Linear.Quaternion:$csinh from linear-1.19.1.3

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 13

Speedup: 1.0×

• 48.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cbrt-cube 64.6%

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

   2. pow3 64.6%

      \[\leadsto \cosh x \cdot \frac{\sqrt[3]{\color{blue}{{\sin y}^{3}}}}{y} \]

3. Applied egg-rr 64.6%

   \[\leadsto \cosh x \cdot \frac{\color{blue}{\sqrt[3]{{\sin y}^{3}}}}{y} \]
4. Step-by-step derivation

   1. *-commutative 64.6%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{{\sin y}^{3}}}{y} \cdot \cosh x} \]

   2. rem-cbrt-cube 99.9%

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

   3. associate-*l/ 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

   \[\leadsto \frac{\sin y \cdot \cosh x}{y} \]

Alternative 2: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\cosh x \leq 2:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (cosh x) 2.0) (/ (sin y) y) (cosh x)))

C

double code(double x, double y) {
	double tmp;
	if (cosh(x) <= 2.0) {
		tmp = sin(y) / y;
	} else {
		tmp = cosh(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (cosh(x) <= 2.0d0) then
        tmp = sin(y) / y
    else
        tmp = cosh(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.cosh(x) <= 2.0) {
		tmp = Math.sin(y) / y;
	} else {
		tmp = Math.cosh(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.cosh(x) <= 2.0:
		tmp = math.sin(y) / y
	else:
		tmp = math.cosh(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (cosh(x) <= 2.0)
		tmp = Float64(sin(y) / y);
	else
		tmp = cosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (cosh(x) <= 2.0)
		tmp = sin(y) / y;
	else
		tmp = cosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Cosh[x], $MachinePrecision], 2.0], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[Cosh[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cosh.f64 x) < 2

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 99.3%

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

   if 2 < (cosh.f64 x)

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 75.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cosh x \leq 2:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\cosh x \cdot \frac{\sin y}{y} \]

2. Final simplification 99.9%

   \[\leadsto \frac{\sin y}{y} \cdot \cosh x \]

Alternative 4: 92.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+137} \lor \neg \left(x \leq -0.054\right) \land \left(x \leq 0.0132 \lor \neg \left(x \leq 1.9 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{1 + x \cdot \left(x \cdot 0.5\right)}{\frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.2e+137)
         (and (not (<= x -0.054)) (or (<= x 0.0132) (not (<= x 1.9e+154)))))
   (/ (+ 1.0 (* x (* x 0.5))) (/ y (sin y)))
   (cosh x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.2e+137) || (!(x <= -0.054) && ((x <= 0.0132) || !(x <= 1.9e+154)))) {
		tmp = (1.0 + (x * (x * 0.5))) / (y / sin(y));
	} else {
		tmp = cosh(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.2d+137)) .or. (.not. (x <= (-0.054d0))) .and. (x <= 0.0132d0) .or. (.not. (x <= 1.9d+154))) then
        tmp = (1.0d0 + (x * (x * 0.5d0))) / (y / sin(y))
    else
        tmp = cosh(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.2e+137) || (!(x <= -0.054) && ((x <= 0.0132) || !(x <= 1.9e+154)))) {
		tmp = (1.0 + (x * (x * 0.5))) / (y / Math.sin(y));
	} else {
		tmp = Math.cosh(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.2e+137) or (not (x <= -0.054) and ((x <= 0.0132) or not (x <= 1.9e+154))):
		tmp = (1.0 + (x * (x * 0.5))) / (y / math.sin(y))
	else:
		tmp = math.cosh(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.2e+137) || (!(x <= -0.054) && ((x <= 0.0132) || !(x <= 1.9e+154))))
		tmp = Float64(Float64(1.0 + Float64(x * Float64(x * 0.5))) / Float64(y / sin(y)));
	else
		tmp = cosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.2e+137) || (~((x <= -0.054)) && ((x <= 0.0132) || ~((x <= 1.9e+154)))))
		tmp = (1.0 + (x * (x * 0.5))) / (y / sin(y));
	else
		tmp = cosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.2e+137], And[N[Not[LessEqual[x, -0.054]], $MachinePrecision], Or[LessEqual[x, 0.0132], N[Not[LessEqual[x, 1.9e+154]], $MachinePrecision]]]], N[(N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Cosh[x], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999998e137 or -0.0539999999999999994 < x < 0.0132 or 1.8999999999999999e154 < x

