Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.9% → 99.9%

Time: 6.8s

Alternatives: 11

Speedup: 1.0×

• 49.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.5%

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

   1. associate-*r/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -7 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 40000000:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -7e-5)
   (sinh y)
   (if (<= (sinh y) 40000000.0) (* (sin x) (/ y x)) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -7e-5) {
		tmp = sinh(y);
	} else if (sinh(y) <= 40000000.0) {
		tmp = sin(x) * (y / x);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-7d-5)) then
        tmp = sinh(y)
    else if (sinh(y) <= 40000000.0d0) then
        tmp = sin(x) * (y / x)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -7e-5) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 40000000.0) {
		tmp = Math.sin(x) * (y / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -7e-5:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 40000000.0:
		tmp = math.sin(x) * (y / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -7e-5)
		tmp = sinh(y);
	elseif (sinh(y) <= 40000000.0)
		tmp = Float64(sin(x) * Float64(y / x));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -7e-5)
		tmp = sinh(y);
	elseif (sinh(y) <= 40000000.0)
		tmp = sin(x) * (y / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -7e-5], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 40000000.0], N[(N[Sin[x], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -6.9999999999999994e-5 or 4e7 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 76.1%

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

   if -6.9999999999999994e-5 < (sinh.f64 y) < 4e7

   1. Initial program 73.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 97.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -7 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 40000000:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 3: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -7 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 40000000:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -7e-5)
   (sinh y)
   (if (<= (sinh y) 40000000.0) (/ y (/ x (sin x))) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -7e-5) {
		tmp = sinh(y);
	} else if (sinh(y) <= 40000000.0) {
		tmp = y / (x / sin(x));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-7d-5)) then
        tmp = sinh(y)
    else if (sinh(y) <= 40000000.0d0) then
        tmp = y / (x / sin(x))
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -7e-5) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 40000000.0) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -7e-5:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 40000000.0:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -7e-5)
		tmp = sinh(y);
	elseif (sinh(y) <= 40000000.0)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -7e-5)
		tmp = sinh(y);
	elseif (sinh(y) <= 40000000.0)
		tmp = y / (x / sin(x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -7e-5], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 40000000.0], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -6.9999999999999994e-5 or 4e7 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 76.1%

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

   if -6.9999999999999994e-5 < (sinh.f64 y) < 4e7

   1. Initial program 73.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. associate-/l* 97.5%

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

   6. Simplified 97.5%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -7 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 40000000:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 4: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -1 \cdot 10^{-17}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 40000000:\\ \;\;\;\;\frac{1}{\frac{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -1e-17)
   (sinh y)
   (if (<= (sinh y) 40000000.0)
     (/ 1.0 (/ (+ 1.0 (* x (* x 0.16666666666666666))) y))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -1e-17) {
		tmp = sinh(y);
	} else if (sinh(y) <= 40000000.0) {
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-1d-17)) then
        tmp = sinh(y)
    else if (sinh(y) <= 40000000.0d0) then
        tmp = 1.0d0 / ((1.0d0 + (x * (x * 0.16666666666666666d0))) / y)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -1e-17) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 40000000.0) {
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -1e-17:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 40000000.0:
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -1e-17)
		tmp = sinh(y);
	elseif (sinh(y) <= 40000000.0)
		tmp = Float64(1.0 / Float64(Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666))) / y));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -1e-17)
		tmp = sinh(y);
	elseif (sinh(y) <= 40000000.0)
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -1e-17], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 40000000.0], N[(1.0 / N[(N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -1.00000000000000007e-17 or 4e7 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 75.8%

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

   if -1.00000000000000007e-17 < (sinh.f64 y) < 4e7

   1. Initial program 73.4%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

      1. associate-*r/ 73.4%

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

      2. clear-num 72.2%

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

   5. Applied egg-rr 72.2%

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

   6. Taylor expanded in y around 0 70.1%

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

      1. associate-/r* 96.3%

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

   8. Simplified 96.3%

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

   9. Taylor expanded in x around 0 78.3%

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

       1. associate-*r/ 78.3%

          \[\leadsto \frac{1}{\frac{1}{y} + \color{blue}{\frac{0.16666666666666666 \cdot {x}^{2}}{y}}} \]

