Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 88.8% → 99.9%

Time: 7.8s

Alternatives: 10

Speedup: 1.0×

• 49.2% 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: 88.8% 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 92.5%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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. Final simplification 99.9%

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

Alternative 2: 85.9% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (sinh y) (- INFINITY)) (not (<= (sinh y) 1e-10)))
   (* (+ 1.0 (* (* x x) -0.16666666666666666)) (sinh y))
   (* (/ (sin x) x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((sinh(y) <= -((double) INFINITY)) || !(sinh(y) <= 1e-10)) {
		tmp = (1.0 + ((x * x) * -0.16666666666666666)) * 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) <= 1e-10)) {
		tmp = (1.0 + ((x * x) * -0.16666666666666666)) * 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) <= 1e-10):
		tmp = (1.0 + ((x * x) * -0.16666666666666666)) * 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) <= 1e-10))
		tmp = Float64(Float64(1.0 + Float64(Float64(x * x) * -0.16666666666666666)) * 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) <= 1e-10)))
		tmp = (1.0 + ((x * x) * -0.16666666666666666)) * 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], 1e-10]], $MachinePrecision]], N[(N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.16666666666666666), $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 1.00000000000000004e-10 < (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 81.0%

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

      1. *-commutative 81.0%

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

      2. unpow2 81.0%

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

   6. Simplified 81.0%

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

   if -inf.0 < (sinh.f64 y) < 1.00000000000000004e-10

   1. Initial program 85.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 85.1%

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

      1. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 98.8%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 90.5%

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

Alternative 3: 86.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 1e-10) (* (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) <= 1e-10) {
		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) <= 1e-10) {
		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) <= 1e-10:
		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) <= 1e-10)
		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) <= 1e-10)
		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], 1e-10], 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 1.00000000000000004e-10 < (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 75.4%

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

   if -inf.0 < (sinh.f64 y) < 1.00000000000000004e-10

   1. Initial program 85.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 85.1%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 87.8%

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

Alternative 4: 86.8% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 1e-10) (* (/ (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) <= 1e-10) {
		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) <= 1e-10) {
		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) <= 1e-10:
		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) <= 1e-10)
		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) <= 1e-10)
		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], 1e-10], 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 1.00000000000000004e-10 < (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 75.4%

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

   if -inf.0 < (sinh.f64 y) < 1.00000000000000004e-10

   1. Initial program 85.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 85.1%

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

      1. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 98.8%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 87.8%

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

Alternative 5: 75.2% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 1e-10)
     (/ y (* x (+ (* x 0.16666666666666666) (/ 1.0 x))))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -((double) INFINITY)) {
		tmp = sinh(y);
	} else if (sinh(y) <= 1e-10) {
		tmp = y / (x * ((x * 0.16666666666666666) + (1.0 / 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) <= 1e-10) {
		tmp = y / (x * ((x * 0.16666666666666666) + (1.0 / 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) <= 1e-10:
		tmp = y / (x * ((x * 0.16666666666666666) + (1.0 / 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) <= 1e-10)
		tmp = Float64(y / Float64(x * Float64(Float64(x * 0.16666666666666666) + Float64(1.0 / 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) <= 1e-10)
		tmp = y / (x * ((x * 0.16666666666666666) + (1.0 / 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], 1e-10], N[(y / N[(x * N[(N[(x * 0.16666666666666666), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -inf.0 or 1.00000000000000004e-10 < (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 75.4%

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

   if -inf.0 < (sinh.f64 y) < 1.00000000000000004e-10

   1. Initial program 85.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 85.1%

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

      1. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around 0 70.2%

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

4. Final simplification 72.7%

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

Alternative 6: 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]

Derivation

1. Initial program 92.5%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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 7: 54.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-121}:\\ \;\;\;\;y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+199)
   (* x (/ y x))
   (if (<= y -3e-121)
     (+ y (* -0.16666666666666666 (* y (* x x))))
     (if (<= y 1.32e+154) (/ x (/ x y)) (sqrt (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+199) {
		tmp = x * (y / x);
	} else if (y <= -3e-121) {
		tmp = y + (-0.16666666666666666 * (y * (x * x)));
	} else if (y <= 1.32e+154) {
		tmp = x / (x / y);
	} 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) :: tmp
    if (y <= (-4.2d+199)) then
        tmp = x * (y / x)
    else if (y <= (-3d-121)) then
        tmp = y + ((-0.16666666666666666d0) * (y * (x * x)))
    else if (y <= 1.32d+154) then
        tmp = x / (x / y)
    else
        tmp = sqrt((y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+199) {
		tmp = x * (y / x);
	} else if (y <= -3e-121) {
		tmp = y + (-0.16666666666666666 * (y * (x * x)));
	} else if (y <= 1.32e+154) {
		tmp = x / (x / y);
	} else {
		tmp = Math.sqrt((y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+199:
		tmp = x * (y / x)
	elif y <= -3e-121:
		tmp = y + (-0.16666666666666666 * (y * (x * x)))
	elif y <= 1.32e+154:
		tmp = x / (x / y)
	else:
		tmp = math.sqrt((y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+199)
		tmp = Float64(x * Float64(y / x));
	elseif (y <= -3e-121)
		tmp = Float64(y + Float64(-0.16666666666666666 * Float64(y * Float64(x * x))));
	elseif (y <= 1.32e+154)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = sqrt(Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+199)
		tmp = x * (y / x);
	elseif (y <= -3e-121)
		tmp = y + (-0.16666666666666666 * (y * (x * x)));
	elseif (y <= 1.32e+154)
		tmp = x / (x / y);
	else
		tmp = sqrt((y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+199], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3e-121], N[(y + N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.32e+154], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.1999999999999999e199

