Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.3% → 99.9%

Time: 10.8s

Alternatives: 12

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: 89.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.3%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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. Final simplification 100.0%

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

Alternative 2: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty \lor \neg \left(\sinh y \leq 2 \cdot 10^{-25}\right):\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (sinh y) (- INFINITY)) (not (<= (sinh y) 2e-25)))
   (* (+ 1.0 (* -0.16666666666666666 (* x x))) (sinh y))
   (* (/ (sin x) x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((sinh(y) <= -((double) INFINITY)) || !(sinh(y) <= 2e-25)) {
		tmp = (1.0 + (-0.16666666666666666 * (x * x))) * sinh(y);
	} else {
		tmp = (sin(x) / x) * y;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if ((Math.sinh(y) <= -Double.POSITIVE_INFINITY) || !(Math.sinh(y) <= 2e-25)) {
		tmp = (1.0 + (-0.16666666666666666 * (x * x))) * Math.sinh(y);
	} else {
		tmp = (Math.sin(x) / x) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.sinh(y) <= -math.inf) or not (math.sinh(y) <= 2e-25):
		tmp = (1.0 + (-0.16666666666666666 * (x * x))) * math.sinh(y)
	else:
		tmp = (math.sin(x) / x) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((sinh(y) <= Float64(-Inf)) || !(sinh(y) <= 2e-25))
		tmp = Float64(Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))) * sinh(y));
	else
		tmp = Float64(Float64(sin(x) / x) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((sinh(y) <= -Inf) || ~((sinh(y) <= 2e-25)))
		tmp = (1.0 + (-0.16666666666666666 * (x * x))) * sinh(y);
	else
		tmp = (sin(x) / x) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[Sinh[y], $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[Sinh[y], $MachinePrecision], 2e-25]], $MachinePrecision]], N[(N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -inf.0 or 2.00000000000000008e-25 < (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 79.6%

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

      1. unpow2 23.1%

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

   6. Simplified 79.6%

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

   if -inf.0 < (sinh.f64 y) < 2.00000000000000008e-25

   1. Initial program 84.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 99.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty \lor \neg \left(\sinh y \leq 2 \cdot 10^{-25}\right):\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \end{array} \]

Alternative 3: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 2e-25) (* (sin x) (/ y x)) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -((double) INFINITY)) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-25) {
		tmp = sin(x) * (y / x);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -Double.POSITIVE_INFINITY) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-25) {
		tmp = Math.sin(x) * (y / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -math.inf:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-25:
		tmp = math.sin(x) * (y / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= Float64(-Inf))
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-25)
		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) <= -Inf)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-25)
		tmp = sin(x) * (y / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], (-Infinity)], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-25], 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) < -inf.0 or 2.00000000000000008e-25 < (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 73.5%

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

   if -inf.0 < (sinh.f64 y) < 2.00000000000000008e-25

   1. Initial program 84.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 83.8%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.5%

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

   6. Simplified 99.5%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 2e-25) (* (/ (sin x) x) y) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -((double) INFINITY)) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-25) {
		tmp = (sin(x) / x) * y;
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -Double.POSITIVE_INFINITY) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-25) {
		tmp = (Math.sin(x) / x) * y;
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -math.inf:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-25:
		tmp = (math.sin(x) / x) * y
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= Float64(-Inf))
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-25)
		tmp = Float64(Float64(sin(x) / x) * y);
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -Inf)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-25)
		tmp = (sin(x) / x) * y;
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], (-Infinity)], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-25], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -inf.0 or 2.00000000000000008e-25 < (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 73.5%

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

   if -inf.0 < (sinh.f64 y) < 2.00000000000000008e-25

   1. Initial program 84.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 99.7%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 5: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 2e-25)
     (/ y (+ 1.0 (* (* x x) 0.16666666666666666)))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -((double) INFINITY)) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-25) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -Double.POSITIVE_INFINITY) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-25) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -math.inf:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-25:
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= Float64(-Inf))
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-25)
		tmp = Float64(y / Float64(1.0 + Float64(Float64(x * x) * 0.16666666666666666)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -Inf)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-25)
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], (-Infinity)], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-25], N[(y / N[(1.0 + N[(N[(x * x), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -inf.0 or 2.00000000000000008e-25 < (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 73.5%