       2. metadata-eval 78.3%

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

       3. distribute-lft-neg-in 78.3%

          \[\leadsto \frac{1}{\frac{1}{y} + \frac{\color{blue}{--0.16666666666666666 \cdot {x}^{2}}}{y}} \]

       4. *-commutative 78.3%

          \[\leadsto \frac{1}{\frac{1}{y} + \frac{-\color{blue}{{x}^{2} \cdot -0.16666666666666666}}{y}} \]

       5. unpow2 78.3%

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

       6. associate-*r* 78.3%

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

       7. distribute-frac-neg 78.3%

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

       8. sub-neg 78.3%

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

       9. div-sub 78.3%

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

       10. associate-*r* 78.3%

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

       11. unpow2 78.3%

           \[\leadsto \frac{1}{\frac{1 - \color{blue}{{x}^{2}} \cdot -0.16666666666666666}{y}} \]

       12. *-commutative 78.3%

           \[\leadsto \frac{1}{\frac{1 - \color{blue}{-0.16666666666666666 \cdot {x}^{2}}}{y}} \]

       13. cancel-sign-sub-inv 78.3%

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

       14. metadata-eval 78.3%

           \[\leadsto \frac{1}{\frac{1 + \color{blue}{0.16666666666666666} \cdot {x}^{2}}{y}} \]

       15. *-commutative 78.3%

           \[\leadsto \frac{1}{\frac{1 + \color{blue}{{x}^{2} \cdot 0.16666666666666666}}{y}} \]

       16. unpow2 78.3%

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

       17. associate-*l* 78.3%

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

   11. Simplified 78.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -1 \cdot 10^{-17}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 40000000:\\ \;\;\;\;\frac{1}{\frac{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 5: 87.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 18:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.2e-5)
   (sinh y)
   (if (<= y 18.0)
     (/ y (/ x (sin x)))
     (if (<= y 5e+226)
       (sinh y)
       (* (sinh y) (+ 1.0 (* (* x x) -0.16666666666666666)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.2e-5) {
		tmp = sinh(y);
	} else if (y <= 18.0) {
		tmp = y / (x / sin(x));
	} else if (y <= 5e+226) {
		tmp = sinh(y);
	} else {
		tmp = sinh(y) * (1.0 + ((x * x) * -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 <= (-7.2d-5)) then
        tmp = sinh(y)
    else if (y <= 18.0d0) then
        tmp = y / (x / sin(x))
    else if (y <= 5d+226) then
        tmp = sinh(y)
    else
        tmp = sinh(y) * (1.0d0 + ((x * x) * (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7.2e-5) {
		tmp = Math.sinh(y);
	} else if (y <= 18.0) {
		tmp = y / (x / Math.sin(x));
	} else if (y <= 5e+226) {
		tmp = Math.sinh(y);
	} else {
		tmp = Math.sinh(y) * (1.0 + ((x * x) * -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.2e-5:
		tmp = math.sinh(y)
	elif y <= 18.0:
		tmp = y / (x / math.sin(x))
	elif y <= 5e+226:
		tmp = math.sinh(y)
	else:
		tmp = math.sinh(y) * (1.0 + ((x * x) * -0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.2e-5)
		tmp = sinh(y);
	elseif (y <= 18.0)
		tmp = Float64(y / Float64(x / sin(x)));
	elseif (y <= 5e+226)
		tmp = sinh(y);
	else
		tmp = Float64(sinh(y) * Float64(1.0 + Float64(Float64(x * x) * -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.2e-5)
		tmp = sinh(y);
	elseif (y <= 18.0)
		tmp = y / (x / sin(x));
	elseif (y <= 5e+226)
		tmp = sinh(y);
	else
		tmp = sinh(y) * (1.0 + ((x * x) * -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.2e-5], N[Sinh[y], $MachinePrecision], If[LessEqual[y, 18.0], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+226], N[Sinh[y], $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000018e-5 or 18 < y < 5.0000000000000005e226

