Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 8.9s

Alternatives: 18

Speedup: 1.0×

• 50.0% 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: 71.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 15:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 15.0)
   (cos x)
   (if (<= y 3.2e+154)
     (/ (sinh y) y)
     (* (cos x) (* y (* y 0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 15.0) {
		tmp = cos(x);
	} else if (y <= 3.2e+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 <= 15.0d0) then
        tmp = cos(x)
    else if (y <= 3.2d+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 <= 15.0) {
		tmp = Math.cos(x);
	} else if (y <= 3.2e+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 <= 15.0:
		tmp = math.cos(x)
	elif y <= 3.2e+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 <= 15.0)
		tmp = cos(x);
	elseif (y <= 3.2e+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 <= 15.0)
		tmp = cos(x);
	elseif (y <= 3.2e+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, 15.0], N[Cos[x], $MachinePrecision], If[LessEqual[y, 3.2e+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 < 15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.2%

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

   if 15 < y < 3.2e154

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.7%

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

   if 3.2e154 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. *-lft-identity 100.0%

         \[\leadsto \color{blue}{1 \cdot \cos x} + 0.16666666666666666 \cdot \left(\cos x \cdot {y}^{2}\right) \]

      3. *-commutative 100.0%

         \[\leadsto 1 \cdot \cos x + 0.16666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot \cos x\right)} \]

      4. associate-*r* 100.0%

         \[\leadsto 1 \cdot \cos x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \cos x} \]

      5. distribute-rgt-out 100.0%

         \[\leadsto \color{blue}{\cos x \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]

      6. unpow2 100.0%

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

   4. Simplified 100.0%

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

   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. *-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. unpow2 100.0%

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

      4. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 15:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\\ \end{array} \]

Alternative 3: 84.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 15:\\ \;\;\;\;\cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 15.0)
   (* (cos x) (+ 1.0 (* 0.16666666666666666 (* y y))))
   (if (<= y 3.2e+154)
     (/ (sinh y) y)
     (* (cos x) (* y (* y 0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 15.0) {
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else if (y <= 3.2e+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 <= 15.0d0) then
        tmp = cos(x) * (1.0d0 + (0.16666666666666666d0 * (y * y)))
    else if (y <= 3.2d+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 <= 15.0) {
		tmp = Math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	} else if (y <= 3.2e+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 <= 15.0:
		tmp = math.cos(x) * (1.0 + (0.16666666666666666 * (y * y)))
	elif y <= 3.2e+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 <= 15.0)
		tmp = Float64(cos(x) * Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y))));
	elseif (y <= 3.2e+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 <= 15.0)
		tmp = cos(x) * (1.0 + (0.16666666666666666 * (y * y)));
	elseif (y <= 3.2e+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, 15.0], N[(N[Cos[x], $MachinePrecision] * N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+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 < 15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.3%

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

      1. +-commutative 85.3%

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

      2. *-lft-identity 85.3%

         \[\leadsto \color{blue}{1 \cdot \cos x} + 0.16666666666666666 \cdot \left(\cos x \cdot {y}^{2}\right) \]

      3. *-commutative 85.3%

         \[\leadsto 1 \cdot \cos x + 0.16666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot \cos x\right)} \]

      4. associate-*r* 85.3%

         \[\leadsto 1 \cdot \cos x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \cos x} \]

      5. distribute-rgt-out 85.3%

         \[\leadsto \color{blue}{\cos x \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]

      6. unpow2 85.3%

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

   4. Simplified 85.3%

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

   if 15 < y < 3.2e154

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 86.7%

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

   if 3.2e154 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. *-lft-identity 100.0%

         \[\leadsto \color{blue}{1 \cdot \cos x} + 0.16666666666666666 \cdot \left(\cos x \cdot {y}^{2}\right) \]

      3. *-commutative 100.0%

         \[\leadsto 1 \cdot \cos x + 0.16666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot \cos x\right)} \]

      4. associate-*r* 100.0%

         \[\leadsto 1 \cdot \cos x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \cos x} \]

      5. distribute-rgt-out 100.0%

         \[\leadsto \color{blue}{\cos x \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]

      6. unpow2 100.0%

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

   4. Simplified 100.0%

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

   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. *-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. unpow2 100.0%

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

      4. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 15:\\ \;\;\;\;\cos x \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cos x \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\\ \end{array} \]

