041666666666666664d0))))
    else
        tmp = (y * y) * ((y * y) * (0.008333333333333333d0 + ((x * x) * (-0.004166666666666667d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.008333333333333333 + ((y * y) * 0.0001984126984126984);
	double t_1 = y * (y * y);
	double t_2 = (y * y) * (y * 0.008333333333333333);
	double t_3 = (y * y) * t_0;
	double t_4 = (y * y) * (y * y);
	double t_5 = (y * y) * t_4;
	double tmp;
	if (y <= 1.6e-5) {
		tmp = Math.cos(x);
	} else if (y <= 1e+34) {
		tmp = (1.0 + ((x * x) * (-0.5 + (x * (x * (0.041666666666666664 + ((x * x) * -0.001388888888888889))))))) * (1.0 + (((0.004629629629629629 + (t_3 * ((t_4 * t_0) * t_0))) * (y * y)) / (0.027777777777777776 + (t_3 * (t_3 - 0.16666666666666666)))));
	} else if (y <= 6e+51) {
		tmp = (y * ((((5.787037037037037e-7 * t_5) * t_1) + (0.004629629629629629 * t_1)) / ((t_2 * t_2) + (((y * 0.16666666666666666) * (y * 0.16666666666666666)) - (t_2 * (y * 0.16666666666666666)))))) + 1.0;
	} else if (y <= 4e+79) {
		tmp = t_5 * (0.0001984126984126984 + ((-0.5 + ((x * x) * ((x * (x * -0.001388888888888889)) + 0.041666666666666664))) * ((x * x) * 0.0001984126984126984)));
	} else if (y <= 3.6e+151) {
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))));
	} else {
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.008333333333333333 + ((y * y) * 0.0001984126984126984)
	t_1 = y * (y * y)
	t_2 = (y * y) * (y * 0.008333333333333333)
	t_3 = (y * y) * t_0
	t_4 = (y * y) * (y * y)
	t_5 = (y * y) * t_4
	tmp = 0
	if y <= 1.6e-5:
		tmp = math.cos(x)
	elif y <= 1e+34:
		tmp = (1.0 + ((x * x) * (-0.5 + (x * (x * (0.041666666666666664 + ((x * x) * -0.001388888888888889))))))) * (1.0 + (((0.004629629629629629 + (t_3 * ((t_4 * t_0) * t_0))) * (y * y)) / (0.027777777777777776 + (t_3 * (t_3 - 0.16666666666666666)))))
	elif y <= 6e+51:
		tmp = (y * ((((5.787037037037037e-7 * t_5) * t_1) + (0.004629629629629629 * t_1)) / ((t_2 * t_2) + (((y * 0.16666666666666666) * (y * 0.16666666666666666)) - (t_2 * (y * 0.16666666666666666)))))) + 1.0
	elif y <= 4e+79:
		tmp = t_5 * (0.0001984126984126984 + ((-0.5 + ((x * x) * ((x * (x * -0.001388888888888889)) + 0.041666666666666664))) * ((x * x) * 0.0001984126984126984)))
	elif y <= 3.6e+151:
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))))
	else:
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.008333333333333333 + Float64(Float64(y * y) * 0.0001984126984126984))
	t_1 = Float64(y * Float64(y * y))
	t_2 = Float64(Float64(y * y) * Float64(y * 0.008333333333333333))
	t_3 = Float64(Float64(y * y) * t_0)
	t_4 = Float64(Float64(y * y) * Float64(y * y))
	t_5 = Float64(Float64(y * y) * t_4)
	tmp = 0.0
	if (y <= 1.6e-5)
		tmp = cos(x);
	elseif (y <= 1e+34)
		tmp = Float64(Float64(1.0 + Float64(Float64(x * x) * Float64(-0.5 + Float64(x * Float64(x * Float64(0.041666666666666664 + Float64(Float64(x * x) * -0.001388888888888889))))))) * Float64(1.0 + Float64(Float64(Float64(0.004629629629629629 + Float64(t_3 * Float64(Float64(t_4 * t_0) * t_0))) * Float64(y * y)) / Float64(0.027777777777777776 + Float64(t_3 * Float64(t_3 - 0.16666666666666666))))));
	elseif (y <= 6e+51)
		tmp = Float64(Float64(y * Float64(Float64(Float64(Float64(5.787037037037037e-7 * t_5) * t_1) + Float64(0.004629629629629629 * t_1)) / Float64(Float64(t_2 * t_2) + Float64(Float64(Float64(y * 0.16666666666666666) * Float64(y * 0.16666666666666666)) - Float64(t_2 * Float64(y * 0.16666666666666666)))))) + 1.0);
	elseif (y <= 4e+79)
		tmp = Float64(t_5 * Float64(0.0001984126984126984 + Float64(Float64(-0.5 + Float64(Float64(x * x) * Float64(Float64(x * Float64(x * -0.001388888888888889)) + 0.041666666666666664))) * Float64(Float64(x * x) * 0.0001984126984126984))));
	elseif (y <= 3.6e+151)