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

   if -inf.0 < (sinh.f64 y) < 2.00000000000000008e-25

   1. Initial program 84.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 83.8%

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

      1. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 73.2%

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

      1. unpow2 73.2%

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

   9. Simplified 73.2%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 6: 58.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \frac{y}{x \cdot x}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+77}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+149}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 6.0 (/ y (* x x)))))
   (if (<= y -4.3e-35)
     (* (/ y x) (/ 6.0 x))
     (if (<= y 1.8)
       (/ y (+ 1.0 (* (* x x) 0.16666666666666666)))
       (if (<= y 3.4e+44)
         t_0
         (if (<= y 1.9e+77)
           (* -0.16666666666666666 (* y (* x x)))
           (if (<= y 5.1e+149) t_0 (sqrt (* y y)))))))))

C

double code(double x, double y) {
	double t_0 = 6.0 * (y / (x * x));
	double tmp;
	if (y <= -4.3e-35) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 1.8) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else if (y <= 3.4e+44) {
		tmp = t_0;
	} else if (y <= 1.9e+77) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else if (y <= 5.1e+149) {
		tmp = t_0;
	} else {
		tmp = sqrt((y * y));
	}
	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 = 6.0d0 * (y / (x * x))
    if (y <= (-4.3d-35)) then
        tmp = (y / x) * (6.0d0 / x)
    else if (y <= 1.8d0) then
        tmp = y / (1.0d0 + ((x * x) * 0.16666666666666666d0))
    else if (y <= 3.4d+44) then
        tmp = t_0
    else if (y <= 1.9d+77) then
        tmp = (-0.16666666666666666d0) * (y * (x * x))
    else if (y <= 5.1d+149) then
        tmp = t_0
    else
        tmp = sqrt((y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 6.0 * (y / (x * x));
	double tmp;
	if (y <= -4.3e-35) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 1.8) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else if (y <= 3.4e+44) {
		tmp = t_0;
	} else if (y <= 1.9e+77) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else if (y <= 5.1e+149) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt((y * y));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 6.0 * (y / (x * x))
	tmp = 0
	if y <= -4.3e-35:
		tmp = (y / x) * (6.0 / x)
	elif y <= 1.8:
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666))
	elif y <= 3.4e+44:
		tmp = t_0
	elif y <= 1.9e+77:
		tmp = -0.16666666666666666 * (y * (x * x))
	elif y <= 5.1e+149:
		tmp = t_0
	else:
		tmp = math.sqrt((y * y))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(6.0 * Float64(y / Float64(x * x)))
	tmp = 0.0
	if (y <= -4.3e-35)
		tmp = Float64(Float64(y / x) * Float64(6.0 / x));
	elseif (y <= 1.8)
		tmp = Float64(y / Float64(1.0 + Float64(Float64(x * x) * 0.16666666666666666)));
	elseif (y <= 3.4e+44)
		tmp = t_0;
	elseif (y <= 1.9e+77)
		tmp = Float64(-0.16666666666666666 * Float64(y * Float64(x * x)));
	elseif (y <= 5.1e+149)
		tmp = t_0;
	else
		tmp = sqrt(Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 6.0 * (y / (x * x));
	tmp = 0.0;
	if (y <= -4.3e-35)
		tmp = (y / x) * (6.0 / x);
	elseif (y <= 1.8)
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	elseif (y <= 3.4e+44)
		tmp = t_0;
	elseif (y <= 1.9e+77)
		tmp = -0.16666666666666666 * (y * (x * x));
	elseif (y <= 5.1e+149)
		tmp = t_0;
	else
		tmp = sqrt((y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-35], N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8], N[(y / N[(1.0 + N[(N[(x * x), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+44], t$95$0, If[LessEqual[y, 1.9e+77], N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e+149], t$95$0, N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.3000000000000002e-35