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 79.3%

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

   if -7.20000000000000018e-5 < y < 18

   1. Initial program 73.9%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. associate-/l* 97.5%

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

   6. Simplified 97.5%

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

   if 5.0000000000000005e226 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 88.9%

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

      1. *-commutative 43.2%

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

      2. unpow2 43.2%

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

   6. Simplified 88.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-5}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 18:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+226}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 6: 62.6% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+163}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -41000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 540:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 10^{+262}:\\ \;\;\;\;y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (/ (/ x y) x))))
   (if (<= y -2.2e+163)
     t_0
     (if (<= y -5.8e+135)
       (/ 1.0 0.0)
       (if (<= y -1.9e+107)
         t_0
         (if (<= y -41000.0)
           (/ 1.0 0.0)
           (if (<= y 540.0)
             t_0
             (if (<= y 5.2e+226)
               (/ 1.0 0.0)
               (if (<= y 1e+262)
                 (* y (+ 1.0 (* (* x x) -0.16666666666666666)))
                 (/ 1.0 0.0))))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 / ((x / y) / x);
	double tmp;
	if (y <= -2.2e+163) {
		tmp = t_0;
	} else if (y <= -5.8e+135) {
		tmp = 1.0 / 0.0;
	} else if (y <= -1.9e+107) {
		tmp = t_0;
	} else if (y <= -41000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 540.0) {
		tmp = t_0;
	} else if (y <= 5.2e+226) {
		tmp = 1.0 / 0.0;
	} else if (y <= 1e+262) {
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666));
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / ((x / y) / x)
    if (y <= (-2.2d+163)) then
        tmp = t_0
    else if (y <= (-5.8d+135)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= (-1.9d+107)) then
        tmp = t_0
    else if (y <= (-41000.0d0)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 540.0d0) then
        tmp = t_0
    else if (y <= 5.2d+226) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 1d+262) then
        tmp = y * (1.0d0 + ((x * x) * (-0.16666666666666666d0)))
    else
        tmp = 1.0d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 / ((x / y) / x);
	double tmp;
	if (y <= -2.2e+163) {
		tmp = t_0;
	} else if (y <= -5.8e+135) {
		tmp = 1.0 / 0.0;
	} else if (y <= -1.9e+107) {
		tmp = t_0;
	} else if (y <= -41000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 540.0) {
		tmp = t_0;
	} else if (y <= 5.2e+226) {
		tmp = 1.0 / 0.0;
	} else if (y <= 1e+262) {
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666));
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 / ((x / y) / x)
	tmp = 0
	if y <= -2.2e+163:
		tmp = t_0
	elif y <= -5.8e+135:
		tmp = 1.0 / 0.0
	elif y <= -1.9e+107:
		tmp = t_0
	elif y <= -41000.0:
		tmp = 1.0 / 0.0
	elif y <= 540.0:
		tmp = t_0
	elif y <= 5.2e+226:
		tmp = 1.0 / 0.0
	elif y <= 1e+262:
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666))
	else:
		tmp = 1.0 / 0.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 / Float64(Float64(x / y) / x))
	tmp = 0.0
	if (y <= -2.2e+163)
		tmp = t_0;
	elseif (y <= -5.8e+135)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= -1.9e+107)
		tmp = t_0;
	elseif (y <= -41000.0)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 540.0)
		tmp = t_0;
	elseif (y <= 5.2e+226)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 1e+262)
		tmp = Float64(y * Float64(1.0 + Float64(Float64(x * x) * -0.16666666666666666)));
	else
		tmp = Float64(1.0 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 / ((x / y) / x);
	tmp = 0.0;
	if (y <= -2.2e+163)
		tmp = t_0;
	elseif (y <= -5.8e+135)
		tmp = 1.0 / 0.0;
	elseif (y <= -1.9e+107)
		tmp = t_0;
	elseif (y <= -41000.0)
		tmp = 1.0 / 0.0;
	elseif (y <= 540.0)
		tmp = t_0;
	elseif (y <= 5.2e+226)
		tmp = 1.0 / 0.0;
	elseif (y <= 1e+262)
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666));
	else
		tmp = 1.0 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[(N[(x / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+163], t$95$0, If[LessEqual[y, -5.8e+135], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, -1.9e+107], t$95$0, If[LessEqual[y, -41000.0], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 540.0], t$95$0, If[LessEqual[y, 5.2e+226], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 1e+262], N[(y * N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / 0.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999986e163 or -5.7999999999999997e135 < y < -1.8999999999999999e107 or -41000 < y < 540

