Linear.Quaternion:$cexp from linear-1.19.1.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.7s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

   \[\leadsto x \cdot \frac{\sin y}{y} \]
4. Add Preprocessing

Alternative 2: 58.0% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot 0.16666666666666666} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.4) x (* (/ 1.0 (* y 0.16666666666666666)) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.4) {
		tmp = x;
	} else {
		tmp = (1.0 / (y * 0.16666666666666666)) * (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 <= 2.4d0) then
        tmp = x
    else
        tmp = (1.0d0 / (y * 0.16666666666666666d0)) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.4) {
		tmp = x;
	} else {
		tmp = (1.0 / (y * 0.16666666666666666)) * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.4:
		tmp = x
	else:
		tmp = (1.0 / (y * 0.16666666666666666)) * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.4)
		tmp = x;
	else
		tmp = Float64(Float64(1.0 / Float64(y * 0.16666666666666666)) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.4)
		tmp = x;
	else
		tmp = (1.0 / (y * 0.16666666666666666)) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.4], x, N[(N[(1.0 / N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.39999999999999991

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.5%

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

   if 2.39999999999999991 < y

   1. Initial program 99.8%

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

      1. associate-*r/ 99.6%

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

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

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

      2. associate-/r/ 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around 0 37.1%

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

   8. Taylor expanded in y around inf 37.1%

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

      1. *-commutative 37.1%

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

   10. Simplified 37.1%

       \[\leadsto \frac{x}{\color{blue}{\left(y \cdot 0.16666666666666666\right)} \cdot y} \]
   11. Step-by-step derivation

       1. *-un-lft-identity 37.1%

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

       2. times-frac 37.2%

          \[\leadsto \color{blue}{\frac{1}{y \cdot 0.16666666666666666} \cdot \frac{x}{y}} \]

   12. Applied egg-rr 37.2%

       \[\leadsto \color{blue}{\frac{1}{y \cdot 0.16666666666666666} \cdot \frac{x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot 0.16666666666666666} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.0% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(y \cdot 0.16666666666666666\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.4) x (/ x (* y (* y 0.16666666666666666)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.4) {
		tmp = x;
	} else {
		tmp = 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 <= 2.4d0) then
        tmp = x
    else
        tmp = x / (y * (y * 0.16666666666666666d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.4) {
		tmp = x;
	} else {
		tmp = x / (y * (y * 0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.4:
		tmp = x
	else:
		tmp = x / (y * (y * 0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.4)
		tmp = x;
	else
		tmp = Float64(x / Float64(y * Float64(y * 0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.4)
		tmp = x;
	else
		tmp = x / (y * (y * 0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.4], x, N[(x / N[(y * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.39999999999999991

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.5%

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

   if 2.39999999999999991 < y

   1. Initial program 99.8%

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

      1. associate-*r/ 99.6%

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

      2. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

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

      2. associate-/r/ 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around 0 37.1%

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

   8. Taylor expanded in y around inf 37.1%

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

      1. *-commutative 37.1%

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

   10. Simplified 37.1%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(y \cdot 0.16666666666666666\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.0% accurate, 9.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-*r/ 84.6%

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

   2. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. clear-num 99.8%

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

   2. associate-/r/ 99.6%

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

6. Applied egg-rr 99.6%

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

7. Taylor expanded in y around 0 67.3%

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

8. Final simplification 67.3%

   \[\leadsto \frac{x}{y \cdot \left(\frac{1}{y} + y \cdot 0.16666666666666666\right)} \]
9. Add Preprocessing

Alternative 5: 57.4% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4e+25) x (* y (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4e+25) {
		tmp = x;
	} else {
		tmp = y * (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 <= 4d+25) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 4e+25) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4e+25:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4e+25)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 4e+25)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4e+25], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.00000000000000036e25

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.2%

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

   if 4.00000000000000036e25 < y

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around 0 4.7%

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

      1. *-commutative 4.7%

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

   7. Simplified 4.7%

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

      1. div-inv 4.7%

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

      2. associate-*l* 39.1%

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

      3. *-commutative 39.1%

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

      4. un-div-inv 39.1%

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

   9. Applied egg-rr 39.1%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.7% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 7.5e-33) x (/ y (/ y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.5e-33) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 7.5d-33) then
        tmp = x
    else
        tmp = y / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 7.5e-33) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.5e-33:
		tmp = x
	else:
		tmp = y / (y / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.5e-33)
		tmp = x;
	else
		tmp = Float64(y / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7.5e-33)
		tmp = x;
	else
		tmp = y / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.5e-33], x, N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5000000000000001e-33

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.2%

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

   if 7.5000000000000001e-33 < y

   1. Initial program 99.8%

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

      1. associate-*r/ 99.0%

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

      2. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-/l* 99.0%

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

      2. div-inv 98.9%

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

      3. *-commutative 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in y around 0 12.6%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{1}{y} \]
   8. Step-by-step derivation

      1. *-commutative 12.6%

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

   9. Simplified 12.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot \frac{1}{y} \]
   10. Step-by-step derivation

       1. div-inv 12.6%

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

       2. associate-/l* 41.4%

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

   11. Applied egg-rr 41.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.9% accurate, 105.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 52.8%

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

4. Final simplification 52.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024017 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))