Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

Alternatives: 10

Speedup: 1.0×

• 48.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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. Final simplification 100.0%

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

Alternative 2: 84.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.29 \lor \neg \left(y \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;\cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y 0.29) (not (<= y 5.4e+149)))
   (* (cos x) (+ 1.0 (* 0.16666666666666666 (* y y))))
   (/ (sinh y) y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= 0.29) || !(y <= 5.4e+149)) {
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else {
		tmp = sinh(y) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= 0.29d0) .or. (.not. (y <= 5.4d+149))) then
        tmp = cos(x) * (1.0d0 + (0.16666666666666666d0 * (y * y)))
    else
        tmp = sinh(y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= 0.29) || !(y <= 5.4e+149)) {
		tmp = Math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else {
		tmp = Math.sinh(y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= 0.29) or not (y <= 5.4e+149):
		tmp = math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)))
	else:
		tmp = math.sinh(y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= 0.29) || !(y <= 5.4e+149))
		tmp = Float64(cos(x) * Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))));
	else
		tmp = Float64(sinh(y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= 0.29) || ~((y <= 5.4e+149)))
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	else
		tmp = sinh(y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, 0.29], N[Not[LessEqual[y, 5.4e+149]], $MachinePrecision]], N[(N[Cos[x], $MachinePrecision] * N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.28999999999999998 or 5.4000000000000002e149 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.2%

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

      1. unpow2 87.2%

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

   4. Simplified 87.2%

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

   if 0.28999999999999998 < y < 5.4000000000000002e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 85.7%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 85.7%

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

      2. associate-/r/ 85.7%

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

      3. rec-exp 85.7%

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

      4. sinh-def 85.7%

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

   6. Simplified 85.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{\sinh y}}} \]
   7. Step-by-step derivation

      1. add-log-exp 85.7%

         \[\leadsto \color{blue}{\log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      2. *-un-lft-identity 85.7%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      3. log-prod 85.7%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      4. metadata-eval 85.7%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right) \]

      5. add-log-exp 85.7%

         \[\leadsto 0 + \color{blue}{\frac{1}{\frac{y}{\sinh y}}} \]

      6. clear-num 85.7%

         \[\leadsto 0 + \color{blue}{\frac{\sinh y}{y}} \]

   8. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{0 + \frac{\sinh y}{y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 85.7%

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

   10. Simplified 85.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.29 \lor \neg \left(y \leq 5.4 \cdot 10^{+149}\right):\\ \;\;\;\;\cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \]

Alternative 3: 72.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.29:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot \left(\cos x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 0.29)
   (cos x)
   (if (<= y 5.4e+149)
     (/ (sinh y) y)
     (* 0.16666666666666666 (* y (* (cos x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.29) {
		tmp = cos(x);
	} else if (y <= 5.4e+149) {
		tmp = sinh(y) / y;
	} else {
		tmp = 0.16666666666666666 * (y * (cos(x) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 0.29d0) then
        tmp = cos(x)
    else if (y <= 5.4d+149) then
        tmp = sinh(y) / y
    else
        tmp = 0.16666666666666666d0 * (y * (cos(x) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 0.29) {
		tmp = Math.cos(x);
	} else if (y <= 5.4e+149) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = 0.16666666666666666 * (y * (Math.cos(x) * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.29:
		tmp = math.cos(x)
	elif y <= 5.4e+149:
		tmp = math.sinh(y) / y
	else:
		tmp = 0.16666666666666666 * (y * (math.cos(x) * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.29)
		tmp = cos(x);
	elseif (y <= 5.4e+149)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(0.16666666666666666 * Float64(y * Float64(cos(x) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.29)
		tmp = cos(x);
	elseif (y <= 5.4e+149)
		tmp = sinh(y) / y;
	else
		tmp = 0.16666666666666666 * (y * (cos(x) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.29], N[Cos[x], $MachinePrecision], If[LessEqual[y, 5.4e+149], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(0.16666666666666666 * N[(y * N[(N[Cos[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 0.28999999999999998