   1. Initial program 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in x around 0 98.8%

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

      1. *-rgt-identity 98.8%

         \[\leadsto \frac{\color{blue}{\sin y \cdot 1}}{y} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      2. associate-*r/ 98.6%

         \[\leadsto \color{blue}{\sin y \cdot \frac{1}{y}} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      3. *-commutative 98.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot {x}^{2}}{y} \cdot 0.5} \]

      4. associate-/l* 98.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y}{\frac{y}{{x}^{2}}}} \cdot 0.5 \]

      5. unpow2 98.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\frac{y}{\color{blue}{x \cdot x}}} \cdot 0.5 \]

      6. associate-/r* 92.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\color{blue}{\frac{\frac{y}{x}}{x}}} \cdot 0.5 \]

      7. associate-/l* 92.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot x}{\frac{y}{x}}} \cdot 0.5 \]

      8. associate-*r/ 92.2%

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

      9. associate-*r* 92.2%

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

      10. distribute-lft-out 92.2%

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

      11. *-commutative 92.2%

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

      12. associate-/r/ 92.2%

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

      13. *-commutative 92.2%

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

   6. Simplified 92.2%

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

   7. Taylor expanded in y around inf 98.8%

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

      1. associate-/l* 98.7%

         \[\leadsto \color{blue}{\frac{1 + 0.5 \cdot {x}^{2}}{\frac{y}{\sin y}}} \]

      2. unpow2 98.7%

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

      3. associate-*r* 98.7%

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

      4. *-commutative 98.7%

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

      5. associate-*l* 98.7%

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

   9. Simplified 98.7%

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

   if -4.1999999999999998e137 < x < -0.0539999999999999994 or 0.0132 < x < 1.8999999999999999e154

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 80.8%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+137} \lor \neg \left(x \leq -0.054\right) \land \left(x \leq 0.0132 \lor \neg \left(x \leq 1.9 \cdot 10^{+154}\right)\right):\\ \;\;\;\;\frac{1 + x \cdot \left(x \cdot 0.5\right)}{\frac{y}{\sin y}}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 5: 87.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.053:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.053)
   (* (cosh x) (+ 1.0 (* -0.16666666666666666 (* y y))))
   (if (<= x 7e-5) (/ (sin y) y) (cosh x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.053) {
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else if (x <= 7e-5) {
		tmp = sin(y) / y;
	} else {
		tmp = cosh(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.053d0)) then
        tmp = cosh(x) * (1.0d0 + ((-0.16666666666666666d0) * (y * y)))
    else if (x <= 7d-5) then
        tmp = sin(y) / y
    else
        tmp = cosh(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.053) {
		tmp = Math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	} else if (x <= 7e-5) {
		tmp = Math.sin(y) / y;
	} else {
		tmp = Math.cosh(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.053:
		tmp = math.cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)))
	elif x <= 7e-5:
		tmp = math.sin(y) / y
	else:
		tmp = math.cosh(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.053)
		tmp = Float64(cosh(x) * Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y))));
	elseif (x <= 7e-5)
		tmp = Float64(sin(y) / y);
	else
		tmp = cosh(x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.053)
		tmp = cosh(x) * (1.0 + (-0.16666666666666666 * (y * y)));
	elseif (x <= 7e-5)
		tmp = sin(y) / y;
	else
		tmp = cosh(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.053], N[(N[Cosh[x], $MachinePrecision] * N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-5], N[(N[Sin[y], $MachinePrecision] / y), $MachinePrecision], N[Cosh[x], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0529999999999999985

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 74.0%

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

      1. unpow2 30.0%

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

   4. Simplified 74.0%

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

   if -0.0529999999999999985 < x < 6.9999999999999994e-5

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 99.3%

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

   if 6.9999999999999994e-5 < x

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in y around 0 83.8%

      \[\leadsto \cosh x \cdot \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.053:\\ \;\;\;\;\cosh x \cdot \left(1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\frac{\sin y}{y}\\ \mathbf{else}:\\ \;\;\;\;\cosh x\\ \end{array} \]