   1. Initial program 80.3%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 80.3%

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

      2. clear-num 79.4%

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

   5. Applied egg-rr 79.4%

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

   6. Taylor expanded in y around 0 54.7%

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

      1. associate-/r* 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in x around 0 71.0%

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

   if -2.19999999999999986e163 < y < -5.7999999999999997e135 or -1.8999999999999999e107 < y < -41000 or 540 < y < 5.2000000000000005e226 or 1e262 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   7. Applied egg-rr 66.3%

      \[\leadsto \frac{1}{\color{blue}{0}} \]

   if 5.2000000000000005e226 < y < 1e262

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 4.7%

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

   5. Taylor expanded in x around 0 66.1%

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

      1. *-commutative 66.1%

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

      2. unpow2 66.1%

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

   7. Simplified 66.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+163}:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+107}:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq -41000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 540:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 10^{+262}:\\ \;\;\;\;y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \]

Alternative 7: 62.9% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+160}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+107}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -45000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 410:\\ \;\;\;\;\frac{1}{\frac{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 10^{+262}:\\ \;\;\;\;y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (/ (/ x y) x))))
   (if (<= y -7e+160)
     t_0
     (if (<= y -7.2e+134)
       (/ 1.0 0.0)
       (if (<= y -1.75e+107)
         t_0
         (if (<= y -45000.0)
           (/ 1.0 0.0)
           (if (<= y 410.0)
             (/ 1.0 (/ (+ 1.0 (* x (* x 0.16666666666666666))) y))
             (if (<= y 5.2e+226)
               (/ 1.0 0.0)
               (if (<= y 1e+262)
                 (* y (+ 1.0 (* (* x x) -0.16666666666666666)))
                 (/ 1.0 0.0))))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 / ((x / y) / x);
	double tmp;
	if (y <= -7e+160) {
		tmp = t_0;
	} else if (y <= -7.2e+134) {
		tmp = 1.0 / 0.0;
	} else if (y <= -1.75e+107) {
		tmp = t_0;
	} else if (y <= -45000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 410.0) {
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y);
	} else if (y <= 5.2e+226) {
		tmp = 1.0 / 0.0;
	} else if (y <= 1e+262) {
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666));
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / ((x / y) / x)
    if (y <= (-7d+160)) then
        tmp = t_0
    else if (y <= (-7.2d+134)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= (-1.75d+107)) then
        tmp = t_0
    else if (y <= (-45000.0d0)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 410.0d0) then
        tmp = 1.0d0 / ((1.0d0 + (x * (x * 0.16666666666666666d0))) / y)
    else if (y <= 5.2d+226) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 1d+262) then
        tmp = y * (1.0d0 + ((x * x) * (-0.16666666666666666d0)))
    else
        tmp = 1.0d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 / ((x / y) / x);
	double tmp;
	if (y <= -7e+160) {
		tmp = t_0;
	} else if (y <= -7.2e+134) {
		tmp = 1.0 / 0.0;
	} else if (y <= -1.75e+107) {
		tmp = t_0;
	} else if (y <= -45000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 410.0) {
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y);
	} else if (y <= 5.2e+226) {
		tmp = 1.0 / 0.0;
	} else if (y <= 1e+262) {
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666));
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 / ((x / y) / x)
	tmp = 0
	if y <= -7e+160:
		tmp = t_0
	elif y <= -7.2e+134:
		tmp = 1.0 / 0.0
	elif y <= -1.75e+107:
		tmp = t_0
	elif y <= -45000.0:
		tmp = 1.0 / 0.0
	elif y <= 410.0:
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y)
	elif y <= 5.2e+226:
		tmp = 1.0 / 0.0
	elif y <= 1e+262:
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666))
	else:
		tmp = 1.0 / 0.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 / Float64(Float64(x / y) / x))
	tmp = 0.0
	if (y <= -7e+160)
		tmp = t_0;
	elseif (y <= -7.2e+134)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= -1.75e+107)
		tmp = t_0;
	elseif (y <= -45000.0)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 410.0)
		tmp = Float64(1.0 / Float64(Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666))) / y));
	elseif (y <= 5.2e+226)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 1e+262)
		tmp = Float64(y * Float64(1.0 + Float64(Float64(x * x) * -0.16666666666666666)));
	else
		tmp = Float64(1.0 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 / ((x / y) / x);
	tmp = 0.0;
	if (y <= -7e+160)
		tmp = t_0;
	elseif (y <= -7.2e+134)
		tmp = 1.0 / 0.0;
	elseif (y <= -1.75e+107)
		tmp = t_0;
	elseif (y <= -45000.0)
		tmp = 1.0 / 0.0;
	elseif (y <= 410.0)
		tmp = 1.0 / ((1.0 + (x * (x * 0.16666666666666666))) / y);
	elseif (y <= 5.2e+226)
		tmp = 1.0 / 0.0;
	elseif (y <= 1e+262)
		tmp = y * (1.0 + ((x * x) * -0.16666666666666666));
	else
		tmp = 1.0 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[(N[(x / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+160], t$95$0, If[LessEqual[y, -7.2e+134], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, -1.75e+107], t$95$0, If[LessEqual[y, -45000.0], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 410.0], N[(1.0 / N[(N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+226], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 1e+262], N[(y * N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / 0.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.00000000000000051e160 or -7.19999999999999976e134 < y < -1.7499999999999999e107