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.2%

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

   if 0.28999999999999998 < y < 5.4000000000000002e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 85.7%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 85.7%

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

      2. associate-/r/ 85.7%

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

      3. rec-exp 85.7%

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

      4. sinh-def 85.7%

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

   6. Simplified 85.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{\sinh y}}} \]
   7. Step-by-step derivation

      1. add-log-exp 85.7%

         \[\leadsto \color{blue}{\log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      2. *-un-lft-identity 85.7%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      3. log-prod 85.7%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      4. metadata-eval 85.7%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right) \]

      5. add-log-exp 85.7%

         \[\leadsto 0 + \color{blue}{\frac{1}{\frac{y}{\sinh y}}} \]

      6. clear-num 85.7%

         \[\leadsto 0 + \color{blue}{\frac{\sinh y}{y}} \]

   8. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{0 + \frac{\sinh y}{y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 85.7%

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

   10. Simplified 85.7%

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

   if 5.4000000000000002e149 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. unpow2 100.0%

         \[\leadsto 0.16666666666666666 \cdot \left(\cos x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot \cos x\right)} \]

      3. associate-*l* 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   7. Simplified 100.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.29:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot \left(\cos x \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 69.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.29:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 0.29)
   (cos x)
   (if (<= y 5.4e+149)
     (/ (sinh y) y)
     (* (* y y) (+ 0.16666666666666666 (* (* x x) -0.08333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.29) {
		tmp = cos(x);
	} else if (y <= 5.4e+149) {
		tmp = sinh(y) / y;
	} else {
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 0.29d0) then
        tmp = cos(x)
    else if (y <= 5.4d+149) then
        tmp = sinh(y) / y
    else
        tmp = (y * y) * (0.16666666666666666d0 + ((x * x) * (-0.08333333333333333d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 0.29) {
		tmp = Math.cos(x);
	} else if (y <= 5.4e+149) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.29:
		tmp = math.cos(x)
	elif y <= 5.4e+149:
		tmp = math.sinh(y) / y
	else:
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.29)
		tmp = cos(x);
	elseif (y <= 5.4e+149)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(Float64(x * x) * -0.08333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.29)
		tmp = cos(x);
	elseif (y <= 5.4e+149)
		tmp = sinh(y) / y;
	else
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.29], N[Cos[x], $MachinePrecision], If[LessEqual[y, 5.4e+149], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(N[(x * x), $MachinePrecision] * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 0.28999999999999998

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.2%

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

   if 0.28999999999999998 < y < 5.4000000000000002e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 85.7%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 85.7%

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

      2. associate-/r/ 85.7%

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

      3. rec-exp 85.7%

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

      4. sinh-def 85.7%

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

   6. Simplified 85.7%

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{\sinh y}}} \]
   7. Step-by-step derivation

      1. add-log-exp 85.7%

         \[\leadsto \color{blue}{\log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      2. *-un-lft-identity 85.7%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      3. log-prod 85.7%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right)} \]

      4. metadata-eval 85.7%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{1}{\frac{y}{\sinh y}}}\right) \]

      5. add-log-exp 85.7%

         \[\leadsto 0 + \color{blue}{\frac{1}{\frac{y}{\sinh y}}} \]

      6. clear-num 85.7%

         \[\leadsto 0 + \color{blue}{\frac{\sinh y}{y}} \]

   8. Applied egg-rr 85.7%

      \[\leadsto \color{blue}{0 + \frac{\sinh y}{y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 85.7%

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

   10. Simplified 85.7%

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

   if 5.4000000000000002e149 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. unpow2 100.0%

         \[\leadsto 0.16666666666666666 \cdot \left(\cos x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot \cos x\right)} \]

      3. associate-*l* 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot \left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   8. Taylor expanded in y around 0 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(0.16666666666666666 \cdot \cos x\right) \cdot {y}^{2}} \]