Alternative 6: 62.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\cosh x \cdot \frac{\sin y}{y} \]

2. Taylor expanded in y around 0 66.3%

   \[\leadsto \cosh x \cdot \color{blue}{1} \]

3. Final simplification 66.3%

   \[\leadsto \cosh x \]

Alternative 7: 53.7% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+148} \lor \neg \left(y \leq 9.2 \cdot 10^{+178}\right):\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 + x \cdot \left(x \cdot 0.5\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.5e+148) (not (<= y 9.2e+178)))
   (* -0.16666666666666666 (* y y))
   (* y (/ (+ 1.0 (* x (* x 0.5))) y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+148) || !(y <= 9.2e+178)) {
		tmp = -0.16666666666666666 * (y * y);
	} else {
		tmp = y * ((1.0 + (x * (x * 0.5))) / 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 <= (-8.5d+148)) .or. (.not. (y <= 9.2d+178))) then
        tmp = (-0.16666666666666666d0) * (y * y)
    else
        tmp = y * ((1.0d0 + (x * (x * 0.5d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+148) || !(y <= 9.2e+178)) {
		tmp = -0.16666666666666666 * (y * y);
	} else {
		tmp = y * ((1.0 + (x * (x * 0.5))) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.5e+148) or not (y <= 9.2e+178):
		tmp = -0.16666666666666666 * (y * y)
	else:
		tmp = y * ((1.0 + (x * (x * 0.5))) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.5e+148) || !(y <= 9.2e+178))
		tmp = Float64(-0.16666666666666666 * Float64(y * y));
	else
		tmp = Float64(y * Float64(Float64(1.0 + Float64(x * Float64(x * 0.5))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.5e+148) || ~((y <= 9.2e+178)))
		tmp = -0.16666666666666666 * (y * y);
	else
		tmp = y * ((1.0 + (x * (x * 0.5))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.5e+148], N[Not[LessEqual[y, 9.2e+178]], $MachinePrecision]], N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e148 or 9.2000000000000003e178 < y

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 45.2%

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

   3. Taylor expanded in y around 0 32.3%

      \[\leadsto \frac{\color{blue}{-0.16666666666666666 \cdot {y}^{3} + y}}{y} \]

   4. Taylor expanded in y around inf 30.7%

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

      1. unpow2 30.7%

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

   6. Simplified 30.7%

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

   if -8.4999999999999996e148 < y < 9.2000000000000003e178

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around 0 82.4%

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

      1. *-rgt-identity 82.4%

         \[\leadsto \frac{\color{blue}{\sin y \cdot 1}}{y} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      2. associate-*r/ 82.3%

         \[\leadsto \color{blue}{\sin y \cdot \frac{1}{y}} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      3. *-commutative 82.3%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot {x}^{2}}{y} \cdot 0.5} \]

      4. associate-/l* 88.8%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y}{\frac{y}{{x}^{2}}}} \cdot 0.5 \]

      5. unpow2 88.8%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\frac{y}{\color{blue}{x \cdot x}}} \cdot 0.5 \]

      6. associate-/r* 86.5%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\color{blue}{\frac{\frac{y}{x}}{x}}} \cdot 0.5 \]

      7. associate-/l* 84.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot x}{\frac{y}{x}}} \cdot 0.5 \]

      8. associate-*r/ 87.0%

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

      9. associate-*r* 87.0%

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

      10. distribute-lft-out 87.0%

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

      11. *-commutative 87.0%

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

      12. associate-/r/ 87.0%

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

      13. *-commutative 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 68.8%

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

   8. Taylor expanded in y around 0 68.8%

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

      1. unpow2 68.8%

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

      2. associate-*r* 68.8%

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

      3. *-commutative 68.8%

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

      4. associate-*l* 68.8%

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

   10. Simplified 68.8%

       \[\leadsto y \cdot \color{blue}{\frac{1 + x \cdot \left(0.5 \cdot x\right)}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+148} \lor \neg \left(y \leq 9.2 \cdot 10^{+178}\right):\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 + x \cdot \left(x \cdot 0.5\right)}{y}\\ \end{array} \]