		tmp = Float64(Float64(Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(y * Float64(y * Float64(Float64(0.0001984126984126984 * Float64(y * y)) + 0.008333333333333333))))) + 1.0) * Float64(1.0 + Float64(Float64(x * x) * Float64(-0.5 + Float64(Float64(x * x) * 0.041666666666666664)))));
	else
		tmp = Float64(Float64(y * y) * Float64(Float64(y * y) * Float64(0.008333333333333333 + Float64(Float64(x * x) * -0.004166666666666667))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.008333333333333333 + ((y * y) * 0.0001984126984126984);
	t_1 = y * (y * y);
	t_2 = (y * y) * (y * 0.008333333333333333);
	t_3 = (y * y) * t_0;
	t_4 = (y * y) * (y * y);
	t_5 = (y * y) * t_4;
	tmp = 0.0;
	if (y <= 1.6e-5)
		tmp = cos(x);
	elseif (y <= 1e+34)
		tmp = (1.0 + ((x * x) * (-0.5 + (x * (x * (0.041666666666666664 + ((x * x) * -0.001388888888888889))))))) * (1.0 + (((0.004629629629629629 + (t_3 * ((t_4 * t_0) * t_0))) * (y * y)) / (0.027777777777777776 + (t_3 * (t_3 - 0.16666666666666666)))));
	elseif (y <= 6e+51)
		tmp = (y * ((((5.787037037037037e-7 * t_5) * t_1) + (0.004629629629629629 * t_1)) / ((t_2 * t_2) + (((y * 0.16666666666666666) * (y * 0.16666666666666666)) - (t_2 * (y * 0.16666666666666666)))))) + 1.0;
	elseif (y <= 4e+79)
		tmp = t_5 * (0.0001984126984126984 + ((-0.5 + ((x * x) * ((x * (x * -0.001388888888888889)) + 0.041666666666666664))) * ((x * x) * 0.0001984126984126984)));
	elseif (y <= 3.6e+151)
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))));
	else
		tmp = (y * y) * ((y * y) * (0.008333333333333333 + ((x * x) * -0.004166666666666667)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.008333333333333333 + N[(N[(y * y), $MachinePrecision] * 0.0001984126984126984), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * y), $MachinePrecision] * N[(y * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * y), $MachinePrecision] * t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y * y), $MachinePrecision] * t$95$4), $MachinePrecision]}, If[LessEqual[y, 1.6e-5], N[Cos[x], $MachinePrecision], If[LessEqual[y, 1e+34], N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(-0.5 + N[(x * N[(x * N[(0.041666666666666664 + N[(N[(x * x), $MachinePrecision] * -0.001388888888888889), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(N[(0.004629629629629629 + N[(t$95$3 * N[(N[(t$95$4 * t$95$0), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision] / N[(0.027777777777777776 + N[(t$95$3 * N[(t$95$3 - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+51], N[(N[(y * N[(N[(N[(N[(5.787037037037037e-7 * t$95$5), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(0.004629629629629629 * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(N[(t$95$2 * t$95$2), $MachinePrecision] + N[(N[(N[(y * 0.16666666666666666), $MachinePrecision] * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] - N[(t$95$2 * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[y, 4e+79], N[(t$95$5 * N[(0.0001984126984126984 + N[(N[(-0.5 + N[(N[(x * x), $MachinePrecision] * N[(N[(x * N[(x * -0.001388888888888889), $MachinePrecision]), $MachinePrecision] + 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(x * x), $MachinePrecision] * 0.0001984126984126984), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+151], N[(N[(N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(y * N[(y * N[(N[(0.0001984126984126984 * N[(y * y), $MachinePrecision]), $MachinePrecision] + 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(-0.5 + N[(N[(x * x), $MachinePrecision] * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * N[(N[(y * y), $MachinePrecision] * N[(0.008333333333333333 + N[(N[(x * x), $MachinePrecision] * -0.004166666666666667), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < 1.59999999999999993e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 1.59999999999999993e-5 < y < 9.99999999999999946e33