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 5.6%

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

      1. associate-/r* 57.3%

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

   8. Simplified 57.3%

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

   9. Taylor expanded in x around 0 57.4%

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

   if -7.00000000000000051e160 < y < -7.19999999999999976e134 or -1.7499999999999999e107 < y < -45000 or 410 < y < 5.2000000000000005e226 or 1e262 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   7. Applied egg-rr 66.3%

      \[\leadsto \frac{1}{\color{blue}{0}} \]

   if -45000 < y < 410

   1. Initial program 74.7%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 74.7%

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

      2. clear-num 73.5%

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

   5. Applied egg-rr 73.5%

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

   6. Taylor expanded in y around 0 68.7%

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

      1. associate-/r* 93.6%

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

   8. Simplified 93.6%

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

   9. Taylor expanded in x around 0 75.9%

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

       1. associate-*r/ 75.9%

          \[\leadsto \frac{1}{\frac{1}{y} + \color{blue}{\frac{0.16666666666666666 \cdot {x}^{2}}{y}}} \]

       2. metadata-eval 75.9%

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

       3. distribute-lft-neg-in 75.9%

          \[\leadsto \frac{1}{\frac{1}{y} + \frac{\color{blue}{--0.16666666666666666 \cdot {x}^{2}}}{y}} \]

       4. *-commutative 75.9%

          \[\leadsto \frac{1}{\frac{1}{y} + \frac{-\color{blue}{{x}^{2} \cdot -0.16666666666666666}}{y}} \]

       5. unpow2 75.9%

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

       6. associate-*r* 75.9%

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

       7. distribute-frac-neg 75.9%

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

       8. sub-neg 75.9%

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

       9. div-sub 75.9%

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

       10. associate-*r* 75.9%

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

       11. unpow2 75.9%

           \[\leadsto \frac{1}{\frac{1 - \color{blue}{{x}^{2}} \cdot -0.16666666666666666}{y}} \]