   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 13.3%

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

      1. associate-/l* 13.2%

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

   6. Simplified 13.2%

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

   7. Taylor expanded in x around 0 3.8%

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

      1. unpow2 3.8%

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

   9. Simplified 3.8%

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

   10. Taylor expanded in x around inf 41.6%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 41.6%

          \[\leadsto \color{blue}{\frac{6 \cdot y}{{x}^{2}}} \]

       2. unpow2 41.6%

          \[\leadsto \frac{6 \cdot y}{\color{blue}{x \cdot x}} \]

       3. times-frac 41.6%

          \[\leadsto \color{blue}{\frac{6}{x} \cdot \frac{y}{x}} \]

   12. Simplified 41.6%

       \[\leadsto \color{blue}{\frac{6}{x} \cdot \frac{y}{x}} \]

   if -4.3000000000000002e-35 < y < 1.80000000000000004

   1. Initial program 83.4%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 82.8%

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

      1. associate-/l* 99.3%

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

   6. Simplified 99.3%

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

   7. Taylor expanded in x around 0 77.1%

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

      1. unpow2 77.1%

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

   9. Simplified 77.1%

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

   if 1.80000000000000004 < y < 3.4e44 or 1.9000000000000001e77 < y < 5.0999999999999997e149

   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 4.1%

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

      1. associate-/l* 4.1%

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

   6. Simplified 4.1%

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

   7. Taylor expanded in x around 0 2.9%

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

      1. unpow2 2.9%

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

   9. Simplified 2.9%

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

   10. Taylor expanded in x around inf 44.7%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. unpow2 44.7%

          \[\leadsto 6 \cdot \frac{y}{\color{blue}{x \cdot x}} \]

   12. Simplified 44.7%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{x \cdot x}} \]

   if 3.4e44 < y < 1.9000000000000001e77

   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 2.6%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. unpow2 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-*r* 51.7%

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

      4. unpow2 51.7%

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

      5. associate-*l* 51.7%

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

   10. Simplified 51.7%

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

   11. Taylor expanded in y around 0 51.7%

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

       1. unpow2 51.7%

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

       2. *-commutative 51.7%

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

   13. Simplified 51.7%

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

   if 5.0999999999999997e149 < 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 y around 0 4.9%

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

      1. associate-/l* 4.9%

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

      2. associate-/r/ 24.7%

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

   6. Simplified 24.7%

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

   7. Taylor expanded in x around 0 24.7%

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

      1. *-commutative 24.7%

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

      2. clear-num 24.7%

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

      3. un-div-inv 24.7%

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

   9. Applied egg-rr 24.7%

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

       1. associate-/r/ 4.9%

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

       2. *-inverses 4.9%

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

       3. *-un-lft-identity 4.9%

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

       4. add-sqr-sqrt 4.9%

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

       5. sqrt-unprod 71.6%

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

   11. Applied egg-rr 71.6%

       \[\leadsto \color{blue}{\sqrt{y \cdot y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+44}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+77}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+149}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \]

Alternative 7: 54.5% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \frac{y}{x \cdot x}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+44} \lor \neg \left(y \leq 1.5 \cdot 10^{+81}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 6.0 (/ y (* x x)))))
   (if (<= y -4.3e-35)
     t_0
     (if (<= y 1.8)
       (/ x (/ x y))
       (if (or (<= y 6e+44) (not (<= y 1.5e+81)))
         t_0
         (* -0.16666666666666666 (* y (* x x))))))))