      2. unpow2 100.0%

         \[\leadsto \left(0.16666666666666666 \cdot \cos x\right) \cdot \color{blue}{\left(y \cdot y\right)} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\left(0.16666666666666666 \cdot \cos x\right) \cdot \left(y \cdot y\right)} \]

   11. Taylor expanded in x around 0 86.7%

       \[\leadsto \color{blue}{\left(0.16666666666666666 + -0.08333333333333333 \cdot {x}^{2}\right)} \cdot \left(y \cdot y\right) \]
   12. Step-by-step derivation

       1. *-commutative 86.7%

          \[\leadsto \left(0.16666666666666666 + \color{blue}{{x}^{2} \cdot -0.08333333333333333}\right) \cdot \left(y \cdot y\right) \]

       2. unpow2 86.7%

          \[\leadsto \left(0.16666666666666666 + \color{blue}{\left(x \cdot x\right)} \cdot -0.08333333333333333\right) \cdot \left(y \cdot y\right) \]

   13. Simplified 86.7%

       \[\leadsto \color{blue}{\left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)} \cdot \left(y \cdot y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.29:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \end{array} \]

Alternative 5: 64.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 270:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 270.0)
   (cos x)
   (if (<= y 5.4e+149)
     (/ 2.0 (* x x))
     (* (* y y) (+ 0.16666666666666666 (* (* x x) -0.08333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 270.0) {
		tmp = cos(x);
	} else if (y <= 5.4e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 270.0d0) then
        tmp = cos(x)
    else if (y <= 5.4d+149) then
        tmp = 2.0d0 / (x * x)
    else
        tmp = (y * y) * (0.16666666666666666d0 + ((x * x) * (-0.08333333333333333d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 270.0) {
		tmp = Math.cos(x);
	} else if (y <= 5.4e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 270.0:
		tmp = math.cos(x)
	elif y <= 5.4e+149:
		tmp = 2.0 / (x * x)
	else:
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 270.0)
		tmp = cos(x);
	elseif (y <= 5.4e+149)
		tmp = Float64(2.0 / Float64(x * x));
	else
		tmp = Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(Float64(x * x) * -0.08333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 270.0)
		tmp = cos(x);
	elseif (y <= 5.4e+149)
		tmp = 2.0 / (x * x);
	else
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 270.0], N[Cos[x], $MachinePrecision], If[LessEqual[y, 5.4e+149], N[(2.0 / N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(N[(x * x), $MachinePrecision] * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 270

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.2%

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

   if 270 < y < 5.4000000000000002e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\cos x}}} \]

   5. Taylor expanded in x around 0 2.5%

      \[\leadsto \frac{1}{\color{blue}{1 + 0.5 \cdot {x}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 2.5%

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

   7. Simplified 2.5%

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

   8. Taylor expanded in x around inf 28.0%

      \[\leadsto \color{blue}{\frac{2}{{x}^{2}}} \]
   9. Step-by-step derivation

      1. unpow2 28.0%

         \[\leadsto \frac{2}{\color{blue}{x \cdot x}} \]

   10. Simplified 28.0%

       \[\leadsto \color{blue}{\frac{2}{x \cdot x}} \]

   if 5.4000000000000002e149 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. unpow2 100.0%

         \[\leadsto 0.16666666666666666 \cdot \left(\cos x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot \cos x\right)} \]

      3. associate-*l* 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot \left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   8. Taylor expanded in y around 0 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(0.16666666666666666 \cdot \cos x\right) \cdot {y}^{2}} \]

      2. unpow2 100.0%

         \[\leadsto \left(0.16666666666666666 \cdot \cos x\right) \cdot \color{blue}{\left(y \cdot y\right)} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\left(0.16666666666666666 \cdot \cos x\right) \cdot \left(y \cdot y\right)} \]

   11. Taylor expanded in x around 0 86.7%

       \[\leadsto \color{blue}{\left(0.16666666666666666 + -0.08333333333333333 \cdot {x}^{2}\right)} \cdot \left(y \cdot y\right) \]
   12. Step-by-step derivation