Alternative 8: 45.6% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -6.1 \cdot 10^{+172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1200:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.5 (* x x))))
   (if (<= x -6.1e+172)
     t_0
     (if (<= x -1200.0)
       (* -0.16666666666666666 (* y y))
       (if (<= x 3.3e-9) 1.0 t_0)))))

C

double code(double x, double y) {
	double t_0 = 0.5 * (x * x);
	double tmp;
	if (x <= -6.1e+172) {
		tmp = t_0;
	} else if (x <= -1200.0) {
		tmp = -0.16666666666666666 * (y * y);
	} else if (x <= 3.3e-9) {
		tmp = 1.0;
	} 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 = 0.5d0 * (x * x)
    if (x <= (-6.1d+172)) then
        tmp = t_0
    else if (x <= (-1200.0d0)) then
        tmp = (-0.16666666666666666d0) * (y * y)
    else if (x <= 3.3d-9) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.5 * (x * x);
	double tmp;
	if (x <= -6.1e+172) {
		tmp = t_0;
	} else if (x <= -1200.0) {
		tmp = -0.16666666666666666 * (y * y);
	} else if (x <= 3.3e-9) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.5 * (x * x)
	tmp = 0
	if x <= -6.1e+172:
		tmp = t_0
	elif x <= -1200.0:
		tmp = -0.16666666666666666 * (y * y)
	elif x <= 3.3e-9:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.5 * Float64(x * x))
	tmp = 0.0
	if (x <= -6.1e+172)
		tmp = t_0;
	elseif (x <= -1200.0)
		tmp = Float64(-0.16666666666666666 * Float64(y * y));
	elseif (x <= 3.3e-9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.5 * (x * x);
	tmp = 0.0;
	if (x <= -6.1e+172)
		tmp = t_0;
	elseif (x <= -1200.0)
		tmp = -0.16666666666666666 * (y * y);
	elseif (x <= 3.3e-9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.1e+172], t$95$0, If[LessEqual[x, -1200.0], N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-9], 1.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0999999999999998e172 or 3.30000000000000018e-9 < x

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 70.2%

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

      1. *-rgt-identity 70.2%

         \[\leadsto \frac{\color{blue}{\sin y \cdot 1}}{y} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      2. associate-*r/ 70.2%

         \[\leadsto \color{blue}{\sin y \cdot \frac{1}{y}} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      3. *-commutative 70.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot {x}^{2}}{y} \cdot 0.5} \]

      4. associate-/l* 80.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y}{\frac{y}{{x}^{2}}}} \cdot 0.5 \]

      5. unpow2 80.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\frac{y}{\color{blue}{x \cdot x}}} \cdot 0.5 \]

      6. associate-/r* 68.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\color{blue}{\frac{\frac{y}{x}}{x}}} \cdot 0.5 \]

      7. associate-/l* 64.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot x}{\frac{y}{x}}} \cdot 0.5 \]

      8. associate-*r/ 69.2%

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

      9. associate-*r* 69.2%

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

      10. distribute-lft-out 69.2%

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

      11. *-commutative 69.2%

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

      12. associate-/r/ 69.2%

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

      13. *-commutative 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in x around inf 52.7%

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

      1. unpow2 52.7%

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

   10. Simplified 52.7%

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

   if -6.0999999999999998e172 < x < -1200

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 2.3%

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

   3. Taylor expanded in y around 0 38.9%

      \[\leadsto \frac{\color{blue}{-0.16666666666666666 \cdot {y}^{3} + y}}{y} \]

   4. Taylor expanded in y around inf 34.1%

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

      1. unpow2 34.1%

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

   6. Simplified 34.1%

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

   if -1200 < x < 3.30000000000000018e-9

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 98.0%

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

   3. Taylor expanded in y around 0 57.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+172}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq -1200:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 9: 45.6% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(x \cdot x\right)\\ \mathbf{if}\;x \leq -6.1 \cdot 10^{+172}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -520:\\ \;\;\;\;y \cdot \left(y \cdot -0.16666666666666666\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.5 (* x x))))
   (if (<= x -6.1e+172)
     t_0
     (if (<= x -520.0)
       (* y (* y -0.16666666666666666))
       (if (<= x 3.3e-9) 1.0 t_0)))))

