Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 9.0s

Alternatives: 7

Speedup: 1.0×

• 49.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 61.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 59:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+151}:\\ \;\;\;\;1 + {x}^{2} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot {y}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 59.0)
   (cos x)
   (if (<= y 7.6e+151)
     (+ 1.0 (* (pow x 2.0) -0.5))
     (+ 1.0 (* 0.16666666666666666 (pow y 2.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 59.0) {
		tmp = cos(x);
	} else if (y <= 7.6e+151) {
		tmp = 1.0 + (pow(x, 2.0) * -0.5);
	} else {
		tmp = 1.0 + (0.16666666666666666 * pow(y, 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 59.0d0) then
        tmp = cos(x)
    else if (y <= 7.6d+151) then
        tmp = 1.0d0 + ((x ** 2.0d0) * (-0.5d0))
    else
        tmp = 1.0d0 + (0.16666666666666666d0 * (y ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 59.0) {
		tmp = Math.cos(x);
	} else if (y <= 7.6e+151) {
		tmp = 1.0 + (Math.pow(x, 2.0) * -0.5);
	} else {
		tmp = 1.0 + (0.16666666666666666 * Math.pow(y, 2.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 59.0:
		tmp = math.cos(x)
	elif y <= 7.6e+151:
		tmp = 1.0 + (math.pow(x, 2.0) * -0.5)
	else:
		tmp = 1.0 + (0.16666666666666666 * math.pow(y, 2.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 59.0)
		tmp = cos(x);
	elseif (y <= 7.6e+151)
		tmp = Float64(1.0 + Float64((x ^ 2.0) * -0.5));
	else
		tmp = Float64(1.0 + Float64(0.16666666666666666 * (y ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 59.0)
		tmp = cos(x);
	elseif (y <= 7.6e+151)
		tmp = 1.0 + ((x ^ 2.0) * -0.5);
	else
		tmp = 1.0 + (0.16666666666666666 * (y ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 59.0], N[Cos[x], $MachinePrecision], If[LessEqual[y, 7.6e+151], N[(1.0 + N[(N[Power[x, 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(0.16666666666666666 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 59

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.0%

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

   if 59 < y < 7.6000000000000001e151

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 3.3%

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

   4. Taylor expanded in x around 0 12.5%

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

      1. *-commutative 12.5%

         \[\leadsto 1 + \color{blue}{{x}^{2} \cdot -0.5} \]

   6. Simplified 12.5%

      \[\leadsto \color{blue}{1 + {x}^{2} \cdot -0.5} \]

   if 7.6000000000000001e151 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around 0 95.7%

      \[\leadsto \color{blue}{1 + 0.16666666666666666 \cdot {y}^{2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 61.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 700:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+153}:\\ \;\;\;\;{x}^{2} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot {y}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 700.0)
   (cos x)
   (if (<= y 2.8e+153)
     (* (pow x 2.0) -0.5)
     (+ 1.0 (* 0.16666666666666666 (pow y 2.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 700.0) {
		tmp = cos(x);
	} else if (y <= 2.8e+153) {
		tmp = pow(x, 2.0) * -0.5;
	} else {
		tmp = 1.0 + (0.16666666666666666 * pow(y, 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 700.0d0) then
        tmp = cos(x)
    else if (y <= 2.8d+153) then
        tmp = (x ** 2.0d0) * (-0.5d0)
    else
        tmp = 1.0d0 + (0.16666666666666666d0 * (y ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 700.0) {
		tmp = Math.cos(x);
	} else if (y <= 2.8e+153) {
		tmp = Math.pow(x, 2.0) * -0.5;
	} else {
		tmp = 1.0 + (0.16666666666666666 * Math.pow(y, 2.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 700.0:
		tmp = math.cos(x)
	elif y <= 2.8e+153:
		tmp = math.pow(x, 2.0) * -0.5
	else:
		tmp = 1.0 + (0.16666666666666666 * math.pow(y, 2.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 700.0)
		tmp = cos(x);
	elseif (y <= 2.8e+153)
		tmp = Float64((x ^ 2.0) * -0.5);
	else
		tmp = Float64(1.0 + Float64(0.16666666666666666 * (y ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 700.0)
		tmp = cos(x);
	elseif (y <= 2.8e+153)
		tmp = (x ^ 2.0) * -0.5;
	else
		tmp = 1.0 + (0.16666666666666666 * (y ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 700.0], N[Cos[x], $MachinePrecision], If[LessEqual[y, 2.8e+153], N[(N[Power[x, 2.0], $MachinePrecision] * -0.5), $MachinePrecision], N[(1.0 + N[(0.16666666666666666 * N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 700