   1. Initial program 100.0%

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

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]

   if 9.99999999999999946e33 < y < 6e51

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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

       \[\leadsto expr\]

   12. Applied egg-rr 0

       \[\leadsto expr\]

   if 6e51 < y < 3.99999999999999987e79

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 y around inf 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 3.99999999999999987e79 < y < 3.6e151

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 3.6e151 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 9: 59.2% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;\left(\left(y \cdot y\right) \cdot \left(0.16666666666666666 + y \cdot \left(y \cdot \left(0.0001984126984126984 \cdot \left(y \cdot y\right) + 0.008333333333333333\right)\right)\right) + 1\right) \cdot \left(1 + \left(x \cdot x\right) \cdot \left(-0.5 + \left(x \cdot x\right) \cdot 0.041666666666666664\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (*
    (+
     (*
      (* y y)
      (+
       0.16666666666666666
       (* y (* y (+ (* 0.0001984126984126984 (* y y)) 0.008333333333333333)))))
     1.0)
    (+ 1.0 (* (* x x) (+ -0.5 (* (* x x) 0.041666666666666664)))))
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))));
	} 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 <= 4.1d+213) then
        tmp = (((y * y) * (0.16666666666666666d0 + (y * (y * ((0.0001984126984126984d0 * (y * y)) + 0.008333333333333333d0))))) + 1.0d0) * (1.0d0 + ((x * x) * ((-0.5d0) + ((x * x) * 0.041666666666666664d0))))
    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 <= 4.1e+213) {
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))));
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))))
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(Float64(Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(y * Float64(y * Float64(Float64(0.0001984126984126984 * Float64(y * y)) + 0.008333333333333333))))) + 1.0) * Float64(1.0 + Float64(Float64(x * x) * Float64(-0.5 + Float64(Float64(x * x) * 0.041666666666666664)))));
	else
		tmp = Float64(x * Float64(x * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.1e+213)
		tmp = (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0) * (1.0 + ((x * x) * (-0.5 + ((x * x) * 0.041666666666666664))));
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(N[(N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(y * N[(y * N[(N[(0.0001984126984126984 * N[(y * y), $MachinePrecision]), $MachinePrecision] + 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * N[(-0.5 + N[(N[(x * x), $MachinePrecision] * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 10: 60.3% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;\frac{y \cdot \left(\left(y \cdot y\right) \cdot \left(0.16666666666666666 + y \cdot \left(y \cdot \left(0.0001984126984126984 \cdot \left(y \cdot y\right) + 0.008333333333333333\right)\right)\right) + 1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (/
    (*
     y
     (+
      (*
       (* y y)
       (+
        0.16666666666666666
        (*
         y
         (* y (+ (* 0.0001984126984126984 (* y y)) 0.008333333333333333)))))
      1.0))
    y)
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = (y * (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0)) / y;
	} 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 <= 4.1d+213) then
        tmp = (y * (((y * y) * (0.16666666666666666d0 + (y * (y * ((0.0001984126984126984d0 * (y * y)) + 0.008333333333333333d0))))) + 1.0d0)) / y
    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 <= 4.1e+213) {
		tmp = (y * (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0)) / y;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = (y * (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0)) / y
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(Float64(y * Float64(Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(y * Float64(y * Float64(Float64(0.0001984126984126984 * Float64(y * y)) + 0.008333333333333333))))) + 1.0)) / y);
	else
		tmp = Float64(x * Float64(x * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.1e+213)
		tmp = (y * (((y * y) * (0.16666666666666666 + (y * (y * ((0.0001984126984126984 * (y * y)) + 0.008333333333333333))))) + 1.0)) / y;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(N[(y * N[(N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(y * N[(y * N[(N[(0.0001984126984126984 * N[(y * y), $MachinePrecision]), $MachinePrecision] + 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 11: 59.3% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;1 + y \cdot \left(y \cdot \left(0.16666666666666666 + \frac{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}{5040 + \frac{-211680}{y \cdot y}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (+
    1.0
    (*
     y
     (*
      y
      (+
       0.16666666666666666
       (/ (* (* y y) (* y y)) (+ 5040.0 (/ -211680.0 (* y y))))))))
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (((y * y) * (y * y)) / (5040.0 + (-211680.0 / (y * y)))))));
	} 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 <= 4.1d+213) then
        tmp = 1.0d0 + (y * (y * (0.16666666666666666d0 + (((y * y) * (y * y)) / (5040.0d0 + ((-211680.0d0) / (y * y)))))))
    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 <= 4.1e+213) {
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (((y * y) * (y * y)) / (5040.0 + (-211680.0 / (y * y)))))));
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (((y * y) * (y * y)) / (5040.0 + (-211680.0 / (y * y)))))))
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(1.0 + Float64(y * Float64(y * Float64(0.16666666666666666 + Float64(Float64(Float64(y * y) * Float64(y * y)) / Float64(5040.0 + Float64(-211680.0 / Float64(y * y))))))));
	else
		tmp = Float64(x * Float64(x * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.1e+213)
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (((y * y) * (y * y)) / (5040.0 + (-211680.0 / (y * y)))))));
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(1.0 + N[(y * N[(y * N[(0.16666666666666666 + N[(N[(N[(y * y), $MachinePrecision] * N[(y * y), $MachinePrecision]), $MachinePrecision] / N[(5040.0 + N[(-211680.0 / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 y around inf 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in x around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 12: 53.1% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \mathbf{if}\;y \leq 45000000:\\ \;\;\;\;y \cdot \left(y \cdot 0.16666666666666666\right) + 1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+78}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+153}:\\ \;\;\;\;y \cdot \left(y \cdot \left(\left(y \cdot y\right) \cdot 0.008333333333333333\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0
         (* (* y y) (+ 0.16666666666666666 (* (* x x) -0.08333333333333333)))))
   (if (<= y 45000000.0)
     (+ (* y (* y 0.16666666666666666)) 1.0)
     (if (<= y 6.8e+78)
       t_0
       (if (<= y 7e+153) (* y (* y (* (* y y) 0.008333333333333333))) t_0)))))