C

double code(double x, double y) {
	double t_0 = 6.0 * (y / (x * x));
	double tmp;
	if (y <= -4.3e-35) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = x / (x / y);
	} else if ((y <= 6e+44) || !(y <= 1.5e+81)) {
		tmp = t_0;
	} else {
		tmp = -0.16666666666666666 * (y * (x * x));
	}
	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 = 6.0d0 * (y / (x * x))
    if (y <= (-4.3d-35)) then
        tmp = t_0
    else if (y <= 1.8d0) then
        tmp = x / (x / y)
    else if ((y <= 6d+44) .or. (.not. (y <= 1.5d+81))) then
        tmp = t_0
    else
        tmp = (-0.16666666666666666d0) * (y * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 6.0 * (y / (x * x));
	double tmp;
	if (y <= -4.3e-35) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = x / (x / y);
	} else if ((y <= 6e+44) || !(y <= 1.5e+81)) {
		tmp = t_0;
	} else {
		tmp = -0.16666666666666666 * (y * (x * x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 6.0 * (y / (x * x))
	tmp = 0
	if y <= -4.3e-35:
		tmp = t_0
	elif y <= 1.8:
		tmp = x / (x / y)
	elif (y <= 6e+44) or not (y <= 1.5e+81):
		tmp = t_0
	else:
		tmp = -0.16666666666666666 * (y * (x * x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(6.0 * Float64(y / Float64(x * x)))
	tmp = 0.0
	if (y <= -4.3e-35)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = Float64(x / Float64(x / y));
	elseif ((y <= 6e+44) || !(y <= 1.5e+81))
		tmp = t_0;
	else
		tmp = Float64(-0.16666666666666666 * Float64(y * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 6.0 * (y / (x * x));
	tmp = 0.0;
	if (y <= -4.3e-35)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = x / (x / y);
	elseif ((y <= 6e+44) || ~((y <= 1.5e+81)))
		tmp = t_0;
	else
		tmp = -0.16666666666666666 * (y * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-35], t$95$0, If[LessEqual[y, 1.8], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6e+44], N[Not[LessEqual[y, 1.5e+81]], $MachinePrecision]], t$95$0, N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3000000000000002e-35 or 1.80000000000000004 < y < 5.99999999999999974e44 or 1.49999999999999999e81 < 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 y around 0 9.5%

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

      1. associate-/l* 9.4%

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

   6. Simplified 9.4%

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

   7. Taylor expanded in x around 0 3.7%

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

      1. unpow2 3.7%

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

   9. Simplified 3.7%

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

   10. Taylor expanded in x around inf 40.7%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. unpow2 40.7%

          \[\leadsto 6 \cdot \frac{y}{\color{blue}{x \cdot x}} \]

   12. Simplified 40.7%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{x \cdot x}} \]

   if -4.3000000000000002e-35 < y < 1.80000000000000004

   1. Initial program 83.4%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 82.8%

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

      1. associate-/l* 99.3%

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

      2. associate-/r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. clear-num 75.8%

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

      3. un-div-inv 76.0%

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

   9. Applied egg-rr 76.0%

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

   if 5.99999999999999974e44 < y < 1.49999999999999999e81

   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 2.6%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. unpow2 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-*r* 51.7%

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

      4. unpow2 51.7%

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

      5. associate-*l* 51.7%

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

   10. Simplified 51.7%

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

   11. Taylor expanded in y around 0 51.7%

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

       1. unpow2 51.7%

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

       2. *-commutative 51.7%

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

   13. Simplified 51.7%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+44} \lor \neg \left(y \leq 1.5 \cdot 10^{+81}\right):\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \end{array} \]