C

double code(double x, double y) {
	double t_0 = 0.5 * (x * x);
	double tmp;
	if (x <= -6.1e+172) {
		tmp = t_0;
	} else if (x <= -520.0) {
		tmp = y * (y * -0.16666666666666666);
	} else if (x <= 3.3e-9) {
		tmp = 1.0;
	} 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 = 0.5d0 * (x * x)
    if (x <= (-6.1d+172)) then
        tmp = t_0
    else if (x <= (-520.0d0)) then
        tmp = y * (y * (-0.16666666666666666d0))
    else if (x <= 3.3d-9) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.5 * (x * x);
	double tmp;
	if (x <= -6.1e+172) {
		tmp = t_0;
	} else if (x <= -520.0) {
		tmp = y * (y * -0.16666666666666666);
	} else if (x <= 3.3e-9) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.5 * (x * x)
	tmp = 0
	if x <= -6.1e+172:
		tmp = t_0
	elif x <= -520.0:
		tmp = y * (y * -0.16666666666666666)
	elif x <= 3.3e-9:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.5 * Float64(x * x))
	tmp = 0.0
	if (x <= -6.1e+172)
		tmp = t_0;
	elseif (x <= -520.0)
		tmp = Float64(y * Float64(y * -0.16666666666666666));
	elseif (x <= 3.3e-9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.5 * (x * x);
	tmp = 0.0;
	if (x <= -6.1e+172)
		tmp = t_0;
	elseif (x <= -520.0)
		tmp = y * (y * -0.16666666666666666);
	elseif (x <= 3.3e-9)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.1e+172], t$95$0, If[LessEqual[x, -520.0], N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e-9], 1.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.0999999999999998e172 or 3.30000000000000018e-9 < x

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 70.2%

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

      1. *-rgt-identity 70.2%

         \[\leadsto \frac{\color{blue}{\sin y \cdot 1}}{y} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      2. associate-*r/ 70.2%

         \[\leadsto \color{blue}{\sin y \cdot \frac{1}{y}} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      3. *-commutative 70.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot {x}^{2}}{y} \cdot 0.5} \]

      4. associate-/l* 80.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y}{\frac{y}{{x}^{2}}}} \cdot 0.5 \]

      5. unpow2 80.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\frac{y}{\color{blue}{x \cdot x}}} \cdot 0.5 \]

      6. associate-/r* 68.2%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\color{blue}{\frac{\frac{y}{x}}{x}}} \cdot 0.5 \]

      7. associate-/l* 64.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot x}{\frac{y}{x}}} \cdot 0.5 \]

      8. associate-*r/ 69.2%

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

      9. associate-*r* 69.2%

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

      10. distribute-lft-out 69.2%

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

      11. *-commutative 69.2%

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

      12. associate-/r/ 69.2%

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

      13. *-commutative 69.2%

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

   6. Simplified 69.2%

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

   7. Taylor expanded in y around 0 63.6%

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

   8. Taylor expanded in x around inf 52.7%

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

      1. unpow2 52.7%

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

   10. Simplified 52.7%

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

   if -6.0999999999999998e172 < x < -520

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 2.3%

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

   3. Taylor expanded in y around 0 38.9%

      \[\leadsto \frac{\color{blue}{-0.16666666666666666 \cdot {y}^{3} + y}}{y} \]

   4. Taylor expanded in y around inf 34.1%

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

      1. unpow2 34.1%

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

      2. *-commutative 34.1%

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

      3. associate-*l* 34.1%

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

   6. Simplified 34.1%

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

   if -520 < x < 3.30000000000000018e-9

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 98.0%

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

   3. Taylor expanded in y around 0 57.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+172}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \mathbf{elif}\;x \leq -520:\\ \;\;\;\;y \cdot \left(y \cdot -0.16666666666666666\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \end{array} \]