Alternative 4: 68.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 15:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 15.0) (cos x) (/ (sinh y) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 15.0) {
		tmp = cos(x);
	} 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 <= 15.0d0) then
        tmp = cos(x)
    else
        tmp = sinh(y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 15.0) {
		tmp = Math.cos(x);
	} else {
		tmp = Math.sinh(y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 15.0:
		tmp = math.cos(x)
	else:
		tmp = math.sinh(y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 15.0)
		tmp = cos(x);
	else
		tmp = Float64(sinh(y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 15.0)
		tmp = cos(x);
	else
		tmp = sinh(y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 15.0], N[Cos[x], $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 15

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.2%

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

   if 15 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.3%

      \[\leadsto \color{blue}{1} \cdot \frac{\sinh y}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 15:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \]

Alternative 5: 61.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+142}:\\ \;\;\;\;t_0 \cdot \left(1 + \left(x \cdot x\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* 0.16666666666666666 (* y y)))))
   (if (<= y 2.8e+43)
     (cos x)
     (if (<= y 8.4e+142) (* t_0 (+ 1.0 (* (* x x) -0.5))) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (0.16666666666666666 * (y * y));
	double tmp;
	if (y <= 2.8e+43) {
		tmp = cos(x);
	} else if (y <= 8.4e+142) {
		tmp = t_0 * (1.0 + ((x * x) * -0.5));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (0.16666666666666666d0 * (y * y))
    if (y <= 2.8d+43) then
        tmp = cos(x)
    else if (y <= 8.4d+142) then
        tmp = t_0 * (1.0d0 + ((x * x) * (-0.5d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (0.16666666666666666 * (y * y));
	double tmp;
	if (y <= 2.8e+43) {
		tmp = Math.cos(x);
	} else if (y <= 8.4e+142) {
		tmp = t_0 * (1.0 + ((x * x) * -0.5));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (0.16666666666666666 * (y * y))
	tmp = 0
	if y <= 2.8e+43:
		tmp = math.cos(x)
	elif y <= 8.4e+142:
		tmp = t_0 * (1.0 + ((x * x) * -0.5))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y)))
	tmp = 0.0
	if (y <= 2.8e+43)
		tmp = cos(x);
	elseif (y <= 8.4e+142)
		tmp = Float64(t_0 * Float64(1.0 + Float64(Float64(x * x) * -0.5)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (0.16666666666666666 * (y * y));
	tmp = 0.0;
	if (y <= 2.8e+43)
		tmp = cos(x);
	elseif (y <= 8.4e+142)
		tmp = t_0 * (1.0 + ((x * x) * -0.5));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.8e+43], N[Cos[x], $MachinePrecision], If[LessEqual[y, 8.4e+142], N[(t$95$0 * N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.80000000000000019e43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 63.4%

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

   if 2.80000000000000019e43 < y < 8.3999999999999999e142

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 5.3%

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

      1. +-commutative 5.3%

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

      2. *-lft-identity 5.3%

         \[\leadsto \color{blue}{1 \cdot \cos x} + 0.16666666666666666 \cdot \left(\cos x \cdot {y}^{2}\right) \]

      3. *-commutative 5.3%

         \[\leadsto 1 \cdot \cos x + 0.16666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot \cos x\right)} \]

      4. associate-*r* 5.3%

         \[\leadsto 1 \cdot \cos x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \cos x} \]

      5. distribute-rgt-out 5.3%

         \[\leadsto \color{blue}{\cos x \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]

      6. unpow2 5.3%

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

   4. Simplified 5.3%

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

   5. Taylor expanded in x around 0 23.7%

      \[\leadsto \color{blue}{\left(1 + -0.5 \cdot {x}^{2}\right)} \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative 68.4%

         \[\leadsto \frac{\left(1 + \color{blue}{{x}^{2} \cdot -0.5}\right) \cdot \sinh y}{y} \]

      2. unpow2 68.4%

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

   7. Simplified 23.7%

      \[\leadsto \color{blue}{\left(1 + \left(x \cdot x\right) \cdot -0.5\right)} \cdot \left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right) \]

   if 8.3999999999999999e142 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.7%

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

      1. +-commutative 94.7%

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

      2. *-lft-identity 94.7%

         \[\leadsto \color{blue}{1 \cdot \cos x} + 0.16666666666666666 \cdot \left(\cos x \cdot {y}^{2}\right) \]