       1. *-commutative 86.7%

          \[\leadsto \left(0.16666666666666666 + \color{blue}{{x}^{2} \cdot -0.08333333333333333}\right) \cdot \left(y \cdot y\right) \]

       2. unpow2 86.7%

          \[\leadsto \left(0.16666666666666666 + \color{blue}{\left(x \cdot x\right)} \cdot -0.08333333333333333\right) \cdot \left(y \cdot y\right) \]

   13. Simplified 86.7%

       \[\leadsto \color{blue}{\left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)} \cdot \left(y \cdot y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 270:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \end{array} \]

Alternative 6: 41.7% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 225:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 225.0)
   1.0
   (if (<= y 5.4e+149)
     (/ 2.0 (* x x))
     (* (* y y) (+ 0.16666666666666666 (* (* x x) -0.08333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 225.0) {
		tmp = 1.0;
	} else if (y <= 5.4e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 225.0d0) then
        tmp = 1.0d0
    else if (y <= 5.4d+149) then
        tmp = 2.0d0 / (x * x)
    else
        tmp = (y * y) * (0.16666666666666666d0 + ((x * x) * (-0.08333333333333333d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 225.0) {
		tmp = 1.0;
	} else if (y <= 5.4e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 225.0:
		tmp = 1.0
	elif y <= 5.4e+149:
		tmp = 2.0 / (x * x)
	else:
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 225.0)
		tmp = 1.0;
	elseif (y <= 5.4e+149)
		tmp = Float64(2.0 / Float64(x * x));
	else
		tmp = Float64(Float64(y * y) * Float64(0.16666666666666666 + Float64(Float64(x * x) * -0.08333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 225.0)
		tmp = 1.0;
	elseif (y <= 5.4e+149)
		tmp = 2.0 / (x * x);
	else
		tmp = (y * y) * (0.16666666666666666 + ((x * x) * -0.08333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 225.0], 1.0, If[LessEqual[y, 5.4e+149], N[(2.0 / N[(x * x), $MachinePrecision]), $MachinePrecision], N[(N[(y * y), $MachinePrecision] * N[(0.16666666666666666 + N[(N[(x * x), $MachinePrecision] * -0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 225

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around 0 28.9%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 28.9%

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

      2. associate-/r/ 28.9%

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

      3. rec-exp 29.0%

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

      4. sinh-def 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in y around 0 40.1%

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

   if 225 < y < 5.4000000000000002e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\cos x}}} \]

   5. Taylor expanded in x around 0 2.5%

      \[\leadsto \frac{1}{\color{blue}{1 + 0.5 \cdot {x}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 2.5%

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

   7. Simplified 2.5%

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

   8. Taylor expanded in x around inf 28.0%

      \[\leadsto \color{blue}{\frac{2}{{x}^{2}}} \]
   9. Step-by-step derivation

      1. unpow2 28.0%

         \[\leadsto \frac{2}{\color{blue}{x \cdot x}} \]

   10. Simplified 28.0%

       \[\leadsto \color{blue}{\frac{2}{x \cdot x}} \]

   if 5.4000000000000002e149 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. unpow2 100.0%

         \[\leadsto 0.16666666666666666 \cdot \left(\cos x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot \cos x\right)} \]

      3. associate-*l* 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot \left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   8. Taylor expanded in y around 0 100.0%

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

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(0.16666666666666666 \cdot \cos x\right) \cdot {y}^{2}} \]

      2. unpow2 100.0%

         \[\leadsto \left(0.16666666666666666 \cdot \cos x\right) \cdot \color{blue}{\left(y \cdot y\right)} \]

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\left(0.16666666666666666 \cdot \cos x\right) \cdot \left(y \cdot y\right)} \]

   11. Taylor expanded in x around 0 86.7%

       \[\leadsto \color{blue}{\left(0.16666666666666666 + -0.08333333333333333 \cdot {x}^{2}\right)} \cdot \left(y \cdot y\right) \]
   12. Step-by-step derivation