Alternative 8: 54.5% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+79}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ y x) (/ 6.0 x))))
   (if (<= y -4.3e-35)
     t_0
     (if (<= y 1.8)
       (/ x (/ x y))
       (if (<= y 5.2e+44)
         (* 6.0 (/ y (* x x)))
         (if (<= y 1.7e+79) (* -0.16666666666666666 (* y (* x x))) t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) * (6.0 / x);
	double tmp;
	if (y <= -4.3e-35) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = x / (x / y);
	} else if (y <= 5.2e+44) {
		tmp = 6.0 * (y / (x * x));
	} else if (y <= 1.7e+79) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} 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 = (y / x) * (6.0d0 / x)
    if (y <= (-4.3d-35)) then
        tmp = t_0
    else if (y <= 1.8d0) then
        tmp = x / (x / y)
    else if (y <= 5.2d+44) then
        tmp = 6.0d0 * (y / (x * x))
    else if (y <= 1.7d+79) then
        tmp = (-0.16666666666666666d0) * (y * (x * x))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) * (6.0 / x);
	double tmp;
	if (y <= -4.3e-35) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = x / (x / y);
	} else if (y <= 5.2e+44) {
		tmp = 6.0 * (y / (x * x));
	} else if (y <= 1.7e+79) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) * (6.0 / x)
	tmp = 0
	if y <= -4.3e-35:
		tmp = t_0
	elif y <= 1.8:
		tmp = x / (x / y)
	elif y <= 5.2e+44:
		tmp = 6.0 * (y / (x * x))
	elif y <= 1.7e+79:
		tmp = -0.16666666666666666 * (y * (x * x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) * Float64(6.0 / x))
	tmp = 0.0
	if (y <= -4.3e-35)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = Float64(x / Float64(x / y));
	elseif (y <= 5.2e+44)
		tmp = Float64(6.0 * Float64(y / Float64(x * x)));
	elseif (y <= 1.7e+79)
		tmp = Float64(-0.16666666666666666 * Float64(y * Float64(x * x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) * (6.0 / x);
	tmp = 0.0;
	if (y <= -4.3e-35)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = x / (x / y);
	elseif (y <= 5.2e+44)
		tmp = 6.0 * (y / (x * x));
	elseif (y <= 1.7e+79)
		tmp = -0.16666666666666666 * (y * (x * x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-35], t$95$0, If[LessEqual[y, 1.8], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+44], N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+79], N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3000000000000002e-35 or 1.70000000000000016e79 < 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 y around 0 10.0%

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

      1. associate-/l* 9.9%

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

   6. Simplified 9.9%

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

   7. Taylor expanded in x around 0 3.7%

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

      1. unpow2 3.7%

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

   9. Simplified 3.7%

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

   10. Taylor expanded in x around inf 41.1%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 41.1%

          \[\leadsto \color{blue}{\frac{6 \cdot y}{{x}^{2}}} \]

       2. unpow2 41.1%

          \[\leadsto \frac{6 \cdot y}{\color{blue}{x \cdot x}} \]

       3. times-frac 41.1%

          \[\leadsto \color{blue}{\frac{6}{x} \cdot \frac{y}{x}} \]

   12. Simplified 41.1%

       \[\leadsto \color{blue}{\frac{6}{x} \cdot \frac{y}{x}} \]

   if -4.3000000000000002e-35 < y < 1.80000000000000004

   1. Initial program 83.4%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 82.8%

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

      1. associate-/l* 99.3%

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

      2. associate-/r/ 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. clear-num 75.8%

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

      3. un-div-inv 76.0%

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

   9. Applied egg-rr 76.0%

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

   if 1.80000000000000004 < y < 5.1999999999999998e44

   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 4.5%

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

      1. associate-/l* 4.5%

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

   6. Simplified 4.5%

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

   7. Taylor expanded in x around 0 2.9%

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

      1. unpow2 2.9%

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

   9. Simplified 2.9%

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

   10. Taylor expanded in x around inf 36.5%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. unpow2 36.5%

          \[\leadsto 6 \cdot \frac{y}{\color{blue}{x \cdot x}} \]

   12. Simplified 36.5%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{x \cdot x}} \]

   if 5.1999999999999998e44 < y < 1.70000000000000016e79

   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 2.6%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. unpow2 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-*r* 51.7%

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

      4. unpow2 51.7%

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

      5. associate-*l* 51.7%

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

   10. Simplified 51.7%

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

   11. Taylor expanded in y around 0 51.7%

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

       1. unpow2 51.7%

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

       2. *-commutative 51.7%

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

   13. Simplified 51.7%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+44}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+79}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \end{array} \]