       12. *-commutative 75.9%

           \[\leadsto \frac{1}{\frac{1 - \color{blue}{-0.16666666666666666 \cdot {x}^{2}}}{y}} \]

       13. cancel-sign-sub-inv 75.9%

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

       14. metadata-eval 75.9%

           \[\leadsto \frac{1}{\frac{1 + \color{blue}{0.16666666666666666} \cdot {x}^{2}}{y}} \]

       15. *-commutative 75.9%

           \[\leadsto \frac{1}{\frac{1 + \color{blue}{{x}^{2} \cdot 0.16666666666666666}}{y}} \]

       16. unpow2 75.9%

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

       17. associate-*l* 75.9%

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

   11. Simplified 75.9%

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

   if 5.2000000000000005e226 < y < 1e262

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 4.7%

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

   5. Taylor expanded in x around 0 66.1%

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

      1. *-commutative 66.1%

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

      2. unpow2 66.1%

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

   7. Simplified 66.1%

      \[\leadsto \color{blue}{\left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)} \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+160}:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+107}:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq -45000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 410:\\ \;\;\;\;\frac{1}{\frac{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 10^{+262}:\\ \;\;\;\;y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \]

Alternative 8: 62.4% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{if}\;y \leq -6 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+135}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -42000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 520:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+262}:\\ \;\;\;\;y \cdot \left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (/ (/ x y) x))))
   (if (<= y -6e+161)
     t_0
     (if (<= y -4e+135)
       (/ 1.0 0.0)
       (if (<= y -8.8e+111)
         t_0
         (if (<= y -42000.0)
           (/ 1.0 0.0)
           (if (<= y 520.0)
             t_0
             (if (<= y 5.2e+226)
               (/ 1.0 0.0)
               (if (<= y 1.1e+262)
                 (* y (* x (* x -0.16666666666666666)))
                 (/ 1.0 0.0))))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 / ((x / y) / x);
	double tmp;
	if (y <= -6e+161) {
		tmp = t_0;
	} else if (y <= -4e+135) {
		tmp = 1.0 / 0.0;
	} else if (y <= -8.8e+111) {
		tmp = t_0;
	} else if (y <= -42000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 520.0) {
		tmp = t_0;
	} else if (y <= 5.2e+226) {
		tmp = 1.0 / 0.0;
	} else if (y <= 1.1e+262) {
		tmp = y * (x * (x * -0.16666666666666666));
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / ((x / y) / x)
    if (y <= (-6d+161)) then
        tmp = t_0
    else if (y <= (-4d+135)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= (-8.8d+111)) then
        tmp = t_0
    else if (y <= (-42000.0d0)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 520.0d0) then
        tmp = t_0
    else if (y <= 5.2d+226) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 1.1d+262) then
        tmp = y * (x * (x * (-0.16666666666666666d0)))
    else
        tmp = 1.0d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 / ((x / y) / x);
	double tmp;
	if (y <= -6e+161) {
		tmp = t_0;
	} else if (y <= -4e+135) {
		tmp = 1.0 / 0.0;
	} else if (y <= -8.8e+111) {
		tmp = t_0;
	} else if (y <= -42000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 520.0) {
		tmp = t_0;
	} else if (y <= 5.2e+226) {
		tmp = 1.0 / 0.0;
	} else if (y <= 1.1e+262) {
		tmp = y * (x * (x * -0.16666666666666666));
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 / ((x / y) / x)
	tmp = 0
	if y <= -6e+161:
		tmp = t_0
	elif y <= -4e+135:
		tmp = 1.0 / 0.0
	elif y <= -8.8e+111:
		tmp = t_0
	elif y <= -42000.0:
		tmp = 1.0 / 0.0
	elif y <= 520.0:
		tmp = t_0
	elif y <= 5.2e+226:
		tmp = 1.0 / 0.0
	elif y <= 1.1e+262:
		tmp = y * (x * (x * -0.16666666666666666))
	else:
		tmp = 1.0 / 0.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 / Float64(Float64(x / y) / x))
	tmp = 0.0
	if (y <= -6e+161)
		tmp = t_0;
	elseif (y <= -4e+135)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= -8.8e+111)
		tmp = t_0;
	elseif (y <= -42000.0)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 520.0)
		tmp = t_0;
	elseif (y <= 5.2e+226)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 1.1e+262)
		tmp = Float64(y * Float64(x * Float64(x * -0.16666666666666666)));
	else
		tmp = Float64(1.0 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 / ((x / y) / x);
	tmp = 0.0;
	if (y <= -6e+161)
		tmp = t_0;
	elseif (y <= -4e+135)
		tmp = 1.0 / 0.0;
	elseif (y <= -8.8e+111)
		tmp = t_0;
	elseif (y <= -42000.0)
		tmp = 1.0 / 0.0;
	elseif (y <= 520.0)
		tmp = t_0;
	elseif (y <= 5.2e+226)
		tmp = 1.0 / 0.0;
	elseif (y <= 1.1e+262)
		tmp = y * (x * (x * -0.16666666666666666));
	else
		tmp = 1.0 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[(N[(x / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e+161], t$95$0, If[LessEqual[y, -4e+135], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, -8.8e+111], t$95$0, If[LessEqual[y, -42000.0], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 520.0], t$95$0, If[LessEqual[y, 5.2e+226], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 1.1e+262], N[(y * N[(x * N[(x * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / 0.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.00000000000000023e161 or -3.99999999999999985e135 < y < -8.79999999999999994e111 or -42000 < y < 520