Alternative 10: 46.8% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+172} \lor \neg \left(x \leq 2.8 \cdot 10^{+149}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6.1e+172) (not (<= x 2.8e+149)))
   (* 0.5 (* x x))
   (+ 1.0 (* -0.16666666666666666 (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6.1e+172) || !(x <= 2.8e+149)) {
		tmp = 0.5 * (x * x);
	} else {
		tmp = 1.0 + (-0.16666666666666666 * (y * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-6.1d+172)) .or. (.not. (x <= 2.8d+149))) then
        tmp = 0.5d0 * (x * x)
    else
        tmp = 1.0d0 + ((-0.16666666666666666d0) * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -6.1e+172) || !(x <= 2.8e+149)) {
		tmp = 0.5 * (x * x);
	} else {
		tmp = 1.0 + (-0.16666666666666666 * (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6.1e+172) or not (x <= 2.8e+149):
		tmp = 0.5 * (x * x)
	else:
		tmp = 1.0 + (-0.16666666666666666 * (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6.1e+172) || !(x <= 2.8e+149))
		tmp = Float64(0.5 * Float64(x * x));
	else
		tmp = Float64(1.0 + Float64(-0.16666666666666666 * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6.1e+172) || ~((x <= 2.8e+149)))
		tmp = 0.5 * (x * x);
	else
		tmp = 1.0 + (-0.16666666666666666 * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6.1e+172], N[Not[LessEqual[x, 2.8e+149]], $MachinePrecision]], N[(0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0999999999999998e172 or 2.7999999999999999e149 < x

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      2. un-div-inv 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 97.4%

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

      1. *-rgt-identity 97.4%

         \[\leadsto \frac{\color{blue}{\sin y \cdot 1}}{y} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      2. associate-*r/ 97.4%

         \[\leadsto \color{blue}{\sin y \cdot \frac{1}{y}} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      3. *-commutative 97.4%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot {x}^{2}}{y} \cdot 0.5} \]

      4. associate-/l* 98.7%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y}{\frac{y}{{x}^{2}}}} \cdot 0.5 \]

      5. unpow2 98.7%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\frac{y}{\color{blue}{x \cdot x}}} \cdot 0.5 \]

      6. associate-/r* 81.5%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\color{blue}{\frac{\frac{y}{x}}{x}}} \cdot 0.5 \]

      7. associate-/l* 80.3%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot x}{\frac{y}{x}}} \cdot 0.5 \]

      8. associate-*r/ 81.5%

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

      9. associate-*r* 81.5%

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

      10. distribute-lft-out 81.5%

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

      11. *-commutative 81.5%

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

      12. associate-/r/ 81.5%

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

      13. *-commutative 81.5%

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

   6. Simplified 81.5%

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

   7. Taylor expanded in y around 0 74.8%

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

   8. Taylor expanded in x around inf 73.6%

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

      1. unpow2 73.6%

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

   10. Simplified 73.6%

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

   if -6.0999999999999998e172 < x < 2.7999999999999999e149

   1. Initial program 99.9%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 71.7%

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

   3. Taylor expanded in y around 0 47.1%

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

      1. unpow2 47.1%

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

   5. Simplified 47.1%

      \[\leadsto \color{blue}{1 + -0.16666666666666666 \cdot \left(y \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.1 \cdot 10^{+172} \lor \neg \left(x \leq 2.8 \cdot 10^{+149}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;1 + -0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 11: 47.8% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+148} \lor \neg \left(y \leq 9.2 \cdot 10^{+178}\right):\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.5e+148) (not (<= y 9.2e+178)))
   (* -0.16666666666666666 (* y y))
   (+ 1.0 (* x (* x 0.5)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+148) || !(y <= 9.2e+178)) {
		tmp = -0.16666666666666666 * (y * y);
	} else {
		tmp = 1.0 + (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 <= (-8.5d+148)) .or. (.not. (y <= 9.2d+178))) then
        tmp = (-0.16666666666666666d0) * (y * y)
    else
        tmp = 1.0d0 + (x * (x * 0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8.5e+148) || !(y <= 9.2e+178)) {
		tmp = -0.16666666666666666 * (y * y);
	} else {
		tmp = 1.0 + (x * (x * 0.5));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.5e+148) or not (y <= 9.2e+178):
		tmp = -0.16666666666666666 * (y * y)
	else:
		tmp = 1.0 + (x * (x * 0.5))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.5e+148) || !(y <= 9.2e+178))
		tmp = Float64(-0.16666666666666666 * Float64(y * y));
	else
		tmp = Float64(1.0 + Float64(x * Float64(x * 0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.5e+148) || ~((y <= 9.2e+178)))
		tmp = -0.16666666666666666 * (y * y);
	else
		tmp = 1.0 + (x * (x * 0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.5e+148], N[Not[LessEqual[y, 9.2e+178]], $MachinePrecision]], N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4999999999999996e148 or 9.2000000000000003e178 < y