Alternative 9: 55.0% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+39}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+77}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ y x) (/ 6.0 x))))
   (if (<= y -4.3e-35)
     t_0
     (if (<= y 1.8)
       (/ y (+ 1.0 (* (* x x) 0.16666666666666666)))
       (if (<= y 6e+39)
         (* 6.0 (/ y (* x x)))
         (if (<= y 1.4e+77) (* -0.16666666666666666 (* y (* x x))) t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) * (6.0 / x);
	double tmp;
	if (y <= -4.3e-35) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else if (y <= 6e+39) {
		tmp = 6.0 * (y / (x * x));
	} else if (y <= 1.4e+77) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} 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 = (y / x) * (6.0d0 / x)
    if (y <= (-4.3d-35)) then
        tmp = t_0
    else if (y <= 1.8d0) then
        tmp = y / (1.0d0 + ((x * x) * 0.16666666666666666d0))
    else if (y <= 6d+39) then
        tmp = 6.0d0 * (y / (x * x))
    else if (y <= 1.4d+77) then
        tmp = (-0.16666666666666666d0) * (y * (x * x))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) * (6.0 / x);
	double tmp;
	if (y <= -4.3e-35) {
		tmp = t_0;
	} else if (y <= 1.8) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else if (y <= 6e+39) {
		tmp = 6.0 * (y / (x * x));
	} else if (y <= 1.4e+77) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) * (6.0 / x)
	tmp = 0
	if y <= -4.3e-35:
		tmp = t_0
	elif y <= 1.8:
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666))
	elif y <= 6e+39:
		tmp = 6.0 * (y / (x * x))
	elif y <= 1.4e+77:
		tmp = -0.16666666666666666 * (y * (x * x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) * Float64(6.0 / x))
	tmp = 0.0
	if (y <= -4.3e-35)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = Float64(y / Float64(1.0 + Float64(Float64(x * x) * 0.16666666666666666)));
	elseif (y <= 6e+39)
		tmp = Float64(6.0 * Float64(y / Float64(x * x)));
	elseif (y <= 1.4e+77)
		tmp = Float64(-0.16666666666666666 * Float64(y * Float64(x * x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) * (6.0 / x);
	tmp = 0.0;
	if (y <= -4.3e-35)
		tmp = t_0;
	elseif (y <= 1.8)
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	elseif (y <= 6e+39)
		tmp = 6.0 * (y / (x * x));
	elseif (y <= 1.4e+77)
		tmp = -0.16666666666666666 * (y * (x * x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e-35], t$95$0, If[LessEqual[y, 1.8], N[(y / N[(1.0 + N[(N[(x * x), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+39], N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+77], N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.3000000000000002e-35 or 1.4e77 < 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 y around 0 10.0%

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

      1. associate-/l* 9.9%

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

   6. Simplified 9.9%

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

   7. Taylor expanded in x around 0 3.7%

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

      1. unpow2 3.7%

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

   9. Simplified 3.7%

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

   10. Taylor expanded in x around inf 41.1%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 41.1%

          \[\leadsto \color{blue}{\frac{6 \cdot y}{{x}^{2}}} \]

       2. unpow2 41.1%

          \[\leadsto \frac{6 \cdot y}{\color{blue}{x \cdot x}} \]

       3. times-frac 41.1%

          \[\leadsto \color{blue}{\frac{6}{x} \cdot \frac{y}{x}} \]

   12. Simplified 41.1%

       \[\leadsto \color{blue}{\frac{6}{x} \cdot \frac{y}{x}} \]

   if -4.3000000000000002e-35 < y < 1.80000000000000004

   1. Initial program 83.4%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 82.8%

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

      1. associate-/l* 99.3%

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

   6. Simplified 99.3%

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

   7. Taylor expanded in x around 0 77.1%

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

      1. unpow2 77.1%

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

   9. Simplified 77.1%

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

   if 1.80000000000000004 < y < 5.9999999999999999e39

   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 4.5%

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

      1. associate-/l* 4.5%

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

   6. Simplified 4.5%

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

   7. Taylor expanded in x around 0 2.9%

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

      1. unpow2 2.9%

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

   9. Simplified 2.9%

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

   10. Taylor expanded in x around inf 36.5%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{{x}^{2}}} \]
   11. Step-by-step derivation

       1. unpow2 36.5%

          \[\leadsto 6 \cdot \frac{y}{\color{blue}{x \cdot x}} \]

