Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 5

Speedup: 1.0×

• 49.7% 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: 72.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.3:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot y}{\frac{y}{\cos x}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 0.3)
   (cos x)
   (if (<= y 1.35e+154) (/ (sinh y) y) (/ (/ (* y y) (/ y (cos x))) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.3) {
		tmp = cos(x);
	} else if (y <= 1.35e+154) {
		tmp = sinh(y) / y;
	} else {
		tmp = ((y * y) / (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 <= 0.3d0) then
        tmp = cos(x)
    else if (y <= 1.35d+154) then
        tmp = sinh(y) / y
    else
        tmp = ((y * y) / (y / cos(x))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 0.3) {
		tmp = Math.cos(x);
	} else if (y <= 1.35e+154) {
		tmp = Math.sinh(y) / y;
	} else {
		tmp = ((y * y) / (y / Math.cos(x))) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.3:
		tmp = math.cos(x)
	elif y <= 1.35e+154:
		tmp = math.sinh(y) / y
	else:
		tmp = ((y * y) / (y / math.cos(x))) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.3)
		tmp = cos(x);
	elseif (y <= 1.35e+154)
		tmp = Float64(sinh(y) / y);
	else
		tmp = Float64(Float64(Float64(y * y) / Float64(y / cos(x))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.3)
		tmp = cos(x);
	elseif (y <= 1.35e+154)
		tmp = sinh(y) / y;
	else
		tmp = ((y * y) / (y / cos(x))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.3], N[Cos[x], $MachinePrecision], If[LessEqual[y, 1.35e+154], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(y * y), $MachinePrecision] / N[(y / N[Cos[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 0.299999999999999989

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.4%

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

   if 0.299999999999999989 < y < 1.35000000000000003e154

   1. Initial program 100.0%

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

      1. add-log-exp 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. log-prod 100.0%

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

      4. metadata-eval 100.0%

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

      5. add-log-exp 100.0%

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

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0 + \cos x \cdot \frac{\sinh y}{y}} \]
   5. Step-by-step derivation

      1. +-lft-identity 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 90.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 90.6%

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

      2. *-commutative 90.6%

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

      3. *-rgt-identity 90.6%

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

      4. metadata-eval 90.6%

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

      5. associate-/l* 90.6%

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

      6. associate-*l/ 90.6%

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

      7. rec-exp 90.6%

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

      8. sinh-def 90.6%

         \[\leadsto \frac{\left(\color{blue}{\sinh y} \cdot 2\right) \cdot 0.5}{y} \]

      9. *-commutative 90.6%

         \[\leadsto \frac{\color{blue}{\left(2 \cdot \sinh y\right)} \cdot 0.5}{y} \]

      10. metadata-eval 90.6%

          \[\leadsto \frac{\left(2 \cdot \sinh y\right) \cdot \color{blue}{\frac{1}{2}}}{y} \]

      11. associate-/l* 90.6%

          \[\leadsto \frac{\color{blue}{\frac{\left(2 \cdot \sinh y\right) \cdot 1}{2}}}{y} \]

      12. *-rgt-identity 90.6%

          \[\leadsto \frac{\frac{\color{blue}{2 \cdot \sinh y}}{2}}{y} \]

      13. *-commutative 90.6%

          \[\leadsto \frac{\frac{\color{blue}{\sinh y \cdot 2}}{2}}{y} \]

      14. associate-/l* 90.6%

          \[\leadsto \frac{\color{blue}{\sinh y \cdot \frac{2}{2}}}{y} \]

      15. metadata-eval 90.6%

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

      16. *-rgt-identity 90.6%

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

   9. Simplified 90.6%

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

   if 1.35000000000000003e154 < y

   1. Initial program 100.0%

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

      1. add-log-exp 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. log-prod 100.0%

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

      4. metadata-eval 100.0%

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

      5. add-log-exp 100.0%

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

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0 + \cos x \cdot \frac{\sinh y}{y}} \]
   5. Step-by-step derivation