       1. *-commutative 86.7%

          \[\leadsto \left(0.16666666666666666 + \color{blue}{{x}^{2} \cdot -0.08333333333333333}\right) \cdot \left(y \cdot y\right) \]

       2. unpow2 86.7%

          \[\leadsto \left(0.16666666666666666 + \color{blue}{\left(x \cdot x\right)} \cdot -0.08333333333333333\right) \cdot \left(y \cdot y\right) \]

   13. Simplified 86.7%

       \[\leadsto \color{blue}{\left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)} \cdot \left(y \cdot y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 225:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot y\right) \cdot \left(0.16666666666666666 + \left(x \cdot x\right) \cdot -0.08333333333333333\right)\\ \end{array} \]

Alternative 7: 41.6% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 170:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 170.0)
   1.0
   (if (<= y 1.6e+149)
     (/ 2.0 (* x x))
     (+ 1.0 (* 0.16666666666666666 (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 170.0) {
		tmp = 1.0;
	} else if (y <= 1.6e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = 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 (y <= 170.0d0) then
        tmp = 1.0d0
    else if (y <= 1.6d+149) then
        tmp = 2.0d0 / (x * x)
    else
        tmp = 1.0d0 + (0.16666666666666666d0 * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 170.0) {
		tmp = 1.0;
	} else if (y <= 1.6e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 170.0:
		tmp = 1.0
	elif y <= 1.6e+149:
		tmp = 2.0 / (x * x)
	else:
		tmp = 1.0 + (0.16666666666666666 * (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 170.0)
		tmp = 1.0;
	elseif (y <= 1.6e+149)
		tmp = Float64(2.0 / Float64(x * x));
	else
		tmp = Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 170.0)
		tmp = 1.0;
	elseif (y <= 1.6e+149)
		tmp = 2.0 / (x * x);
	else
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 170.0], 1.0, If[LessEqual[y, 1.6e+149], N[(2.0 / N[(x * x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 170

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around 0 28.9%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 28.9%

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

      2. associate-/r/ 28.9%

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

      3. rec-exp 29.0%

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

      4. sinh-def 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in y around 0 40.1%

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

   if 170 < y < 1.6000000000000001e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\cos x}}} \]

   5. Taylor expanded in x around 0 2.5%

      \[\leadsto \frac{1}{\color{blue}{1 + 0.5 \cdot {x}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 2.5%

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

   7. Simplified 2.5%

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

   8. Taylor expanded in x around inf 28.0%

      \[\leadsto \color{blue}{\frac{2}{{x}^{2}}} \]
   9. Step-by-step derivation

      1. unpow2 28.0%

         \[\leadsto \frac{2}{\color{blue}{x \cdot x}} \]

   10. Simplified 28.0%

       \[\leadsto \color{blue}{\frac{2}{x \cdot x}} \]

   if 1.6000000000000001e149 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 76.7%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 76.7%

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

      2. associate-/r/ 76.7%

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

      3. rec-exp 76.7%

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

      4. sinh-def 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in y around 0 76.7%

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

      1. unpow2 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 170:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 8: 41.6% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 340:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 340.0)
   1.0
   (if (<= y 1.6e+149) (/ 2.0 (* x x)) (* 0.16666666666666666 (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 340.0) {
		tmp = 1.0;
	} else if (y <= 1.6e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = 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 (y <= 340.0d0) then
        tmp = 1.0d0
    else if (y <= 1.6d+149) then
        tmp = 2.0d0 / (x * x)
    else
        tmp = 0.16666666666666666d0 * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 340.0) {
		tmp = 1.0;
	} else if (y <= 1.6e+149) {
		tmp = 2.0 / (x * x);
	} else {
		tmp = 0.16666666666666666 * (y * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 340.0:
		tmp = 1.0
	elif y <= 1.6e+149:
		tmp = 2.0 / (x * x)
	else:
		tmp = 0.16666666666666666 * (y * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 340.0)
		tmp = 1.0;
	elseif (y <= 1.6e+149)
		tmp = Float64(2.0 / Float64(x * x));
	else
		tmp = Float64(0.16666666666666666 * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 340.0)
		tmp = 1.0;
	elseif (y <= 1.6e+149)
		tmp = 2.0 / (x * x);
	else
		tmp = 0.16666666666666666 * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 340.0], 1.0, If[LessEqual[y, 1.6e+149], N[(2.0 / N[(x * x), $MachinePrecision]), $MachinePrecision], N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 340