   12. Simplified 36.5%

       \[\leadsto \color{blue}{6 \cdot \frac{y}{x \cdot x}} \]

   if 5.9999999999999999e39 < y < 1.4e77

   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 2.6%

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

   5. Taylor expanded in x around 0 51.7%

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

      1. unpow2 51.7%

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

   7. Simplified 51.7%

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

   8. Taylor expanded in x around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-*r* 51.7%

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

      4. unpow2 51.7%

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

      5. associate-*l* 51.7%

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

   10. Simplified 51.7%

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

   11. Taylor expanded in y around 0 51.7%

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

       1. unpow2 51.7%

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

       2. *-commutative 51.7%

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

   13. Simplified 51.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 1.8:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+39}:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+77}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \end{array} \]

Alternative 10: 50.4% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+151}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 7.2e+131)
   (* x (/ y x))
   (if (<= x 1.4e+151) (* -0.16666666666666666 (* y (* x x))) (/ x (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 7.2e+131) {
		tmp = x * (y / x);
	} else if (x <= 1.4e+151) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else {
		tmp = x / (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 7.2d+131) then
        tmp = x * (y / x)
    else if (x <= 1.4d+151) then
        tmp = (-0.16666666666666666d0) * (y * (x * x))
    else
        tmp = x / (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 7.2e+131) {
		tmp = x * (y / x);
	} else if (x <= 1.4e+151) {
		tmp = -0.16666666666666666 * (y * (x * x));
	} else {
		tmp = x / (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 7.2e+131:
		tmp = x * (y / x)
	elif x <= 1.4e+151:
		tmp = -0.16666666666666666 * (y * (x * x))
	else:
		tmp = x / (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 7.2e+131)
		tmp = Float64(x * Float64(y / x));
	elseif (x <= 1.4e+151)
		tmp = Float64(-0.16666666666666666 * Float64(y * Float64(x * x)));
	else
		tmp = Float64(x / Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 7.2e+131)
		tmp = x * (y / x);
	elseif (x <= 1.4e+151)
		tmp = -0.16666666666666666 * (y * (x * x));
	else
		tmp = x / (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 7.2e+131], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e+151], N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 7.20000000000000063e131

   1. Initial program 90.8%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 41.0%

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

      1. associate-/l* 50.2%

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

      2. associate-/r/ 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in x around 0 52.0%

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

   if 7.20000000000000063e131 < x < 1.39999999999999994e151

   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 17.4%

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

   5. Taylor expanded in x around 0 71.6%

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

      1. unpow2 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

      3. associate-*r* 71.6%

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

      4. unpow2 71.6%

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

      5. associate-*l* 71.6%

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

   10. Simplified 71.6%

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

   11. Taylor expanded in y around 0 71.6%

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

       1. unpow2 71.6%

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

       2. *-commutative 71.6%

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

   13. Simplified 71.6%

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

   if 1.39999999999999994e151 < x

   1. Initial program 99.9%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 63.8%

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

      1. associate-/l* 63.7%

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

      2. associate-/r/ 63.7%

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

   6. Simplified 63.7%

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

   7. Taylor expanded in x around 0 35.8%

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

      1. *-commutative 35.8%

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

      2. clear-num 35.8%

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

      3. un-div-inv 35.8%

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

   9. Applied egg-rr 35.8%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+151}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \]

Alternative 11: 50.0% accurate, 41.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x * (y / x)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.3%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 43.3%

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

   1. associate-/l* 51.0%

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

   2. associate-/r/ 62.3%

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

6. Simplified 62.3%

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

7. Taylor expanded in x around 0 48.6%

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

8. Final simplification 48.6%

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

Alternative 12: 27.9% 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 92.3%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 43.3%

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

   1. associate-/l* 51.0%

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

   2. associate-/r/ 62.3%

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

6. Simplified 62.3%

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

7. Taylor expanded in x around 0 26.2%

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

8. Final simplification 26.2%

   \[\leadsto y \]

Developer target: 99.8% 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 2023275 
(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))