C

double code(double x, double y) {
	double t_0 = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	double tmp;
	if (y <= 45000000.0) {
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	} else if (y <= 6.8e+78) {
		tmp = t_0;
	} else if (y <= 7e+153) {
		tmp = y * (y * ((y * y) * 0.008333333333333333));
	} 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 = (y * y) * (0.16666666666666666d0 + ((x * x) * (-0.08333333333333333d0)))
    if (y <= 45000000.0d0) then
        tmp = (y * (y * 0.16666666666666666d0)) + 1.0d0
    else if (y <= 6.8d+78) then
        tmp = t_0
    else if (y <= 7d+153) then
        tmp = y * (y * ((y * y) * 0.008333333333333333d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	double tmp;
	if (y <= 45000000.0) {
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	} else if (y <= 6.8e+78) {
		tmp = t_0;
	} else if (y <= 7e+153) {
		tmp = y * (y * ((y * y) * 0.008333333333333333));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333))
	tmp = 0
	if y <= 45000000.0:
		tmp = (y * (y * 0.16666666666666666)) + 1.0
	elif y <= 6.8e+78:
		tmp = t_0
	elif y <= 7e+153:
		tmp = y * (y * ((y * y) * 0.008333333333333333))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(Float64(x * x) * -0.08333333333333333)))
	tmp = 0.0
	if (y <= 45000000.0)
		tmp = Float64(Float64(y * Float64(y * 0.16666666666666666)) + 1.0);
	elseif (y <= 6.8e+78)
		tmp = t_0;
	elseif (y <= 7e+153)
		tmp = Float64(y * Float64(y * Float64(Float64(y * y) * 0.008333333333333333)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	tmp = 0.0;
	if (y <= 45000000.0)
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	elseif (y <= 6.8e+78)
		tmp = t_0;
	elseif (y <= 7e+153)
		tmp = y * (y * ((y * y) * 0.008333333333333333));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(N[(x * x), $MachinePrecision] * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 45000000.0], N[(N[(y * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], If[LessEqual[y, 6.8e+78], t$95$0, If[LessEqual[y, 7e+153], N[(y * N[(y * N[(N[(y * y), $MachinePrecision] * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < 4.5e7

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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 4.5e7 < y < 6.80000000000000014e78 or 6.9999999999999998e153 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 6.80000000000000014e78 < y < 6.9999999999999998e153