   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. Taylor expanded in y around 0 6.0%

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

      1. associate-/l* 6.0%

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

      2. associate-/r/ 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in x around 0 59.1%

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

   if -4.1999999999999999e199 < y < -2.9999999999999999e-121

   1. Initial program 98.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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. Taylor expanded in y around 0 38.5%

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

      1. associate-/l* 40.1%

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

      2. associate-/r/ 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in x around 0 37.0%

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

      1. associate-*r* 37.0%

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

      2. unpow2 37.0%

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

   9. Simplified 37.0%

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

   10. Taylor expanded in y around 0 37.0%

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

       1. unpow2 37.0%

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

   12. Simplified 37.0%

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

   if -2.9999999999999999e-121 < y < 1.31999999999999998e154

   1. Initial program 87.0%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 62.8%

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

      1. associate-/l* 75.7%

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

      2. associate-/r/ 80.5%

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

   6. Simplified 80.5%

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

   7. Taylor expanded in x around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. clear-num 61.1%

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

      3. un-div-inv 60.5%

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

   9. Applied egg-rr 60.5%

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

   if 1.31999999999999998e154 < 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. Taylor expanded in y around 0 5.0%

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

      1. associate-/l* 5.0%

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

      2. associate-/r/ 35.1%

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

   6. Simplified 35.1%

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

   7. Taylor expanded in x around 0 35.0%

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

      1. associate-/r/ 4.9%

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

      2. *-inverses 4.9%

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

      3. div-inv 4.9%

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

      4. metadata-eval 4.9%

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

      5. *-commutative 4.9%

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

      6. *-un-lft-identity 4.9%

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

      7. add-sqr-sqrt 4.9%

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

      8. sqrt-unprod 78.6%

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

   9. Applied egg-rr 78.6%

      \[\leadsto \color{blue}{\sqrt{y \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+199}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-121}:\\ \;\;\;\;y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \]

Alternative 8: 48.9% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-121}:\\ \;\;\;\;y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.9e+195)
   (* x (/ y x))
   (if (<= y -2.7e-121)
     (+ y (* -0.16666666666666666 (* y (* x x))))
     (/ x (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+195) {
		tmp = x * (y / x);
	} else if (y <= -2.7e-121) {
		tmp = y + (-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 (y <= (-2.9d+195)) then
        tmp = x * (y / x)
    else if (y <= (-2.7d-121)) then
        tmp = y + ((-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 (y <= -2.9e+195) {
		tmp = x * (y / x);
	} else if (y <= -2.7e-121) {
		tmp = y + (-0.16666666666666666 * (y * (x * x)));
	} else {
		tmp = x / (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.9e+195:
		tmp = x * (y / x)
	elif y <= -2.7e-121:
		tmp = y + (-0.16666666666666666 * (y * (x * x)))
	else:
		tmp = x / (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.9e+195)
		tmp = Float64(x * Float64(y / x));
	elseif (y <= -2.7e-121)
		tmp = Float64(y + 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 (y <= -2.9e+195)
		tmp = x * (y / x);
	elseif (y <= -2.7e-121)
		tmp = y + (-0.16666666666666666 * (y * (x * x)));
	else
		tmp = x / (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.9e+195], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-121], N[(y + N[(-0.16666666666666666 * N[(y * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999992e195

   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. Taylor expanded in y around 0 6.0%

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

      1. associate-/l* 6.0%

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

      2. associate-/r/ 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in x around 0 59.1%

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

   if -2.89999999999999992e195 < y < -2.7000000000000002e-121

   1. Initial program 98.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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. Taylor expanded in y around 0 38.5%

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

      1. associate-/l* 40.1%

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

      2. associate-/r/ 44.4%

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

   6. Simplified 44.4%

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

   7. Taylor expanded in x around 0 37.0%

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

      1. associate-*r* 37.0%

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

      2. unpow2 37.0%

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

   9. Simplified 37.0%

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

   10. Taylor expanded in y around 0 37.0%

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

       1. unpow2 37.0%

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

   12. Simplified 37.0%

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

   if -2.7000000000000002e-121 < y

   1. Initial program 89.1%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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. Taylor expanded in y around 0 53.1%

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

      1. associate-/l* 63.9%

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

      2. associate-/r/ 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in x around 0 55.9%

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

      1. *-commutative 55.9%

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

      2. clear-num 56.8%

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

      3. un-div-inv 56.2%

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

   9. Applied egg-rr 56.2%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+195}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-121}:\\ \;\;\;\;y + -0.16666666666666666 \cdot \left(y \cdot \left(x \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \]

Alternative 9: 49.8% 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 92.5%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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. Taylor expanded in y around 0 45.4%

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

   1. associate-/l* 52.8%

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

   2. associate-/r/ 64.2%

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

6. Simplified 64.2%

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

7. Taylor expanded in x around 0 47.8%

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

8. Final simplification 47.8%

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

Alternative 10: 28.8% 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 92.5%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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. Taylor expanded in y around 0 45.4%

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

   1. associate-/l* 52.8%

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

   2. associate-/r/ 64.2%

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

6. Simplified 64.2%

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

7. Taylor expanded in x around 0 24.0%

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

8. Final simplification 24.0%

   \[\leadsto y \]

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 2023199 
(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))