   1. Initial program 99.8%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 45.2%

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

   3. Taylor expanded in y around 0 32.3%

      \[\leadsto \frac{\color{blue}{-0.16666666666666666 \cdot {y}^{3} + y}}{y} \]

   4. Taylor expanded in y around inf 30.7%

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

      1. unpow2 30.7%

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

   6. Simplified 30.7%

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

   if -8.4999999999999996e148 < y < 9.2000000000000003e178

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around 0 82.4%

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

      1. *-rgt-identity 82.4%

         \[\leadsto \frac{\color{blue}{\sin y \cdot 1}}{y} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      2. associate-*r/ 82.3%

         \[\leadsto \color{blue}{\sin y \cdot \frac{1}{y}} + 0.5 \cdot \frac{\sin y \cdot {x}^{2}}{y} \]

      3. *-commutative 82.3%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot {x}^{2}}{y} \cdot 0.5} \]

      4. associate-/l* 88.8%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y}{\frac{y}{{x}^{2}}}} \cdot 0.5 \]

      5. unpow2 88.8%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\frac{y}{\color{blue}{x \cdot x}}} \cdot 0.5 \]

      6. associate-/r* 86.5%

         \[\leadsto \sin y \cdot \frac{1}{y} + \frac{\sin y}{\color{blue}{\frac{\frac{y}{x}}{x}}} \cdot 0.5 \]

      7. associate-/l* 84.6%

         \[\leadsto \sin y \cdot \frac{1}{y} + \color{blue}{\frac{\sin y \cdot x}{\frac{y}{x}}} \cdot 0.5 \]

      8. associate-*r/ 87.0%

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

      9. associate-*r* 87.0%

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

      10. distribute-lft-out 87.0%

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

      11. *-commutative 87.0%

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

      12. associate-/r/ 87.0%

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

      13. *-commutative 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in y around 0 61.8%

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

      1. unpow2 61.8%

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

      2. associate-*r* 61.8%

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

      3. *-commutative 61.8%

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

      4. associate-*l* 61.8%

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

   9. Simplified 61.8%

      \[\leadsto \color{blue}{1 + x \cdot \left(0.5 \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+148} \lor \neg \left(y \leq 9.2 \cdot 10^{+178}\right):\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x \cdot 0.5\right)\\ \end{array} \]

Alternative 12: 30.4% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1200:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1200.0) (* -0.16666666666666666 (* y y)) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1200.0) {
		tmp = -0.16666666666666666 * (y * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1200.0d0)) then
        tmp = (-0.16666666666666666d0) * (y * y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1200.0) {
		tmp = -0.16666666666666666 * (y * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1200.0:
		tmp = -0.16666666666666666 * (y * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1200.0)
		tmp = Float64(-0.16666666666666666 * Float64(y * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1200.0)
		tmp = -0.16666666666666666 * (y * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1200.0], N[(-0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1200

   1. Initial program 100.0%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 2.5%

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

   3. Taylor expanded in y around 0 32.7%

      \[\leadsto \frac{\color{blue}{-0.16666666666666666 \cdot {y}^{3} + y}}{y} \]

   4. Taylor expanded in y around inf 30.2%

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

      1. unpow2 30.2%

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

   6. Simplified 30.2%

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

   if -1200 < x

   1. Initial program 99.9%

      \[\cosh x \cdot \frac{\sin y}{y} \]

   2. Taylor expanded in x around 0 64.1%

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

   3. Taylor expanded in y around 0 37.5%

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

4. Final simplification 36.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1200:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 27.6% 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 99.9%

   \[\cosh x \cdot \frac{\sin y}{y} \]

2. Taylor expanded in x around 0 52.6%

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

3. Taylor expanded in y around 0 30.8%

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

4. Final simplification 30.8%

   \[\leadsto 1 \]

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))