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 63.7%

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

   if 700 < y < 2.79999999999999985e153

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{\color{blue}{y \cdot \cos x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 3.1%

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

   7. Simplified 3.1%

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

   8. Taylor expanded in x around 0 14.8%

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

   9. Taylor expanded in x around inf 11.7%

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

       1. *-commutative 11.7%

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

   11. Simplified 11.7%

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

   if 2.79999999999999985e153 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around 0 95.7%

      \[\leadsto \color{blue}{1 + 0.16666666666666666 \cdot {y}^{2}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 69.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-5}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{y}}{\frac{1}{\sinh y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 4.5e-5) (cos x) (/ (/ 1.0 y) (/ 1.0 (sinh y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.5e-5) {
		tmp = cos(x);
	} else {
		tmp = (1.0 / y) / (1.0 / sinh(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 <= 4.5d-5) then
        tmp = cos(x)
    else
        tmp = (1.0d0 / y) / (1.0d0 / sinh(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4.5e-5) {
		tmp = Math.cos(x);
	} else {
		tmp = (1.0 / y) / (1.0 / Math.sinh(y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.5e-5:
		tmp = math.cos(x)
	else:
		tmp = (1.0 / y) / (1.0 / math.sinh(y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.5e-5)
		tmp = cos(x);
	else
		tmp = Float64(Float64(1.0 / y) / Float64(1.0 / sinh(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4.5e-5)
		tmp = cos(x);
	else
		tmp = (1.0 / y) / (1.0 / sinh(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.5e-5], N[Cos[x], $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] / N[(1.0 / N[Sinh[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.50000000000000028e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 64.1%

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

   if 4.50000000000000028e-5 < y

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.9%

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

      2. pow3 99.9%

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

   4. Applied egg-rr 99.9%

      \[\leadsto \cos x \cdot \frac{\color{blue}{{\left(\sqrt[3]{\sinh y}\right)}^{3}}}{y} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 100.0%

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

      2. remove-double-div 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 99.9%

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

      3. associate-/r* 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around 0 79.1%

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

Alternative 5: 53.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 720:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;{x}^{2} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 720.0) (cos x) (* (pow x 2.0) -0.5)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 720.0) {
		tmp = cos(x);
	} else {
		tmp = pow(x, 2.0) * -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 <= 720.0d0) then
        tmp = cos(x)
    else
        tmp = (x ** 2.0d0) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 720.0) {
		tmp = Math.cos(x);
	} else {
		tmp = Math.pow(x, 2.0) * -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 720.0:
		tmp = math.cos(x)
	else:
		tmp = math.pow(x, 2.0) * -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 720.0)
		tmp = cos(x);
	else
		tmp = Float64((x ^ 2.0) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 720.0)
		tmp = cos(x);
	else
		tmp = (x ^ 2.0) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 720.0], N[Cos[x], $MachinePrecision], N[(N[Power[x, 2.0], $MachinePrecision] * -0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 720

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 63.7%

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

   if 720 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 3.1%

      \[\leadsto \frac{\color{blue}{y \cdot \cos x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 3.1%

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

   7. Simplified 3.1%

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

   8. Taylor expanded in x around 0 12.0%

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

   9. Taylor expanded in x around inf 9.5%

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

       1. *-commutative 9.5%

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

   11. Simplified 9.5%

       \[\leadsto \color{blue}{{x}^{2} \cdot -0.5} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 51.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0 48.5%

   \[\leadsto \color{blue}{\cos x} \]
4. Add Preprocessing

Alternative 7: 28.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. associate-*l/ 99.9%

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in y around 0 48.5%

   \[\leadsto \frac{\color{blue}{y \cdot \cos x}}{y} \]
6. Step-by-step derivation

   1. *-commutative 48.5%

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

7. Simplified 48.5%

   \[\leadsto \frac{\color{blue}{\cos x \cdot y}}{y} \]
8. Step-by-step derivation

   1. *-commutative 48.5%

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

   2. associate-/l* 48.4%

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

9. Applied egg-rr 48.4%

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

10. Taylor expanded in x around 0 28.4%

    \[\leadsto \color{blue}{1} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))