      3. *-commutative 94.7%

         \[\leadsto 1 \cdot \cos x + 0.16666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot \cos x\right)} \]

      4. associate-*r* 94.7%

         \[\leadsto 1 \cdot \cos x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \cos x} \]

      5. distribute-rgt-out 94.7%

         \[\leadsto \color{blue}{\cos x \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]

      6. unpow2 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in x around 0 74.1%

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

      1. unpow2 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{+43}:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{+142}:\\ \;\;\;\;\left(1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\right) \cdot \left(1 + \left(x \cdot x\right) \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 6: 30.8% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4.7e+60) 1.0 (* (* x x) -0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.7e+60) {
		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 <= 4.7d+60) 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 <= 4.7e+60) {
		tmp = 1.0;
	} else {
		tmp = (x * x) * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.7e+60:
		tmp = 1.0
	else:
		tmp = (x * x) * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.7e+60)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x * x) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.7e+60)
		tmp = 1.0;
	else
		tmp = (x * x) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.7e+60], 1.0, N[(N[(x * x), $MachinePrecision] * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.6999999999999998e60

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   5. Applied egg-rr 29.0%

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

   if 4.6999999999999998e60 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 62.0%

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

      1. *-commutative 62.0%

         \[\leadsto \frac{\left(1 + \color{blue}{{x}^{2} \cdot -0.5}\right) \cdot \sinh y}{y} \]

      2. unpow2 62.0%

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

   6. Simplified 62.0%

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

   7. Taylor expanded in y around 0 21.4%

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

   8. Taylor expanded in x around inf 11.3%

      \[\leadsto \color{blue}{-0.5 \cdot {x}^{2}} \]
   9. Step-by-step derivation

      1. *-commutative 11.3%

         \[\leadsto \color{blue}{{x}^{2} \cdot -0.5} \]

      2. unpow2 11.3%

         \[\leadsto \color{blue}{\left(x \cdot x\right)} \cdot -0.5 \]

   10. Simplified 11.3%

       \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot -0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.7 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot x\right) \cdot -0.5\\ \end{array} \]

Alternative 7: 47.4% accurate, 29.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 77.7%

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

   1. +-commutative 77.7%

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

   2. *-lft-identity 77.7%

      \[\leadsto \color{blue}{1 \cdot \cos x} + 0.16666666666666666 \cdot \left(\cos x \cdot {y}^{2}\right) \]

   3. *-commutative 77.7%

      \[\leadsto 1 \cdot \cos x + 0.16666666666666666 \cdot \color{blue}{\left({y}^{2} \cdot \cos x\right)} \]

   4. associate-*r* 77.7%

      \[\leadsto 1 \cdot \cos x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{2}\right) \cdot \cos x} \]

   5. distribute-rgt-out 77.7%

      \[\leadsto \color{blue}{\cos x \cdot \left(1 + 0.16666666666666666 \cdot {y}^{2}\right)} \]

   6. unpow2 77.7%

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

4. Simplified 77.7%

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

5. Taylor expanded in x around 0 44.6%

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

   1. unpow2 44.6%

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

7. Simplified 44.6%

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

8. Final simplification 44.6%

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

Alternative 8: 3.4% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ -3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -3.0)

C

double code(double x, double y) {
	return -3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -3.0d0
end function

Java

public static double code(double x, double y) {
	return -3.0;
}

Python

def code(x, y):
	return -3.0

Julia

function code(x, y)
	return -3.0
end

MATLAB

function tmp = code(x, y)
	tmp = -3.0;
end

Wolfram

code[x_, y_] := -3.0

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 3.6%

   \[\leadsto \color{blue}{-3} \]

6. Final simplification 3.6%

   \[\leadsto -3 \]

Alternative 9: 3.9% 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%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 4.2%

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

6. Final simplification 4.2%

   \[\leadsto -1 \]

Alternative 10: 7.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.015625 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.015625)

C

double code(double x, double y) {
	return 0.015625;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.015625d0
end function

Java

public static double code(double x, double y) {
	return 0.015625;
}

Python

def code(x, y):
	return 0.015625

Julia

function code(x, y)
	return 0.015625
end

MATLAB

function tmp = code(x, y)
	tmp = 0.015625;
end

Wolfram

code[x_, y_] := 0.015625

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 6.8%

   \[\leadsto \color{blue}{0.015625} \]