   1. Initial program 80.3%

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

      1. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 80.3%

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

      2. clear-num 79.4%

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

   5. Applied egg-rr 79.4%

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

   6. Taylor expanded in y around 0 54.7%

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

      1. associate-/r* 85.6%

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

   8. Simplified 85.6%

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

   9. Taylor expanded in x around 0 71.0%

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

   if -6.00000000000000023e161 < y < -3.99999999999999985e135 or -8.79999999999999994e111 < y < -42000 or 520 < y < 5.2000000000000005e226 or 1.10000000000000005e262 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   7. Applied egg-rr 66.3%

      \[\leadsto \frac{1}{\color{blue}{0}} \]

   if 5.2000000000000005e226 < y < 1.10000000000000005e262

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 4.7%

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

   5. Taylor expanded in x around 0 66.1%

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

      1. *-commutative 66.1%

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

      2. unpow2 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-*r* 64.6%

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

      3. unpow2 64.6%

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

      4. associate-*r* 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+135}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{+111}:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq -42000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 520:\\ \;\;\;\;\frac{1}{\frac{\frac{x}{y}}{x}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226}:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+262}:\\ \;\;\;\;y \cdot \left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \]

Alternative 9: 48.8% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -41000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 430:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226} \lor \neg \left(y \leq 8.2 \cdot 10^{+264}\right):\\ \;\;\;\;\frac{1}{0}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -41000.0)
   (/ 1.0 0.0)
   (if (<= y 430.0)
     y
     (if (or (<= y 5.2e+226) (not (<= y 8.2e+264)))
       (/ 1.0 0.0)
       (* y (* x (* x -0.16666666666666666)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -41000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 430.0) {
		tmp = y;
	} else if ((y <= 5.2e+226) || !(y <= 8.2e+264)) {
		tmp = 1.0 / 0.0;
	} else {
		tmp = y * (x * (x * -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 <= (-41000.0d0)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 430.0d0) then
        tmp = y
    else if ((y <= 5.2d+226) .or. (.not. (y <= 8.2d+264))) then
        tmp = 1.0d0 / 0.0d0
    else
        tmp = y * (x * (x * (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -41000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 430.0) {
		tmp = y;
	} else if ((y <= 5.2e+226) || !(y <= 8.2e+264)) {
		tmp = 1.0 / 0.0;
	} else {
		tmp = y * (x * (x * -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -41000.0:
		tmp = 1.0 / 0.0
	elif y <= 430.0:
		tmp = y
	elif (y <= 5.2e+226) or not (y <= 8.2e+264):
		tmp = 1.0 / 0.0
	else:
		tmp = y * (x * (x * -0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -41000.0)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 430.0)
		tmp = y;
	elseif ((y <= 5.2e+226) || !(y <= 8.2e+264))
		tmp = Float64(1.0 / 0.0);
	else
		tmp = Float64(y * Float64(x * Float64(x * -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -41000.0)
		tmp = 1.0 / 0.0;
	elseif (y <= 430.0)
		tmp = y;
	elseif ((y <= 5.2e+226) || ~((y <= 8.2e+264)))
		tmp = 1.0 / 0.0;
	else
		tmp = y * (x * (x * -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -41000.0], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 430.0], y, If[Or[LessEqual[y, 5.2e+226], N[Not[LessEqual[y, 8.2e+264]], $MachinePrecision]], N[(1.0 / 0.0), $MachinePrecision], N[(y * N[(x * N[(x * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -41000 or 430 < y < 5.2000000000000005e226 or 8.1999999999999999e264 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   7. Applied egg-rr 51.3%