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around 0 28.9%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 28.9%

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

      2. associate-/r/ 28.9%

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

      3. rec-exp 29.0%

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

      4. sinh-def 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in y around 0 40.1%

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

   if 340 < y < 1.6000000000000001e149

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{1}{\color{blue}{\frac{1}{\cos x}}} \]

   5. Taylor expanded in x around 0 2.5%

      \[\leadsto \frac{1}{\color{blue}{1 + 0.5 \cdot {x}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 2.5%

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

   7. Simplified 2.5%

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

   8. Taylor expanded in x around inf 28.0%

      \[\leadsto \color{blue}{\frac{2}{{x}^{2}}} \]
   9. Step-by-step derivation

      1. unpow2 28.0%

         \[\leadsto \frac{2}{\color{blue}{x \cdot x}} \]

   10. Simplified 28.0%

       \[\leadsto \color{blue}{\frac{2}{x \cdot x}} \]

   if 1.6000000000000001e149 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. unpow2 100.0%

         \[\leadsto 0.16666666666666666 \cdot \left(\cos x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. *-commutative 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot \cos x\right)} \]

      3. associate-*l* 100.0%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot \left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   8. Taylor expanded in x around 0 76.7%

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

      1. unpow2 76.7%

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

   10. Simplified 76.7%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 340:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;\frac{2}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 9: 38.8% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.0) 1.0 (* 0.16666666666666666 (* y y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = 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 (y <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = 0.16666666666666666d0 * (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = 0.16666666666666666 * (y * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.0:
		tmp = 1.0
	else:
		tmp = 0.16666666666666666 * (y * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(0.16666666666666666 * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.0)
		tmp = 1.0;
	else
		tmp = 0.16666666666666666 * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.0], 1.0, N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. clear-num 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around 0 28.9%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
   5. Step-by-step derivation

      1. *-commutative 28.9%

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

      2. associate-/r/ 28.9%

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

      3. rec-exp 29.0%

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

      4. sinh-def 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in y around 0 40.1%

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

   if 2 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 48.6%

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

      1. unpow2 48.6%

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

   4. Simplified 48.6%

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

   5. Taylor expanded in y around inf 48.6%

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

      1. unpow2 48.6%

         \[\leadsto 0.16666666666666666 \cdot \left(\cos x \cdot \color{blue}{\left(y \cdot y\right)}\right) \]

      2. *-commutative 48.6%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(\left(y \cdot y\right) \cdot \cos x\right)} \]

      3. associate-*l* 48.6%

         \[\leadsto 0.16666666666666666 \cdot \color{blue}{\left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   7. Simplified 48.6%

      \[\leadsto \color{blue}{0.16666666666666666 \cdot \left(y \cdot \left(y \cdot \cos x\right)\right)} \]

   8. Taylor expanded in x around 0 37.6%

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

      1. unpow2 37.6%

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

   10. Simplified 37.6%

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

4. Final simplification 39.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 10: 29.1% 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. Step-by-step derivation

   1. associate-*r/ 99.9%

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

   2. clear-num 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in x around 0 42.3%

   \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{y}{e^{y} - \frac{1}{e^{y}}}}} \]
5. Step-by-step derivation

   1. *-commutative 42.3%

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

   2. associate-/r/ 42.3%

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

   3. rec-exp 42.3%

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

   4. sinh-def 69.2%

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

6. Simplified 69.2%

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

7. Taylor expanded in y around 0 30.6%

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

8. Final simplification 30.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))