6. Final simplification 6.8%

   \[\leadsto 0.015625 \]

Alternative 11: 7.1% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.027777777777777776 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.027777777777777776)

C

double code(double x, double y) {
	return 0.027777777777777776;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.027777777777777776d0
end function

Java

public static double code(double x, double y) {
	return 0.027777777777777776;
}

Python

def code(x, y):
	return 0.027777777777777776

Julia

function code(x, y)
	return 0.027777777777777776
end

MATLAB

function tmp = code(x, y)
	tmp = 0.027777777777777776;
end

Wolfram

code[x_, y_] := 0.027777777777777776

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 7.0%

   \[\leadsto \color{blue}{0.027777777777777776} \]

6. Final simplification 7.0%

   \[\leadsto 0.027777777777777776 \]

Alternative 12: 7.4% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.0625 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0625)

C

double code(double x, double y) {
	return 0.0625;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0625d0
end function

Java

public static double code(double x, double y) {
	return 0.0625;
}

Python

def code(x, y):
	return 0.0625

Julia

function code(x, y)
	return 0.0625
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0625;
end

Wolfram

code[x_, y_] := 0.0625

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 7.2%

   \[\leadsto \color{blue}{0.0625} \]

6. Final simplification 7.2%

   \[\leadsto 0.0625 \]

Alternative 13: 7.6% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.125 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.125)

C

double code(double x, double y) {
	return 0.125;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.125d0
end function

Java

public static double code(double x, double y) {
	return 0.125;
}

Python

def code(x, y):
	return 0.125

Julia

function code(x, y)
	return 0.125
end

MATLAB

function tmp = code(x, y)
	tmp = 0.125;
end

Wolfram

code[x_, y_] := 0.125

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 7.5%

   \[\leadsto \color{blue}{0.125} \]

6. Final simplification 7.5%

   \[\leadsto 0.125 \]

Alternative 14: 7.7% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.16666666666666666 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.16666666666666666)

C

double code(double x, double y) {
	return 0.16666666666666666;
}

Fortran

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

Java

public static double code(double x, double y) {
	return 0.16666666666666666;
}

Python

def code(x, y):
	return 0.16666666666666666

Julia

function code(x, y)
	return 0.16666666666666666
end

MATLAB

function tmp = code(x, y)
	tmp = 0.16666666666666666;
end

Wolfram

code[x_, y_] := 0.16666666666666666

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 7.6%

   \[\leadsto \color{blue}{0.16666666666666666} \]

6. Final simplification 7.6%

   \[\leadsto 0.16666666666666666 \]

Alternative 15: 8.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.25 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.25)

C

double code(double x, double y) {
	return 0.25;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.25d0
end function

Java

public static double code(double x, double y) {
	return 0.25;
}

Python

def code(x, y):
	return 0.25

Julia

function code(x, y)
	return 0.25
end

MATLAB

function tmp = code(x, y)
	tmp = 0.25;
end

Wolfram

code[x_, y_] := 0.25

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 7.8%

   \[\leadsto \color{blue}{0.25} \]

6. Final simplification 7.8%

   \[\leadsto 0.25 \]

Alternative 16: 8.1% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.3333333333333333)

C

double code(double x, double y) {
	return 0.3333333333333333;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.3333333333333333d0
end function

Java

public static double code(double x, double y) {
	return 0.3333333333333333;
}

Python

def code(x, y):
	return 0.3333333333333333

Julia

function code(x, y)
	return 0.3333333333333333
end

MATLAB

function tmp = code(x, y)
	tmp = 0.3333333333333333;
end

Wolfram

code[x_, y_] := 0.3333333333333333

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 8.0%

   \[\leadsto \color{blue}{0.3333333333333333} \]

6. Final simplification 8.0%

   \[\leadsto 0.3333333333333333 \]

Alternative 17: 8.6% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.5)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.5

Julia

function code(x, y)
	return 0.5
end

MATLAB

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

Wolfram

code[x_, y_] := 0.5

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 8.3%

   \[\leadsto \color{blue}{0.5} \]

6. Final simplification 8.3%

   \[\leadsto 0.5 \]

Alternative 18: 28.7% 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%

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

3. Applied egg-rr 99.9%

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

5. Applied egg-rr 23.8%

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

6. Final simplification 23.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))