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

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

Alternative 13: 59.3% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;1 + y \cdot \left(y \cdot \left(0.16666666666666666 + y \cdot \left(y \cdot \left(0.008333333333333333 + \left(y \cdot y\right) \cdot 0.0001984126984126984\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (+
    1.0
    (*
     y
     (*
      y
      (+
       0.16666666666666666
       (*
        y
        (* y (+ 0.008333333333333333 (* (* y y) 0.0001984126984126984))))))))
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (y * (y * (0.008333333333333333 + ((y * y) * 0.0001984126984126984)))))));
	} 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 <= 4.1d+213) then
        tmp = 1.0d0 + (y * (y * (0.16666666666666666d0 + (y * (y * (0.008333333333333333d0 + ((y * y) * 0.0001984126984126984d0)))))))
    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 <= 4.1e+213) {
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (y * (y * (0.008333333333333333 + ((y * y) * 0.0001984126984126984)))))));
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (y * (y * (0.008333333333333333 + ((y * y) * 0.0001984126984126984)))))))
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(1.0 + Float64(y * Float64(y * Float64(0.16666666666666666 + Float64(y * Float64(y * Float64(0.008333333333333333 + Float64(Float64(y * y) * 0.0001984126984126984))))))));
	else
		tmp = Float64(x * Float64(x * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.1e+213)
		tmp = 1.0 + (y * (y * (0.16666666666666666 + (y * (y * (0.008333333333333333 + ((y * y) * 0.0001984126984126984)))))));
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(1.0 + N[(y * N[(y * N[(0.16666666666666666 + N[(y * N[(y * N[(0.008333333333333333 + N[(N[(y * y), $MachinePrecision] * 0.0001984126984126984), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 0 0

      \[\leadsto expr\]

   11. Simplified 0

       \[\leadsto expr\]

   if 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 14: 58.3% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(0.16666666666666666 + y \cdot \left(y \cdot 0.008333333333333333\right)\right)\right) + 1\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (/
    (*
     y
     (+
      (* y (* y (+ 0.16666666666666666 (* y (* y 0.008333333333333333)))))
      1.0))
    y)
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = (y * ((y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0)) / y;
	} 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 <= 4.1d+213) then
        tmp = (y * ((y * (y * (0.16666666666666666d0 + (y * (y * 0.008333333333333333d0))))) + 1.0d0)) / y
    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 <= 4.1e+213) {
		tmp = (y * ((y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0)) / y;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = (y * ((y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0)) / y
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(Float64(y * Float64(Float64(y * Float64(y * Float64(0.16666666666666666 + Float64(y * Float64(y * 0.008333333333333333))))) + 1.0)) / y);
	else
		tmp = Float64(x * Float64(x * -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.1e+213)
		tmp = (y * ((y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0)) / y;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(N[(y * N[(N[(y * N[(y * N[(0.16666666666666666 + N[(y * N[(y * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 15: 56.8% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \left(y \cdot \left(0.16666666666666666 + y \cdot \left(y \cdot 0.008333333333333333\right)\right)\right) + 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (+ (* y (* y (+ 0.16666666666666666 (* y (* y 0.008333333333333333))))) 1.0)
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = (y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 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 <= 4.1d+213) then
        tmp = (y * (y * (0.16666666666666666d0 + (y * (y * 0.008333333333333333d0))))) + 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 <= 4.1e+213) {
		tmp = (y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = (y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(Float64(y * Float64(y * Float64(0.16666666666666666 + Float64(y * Float64(y * 0.008333333333333333))))) + 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 <= 4.1e+213)
		tmp = (y * (y * (0.16666666666666666 + (y * (y * 0.008333333333333333))))) + 1.0;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(N[(y * N[(y * N[(0.16666666666666666 + N[(y * N[(y * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 16: 56.7% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.1 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \left(y \cdot \left(\left(y \cdot y\right) \cdot 0.008333333333333333\right)\right) + 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.1e+213)
   (+ (* y (* y (* (* y y) 0.008333333333333333))) 1.0)
   (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.1e+213) {
		tmp = (y * (y * ((y * y) * 0.008333333333333333))) + 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 <= 4.1d+213) then
        tmp = (y * (y * ((y * y) * 0.008333333333333333d0))) + 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 <= 4.1e+213) {
		tmp = (y * (y * ((y * y) * 0.008333333333333333))) + 1.0;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.1e+213:
		tmp = (y * (y * ((y * y) * 0.008333333333333333))) + 1.0
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.1e+213)
		tmp = Float64(Float64(y * Float64(y * Float64(Float64(y * y) * 0.008333333333333333))) + 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 <= 4.1e+213)
		tmp = (y * (y * ((y * y) * 0.008333333333333333))) + 1.0;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.1e+213], N[(N[(y * N[(y * N[(N[(y * y), $MachinePrecision] * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0999999999999997e213