      1. +-lft-identity 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 3.1%

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

      1. associate-*r/ 3.1%

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

   9. Applied egg-rr 3.1%

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

       1. *-commutative 3.1%

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

       2. *-un-lft-identity 3.1%

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

       3. rgt-mult-inverse 3.1%

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

       4. un-div-inv 3.1%

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

       5. associate-/r/ 3.1%

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

       6. frac-2neg 3.1%

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

       7. associate-*l/ 100.0%

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

       8. distribute-neg-frac2 100.0%

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

   11. Applied egg-rr 100.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.3:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot y}{\frac{y}{\cos x}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.3:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 0.3) (cos x) (/ (sinh y) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.3) {
		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 <= 0.3d0) 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 <= 0.3) {
		tmp = Math.cos(x);
	} else {
		tmp = Math.sinh(y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.3:
		tmp = math.cos(x)
	else:
		tmp = math.sinh(y) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.3)
		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 <= 0.3)
		tmp = cos(x);
	else
		tmp = sinh(y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.3], N[Cos[x], $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.299999999999999989

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 69.4%

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

   if 0.299999999999999989 < y

   1. Initial program 100.0%

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

      1. add-log-exp 100.0%

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

      2. *-un-lft-identity 100.0%

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

      3. log-prod 100.0%

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

      4. metadata-eval 100.0%

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

      5. add-log-exp 100.0%

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

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0 + \cos x \cdot \frac{\sinh y}{y}} \]
   5. Step-by-step derivation

      1. +-lft-identity 100.0%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 87.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. *-rgt-identity 87.7%

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

      4. metadata-eval 87.7%

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

      5. associate-/l* 87.7%

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

      6. associate-*l/ 87.7%

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

      7. rec-exp 87.7%

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

      8. sinh-def 87.7%

         \[\leadsto \frac{\left(\color{blue}{\sinh y} \cdot 2\right) \cdot 0.5}{y} \]

      9. *-commutative 87.7%

         \[\leadsto \frac{\color{blue}{\left(2 \cdot \sinh y\right)} \cdot 0.5}{y} \]

      10. metadata-eval 87.7%

          \[\leadsto \frac{\left(2 \cdot \sinh y\right) \cdot \color{blue}{\frac{1}{2}}}{y} \]

      11. associate-/l* 87.7%

          \[\leadsto \frac{\color{blue}{\frac{\left(2 \cdot \sinh y\right) \cdot 1}{2}}}{y} \]

      12. *-rgt-identity 87.7%

          \[\leadsto \frac{\frac{\color{blue}{2 \cdot \sinh y}}{2}}{y} \]

      13. *-commutative 87.7%

          \[\leadsto \frac{\frac{\color{blue}{\sinh y \cdot 2}}{2}}{y} \]

      14. associate-/l* 87.7%

          \[\leadsto \frac{\color{blue}{\sinh y \cdot \frac{2}{2}}}{y} \]

      15. metadata-eval 87.7%

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

      16. *-rgt-identity 87.7%

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

   9. Simplified 87.7%

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

Alternative 4: 51.0% 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 50.5%

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

Alternative 5: 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. Add Preprocessing
3. Step-by-step derivation

   1. add-log-exp 99.7%

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

   2. *-un-lft-identity 99.7%

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

   3. log-prod 99.7%

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

   4. metadata-eval 99.7%

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

   5. add-log-exp 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{0 + \cos x \cdot \frac{\sinh y}{y}} \]
5. Step-by-step derivation

   1. +-lft-identity 100.0%

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

   2. associate-*r/ 99.9%

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

   3. *-commutative 99.9%

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

   4. associate-/l* 99.9%

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

6. Simplified 99.9%

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

7. Taylor expanded in y around 0 50.4%

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

8. Taylor expanded in x around 0 27.2%

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))