      \[\leadsto \frac{1}{\color{blue}{0}} \]

   if -41000 < y < 430

   1. Initial program 74.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 94.9%

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

   5. Taylor expanded in x around 0 51.1%

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

   if 5.2000000000000005e226 < y < 8.1999999999999999e264

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 4.7%

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

   5. Taylor expanded in x around 0 66.1%

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

      1. *-commutative 66.1%

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

      2. unpow2 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in x around inf 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-*r* 64.6%

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

      3. unpow2 64.6%

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

      4. associate-*r* 64.6%

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

   10. Simplified 64.6%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -41000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 430:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+226} \lor \neg \left(y \leq 8.2 \cdot 10^{+264}\right):\\ \;\;\;\;\frac{1}{0}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(x \cdot -0.16666666666666666\right)\right)\\ \end{array} \]

Alternative 10: 50.4% accurate, 28.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -41000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 510:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -41000.0) (/ 1.0 0.0) (if (<= y 510.0) y (/ 1.0 0.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -41000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 510.0) {
		tmp = y;
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-41000.0d0)) then
        tmp = 1.0d0 / 0.0d0
    else if (y <= 510.0d0) then
        tmp = y
    else
        tmp = 1.0d0 / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -41000.0) {
		tmp = 1.0 / 0.0;
	} else if (y <= 510.0) {
		tmp = y;
	} else {
		tmp = 1.0 / 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -41000.0:
		tmp = 1.0 / 0.0
	elif y <= 510.0:
		tmp = y
	else:
		tmp = 1.0 / 0.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -41000.0)
		tmp = Float64(1.0 / 0.0);
	elseif (y <= 510.0)
		tmp = y;
	else
		tmp = Float64(1.0 / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -41000.0)
		tmp = 1.0 / 0.0;
	elseif (y <= 510.0)
		tmp = y;
	else
		tmp = 1.0 / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -41000.0], N[(1.0 / 0.0), $MachinePrecision], If[LessEqual[y, 510.0], y, N[(1.0 / 0.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -41000 or 510 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

      1. associate-*r/ 100.0%

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

      2. clear-num 100.0%

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

   5. Applied egg-rr 100.0%

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

   7. Applied egg-rr 49.2%

      \[\leadsto \frac{1}{\color{blue}{0}} \]

   if -41000 < y < 510

   1. Initial program 74.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 94.9%

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

   5. Taylor expanded in x around 0 51.1%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -41000:\\ \;\;\;\;\frac{1}{0}\\ \mathbf{elif}\;y \leq 510:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{0}\\ \end{array} \]

Alternative 11: 28.2% accurate, 205.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 87.5%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 49.0%

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

5. Taylor expanded in x around 0 27.3%

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

6. Final simplification 27.3%

   \[\leadsto y \]

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024034 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

  (/ (* (sin x) (sinh y)) x))