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 4.0999999999999997e213 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 17: 52.0% accurate, 14.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5:\\ \;\;\;\;y \cdot \left(y \cdot 0.16666666666666666\right) + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(\left(y \cdot y\right) \cdot 0.008333333333333333\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 5.0)
   (+ (* y (* y 0.16666666666666666)) 1.0)
   (* y (* y (* (* y y) 0.008333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 5.0) {
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	} else {
		tmp = y * (y * ((y * y) * 0.008333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 5.0d0) then
        tmp = (y * (y * 0.16666666666666666d0)) + 1.0d0
    else
        tmp = y * (y * ((y * y) * 0.008333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 5.0) {
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	} else {
		tmp = y * (y * ((y * y) * 0.008333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 5.0:
		tmp = (y * (y * 0.16666666666666666)) + 1.0
	else:
		tmp = y * (y * ((y * y) * 0.008333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 5.0)
		tmp = Float64(Float64(y * Float64(y * 0.16666666666666666)) + 1.0);
	else
		tmp = Float64(y * Float64(y * Float64(Float64(y * y) * 0.008333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.0)
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	else
		tmp = y * (y * ((y * y) * 0.008333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 5.0], N[(N[(y * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(y * N[(y * N[(N[(y * y), $MachinePrecision] * 0.008333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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 5 < y

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

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

Alternative 18: 48.6% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.4 \cdot 10^{+159}:\\ \;\;\;\;\left(y \cdot y\right) \cdot 0.16666666666666666 + 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.4e+159) (+ (* (* y y) 0.16666666666666666) 1.0) (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.4e+159) {
		tmp = ((y * y) * 0.16666666666666666) + 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 <= 3.4d+159) then
        tmp = ((y * y) * 0.16666666666666666d0) + 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 <= 3.4e+159) {
		tmp = ((y * y) * 0.16666666666666666) + 1.0;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.4e+159:
		tmp = ((y * y) * 0.16666666666666666) + 1.0
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.4e+159)
		tmp = Float64(Float64(Float64(y * y) * 0.16666666666666666) + 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 <= 3.4e+159)
		tmp = ((y * y) * 0.16666666666666666) + 1.0;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.4e+159], N[(N[(N[(y * y), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] + 1.0), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.39999999999999991e159

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if 3.39999999999999991e159 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 19: 48.6% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.4 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \left(y \cdot 0.16666666666666666\right) + 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.4e+159) (+ (* y (* y 0.16666666666666666)) 1.0) (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.4e+159) {
		tmp = (y * (y * 0.16666666666666666)) + 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 <= 3.4d+159) then
        tmp = (y * (y * 0.16666666666666666d0)) + 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 <= 3.4e+159) {
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.4e+159:
		tmp = (y * (y * 0.16666666666666666)) + 1.0
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.4e+159)
		tmp = Float64(Float64(y * Float64(y * 0.16666666666666666)) + 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 <= 3.4e+159)
		tmp = (y * (y * 0.16666666666666666)) + 1.0;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.4e+159], N[(N[(y * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.39999999999999991e159

   1. Initial program 100.0%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   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 3.39999999999999991e159 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 20: 32.3% accurate, 20.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 86000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 86000000.0) 1.0 (* x (* x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 86000000.0) {
		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 (y <= 86000000.0d0) 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 (y <= 86000000.0) {
		tmp = 1.0;
	} else {
		tmp = x * (x * -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 86000000.0:
		tmp = 1.0
	else:
		tmp = x * (x * -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 86000000.0)
		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 (y <= 86000000.0)
		tmp = 1.0;
	else
		tmp = x * (x * -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 86000000.0], 1.0, N[(x * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.6e7

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 8.6e7 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   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 21: 33.3% 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 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]
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 22: 29.4% 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 100.0%

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

Reproduce

herbie shell --seed 2024110 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))