Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.5% → 99.9%

Time: 8.1s

Alternatives: 11

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.5% 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 87.5%

   \[\frac{\sin x \cdot \sinh y}{x} \]
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: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -2e+34)
   (sinh y)
   (if (<= (sinh y) 2e-10)
     (* (/ (sin x) x) y)
     (* (sinh y) (+ 1.0 (* (* x x) -0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -2e+34) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-10) {
		tmp = (sin(x) / x) * y;
	} else {
		tmp = sinh(y) * (1.0 + ((x * x) * -0.16666666666666666));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-2d+34)) then
        tmp = sinh(y)
    else if (sinh(y) <= 2d-10) then
        tmp = (sin(x) / x) * y
    else
        tmp = sinh(y) * (1.0d0 + ((x * x) * (-0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -2e+34) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-10) {
		tmp = (Math.sin(x) / x) * y;
	} else {
		tmp = Math.sinh(y) * (1.0 + ((x * x) * -0.16666666666666666));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -2e+34:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-10:
		tmp = (math.sin(x) / x) * y
	else:
		tmp = math.sinh(y) * (1.0 + ((x * x) * -0.16666666666666666))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -2e+34)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-10)
		tmp = Float64(Float64(sin(x) / x) * y);
	else
		tmp = Float64(sinh(y) * Float64(1.0 + Float64(Float64(x * x) * -0.16666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -2e+34)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-10)
		tmp = (sin(x) / x) * y;
	else
		tmp = sinh(y) * (1.0 + ((x * x) * -0.16666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -2e+34], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-10], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] * N[(1.0 + N[(N[(x * x), $MachinePrecision] * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (sinh.f64 y) < -1.99999999999999989e34

   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 90.8%

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

   if -1.99999999999999989e34 < (sinh.f64 y) < 2.00000000000000007e-10

   1. Initial program 74.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 74.7%

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

      1. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   8. Applied egg-rr 99.9%

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

   if 2.00000000000000007e-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 84.6%

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

      1. *-commutative 84.6%

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

      2. unpow2 84.6%

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

   6. Simplified 84.6%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \left(1 + \left(x \cdot x\right) \cdot -0.16666666666666666\right)\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -5 \cdot 10^{-18}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -5e-18)
   (sinh y)
   (if (<= (sinh y) 2e-10) (* (sin x) (/ y x)) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -5e-18) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-10) {
		tmp = sin(x) * (y / x);
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-5d-18)) then
        tmp = sinh(y)
    else if (sinh(y) <= 2d-10) then
        tmp = sin(x) * (y / x)
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -5e-18) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-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) <= -5e-18:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-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) <= -5e-18)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-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) <= -5e-18)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-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], -5e-18], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-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) < -5.00000000000000036e-18 or 2.00000000000000007e-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 80.2%

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

   if -5.00000000000000036e-18 < (sinh.f64 y) < 2.00000000000000007e-10

   1. Initial program 74.5%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 74.5%

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

      1. associate-/l* 99.9%

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

      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 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -5 \cdot 10^{-18}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 4: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -2e+34)
   (sinh y)
   (if (<= (sinh y) 2e-10) (* (/ (sin x) x) y) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -2e+34) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-10) {
		tmp = (sin(x) / x) * y;
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-2d+34)) then
        tmp = sinh(y)
    else if (sinh(y) <= 2d-10) then
        tmp = (sin(x) / x) * y
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -2e+34) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-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) <= -2e+34:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-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) <= -2e+34)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-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) <= -2e+34)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-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], -2e+34], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-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) < -1.99999999999999989e34 or 2.00000000000000007e-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 80.0%

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

   if -1.99999999999999989e34 < (sinh.f64 y) < 2.00000000000000007e-10

   1. Initial program 74.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 74.7%

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

      1. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   8. Applied egg-rr 99.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 5: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -2e+34)
   (sinh y)
   (if (<= (sinh y) 2e-10)
     (/ y (+ 1.0 (* x (* x 0.16666666666666666))))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -2e+34) {
		tmp = sinh(y);
	} else if (sinh(y) <= 2e-10) {
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-2d+34)) then
        tmp = sinh(y)
    else if (sinh(y) <= 2d-10) then
        tmp = y / (1.0d0 + (x * (x * 0.16666666666666666d0)))
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -2e+34) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 2e-10) {
		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) <= -2e+34:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 2e-10:
		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) <= -2e+34)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-10)
		tmp = Float64(y / Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666))));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -2e+34)
		tmp = sinh(y);
	elseif (sinh(y) <= 2e-10)
		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], -2e+34], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 2e-10], N[(y / N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -1.99999999999999989e34 or 2.00000000000000007e-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 80.0%

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

   if -1.99999999999999989e34 < (sinh.f64 y) < 2.00000000000000007e-10

   1. Initial program 74.7%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 74.7%

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

      1. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 75.8%

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

      1. *-commutative 75.8%

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

      2. unpow2 75.8%

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

   9. Simplified 75.8%

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

   10. Taylor expanded in x around 0 75.8%

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

       1. *-commutative 75.8%

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

       2. unpow2 75.8%

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

       3. associate-*r* 75.8%

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

   12. Simplified 75.8%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 2 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

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 87.5%

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

   1. associate-*r/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 7: 57.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -280000000000:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -280000000000.0)
   (* 6.0 (/ y (* x x)))
   (if (<= y 4.6e+142)
     (/ (/ y x) (+ (* x 0.16666666666666666) (/ 1.0 x)))
     (sqrt (* y y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -280000000000.0) {
		tmp = 6.0 * (y / (x * x));
	} else if (y <= 4.6e+142) {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	} 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 <= (-280000000000.0d0)) then
        tmp = 6.0d0 * (y / (x * x))
    else if (y <= 4.6d+142) then
        tmp = (y / x) / ((x * 0.16666666666666666d0) + (1.0d0 / x))
    else
        tmp = sqrt((y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -280000000000.0) {
		tmp = 6.0 * (y / (x * x));
	} else if (y <= 4.6e+142) {
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	} else {
		tmp = Math.sqrt((y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -280000000000.0:
		tmp = 6.0 * (y / (x * x))
	elif y <= 4.6e+142:
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x))
	else:
		tmp = math.sqrt((y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -280000000000.0)
		tmp = Float64(6.0 * Float64(y / Float64(x * x)));
	elseif (y <= 4.6e+142)
		tmp = Float64(Float64(y / x) / Float64(Float64(x * 0.16666666666666666) + Float64(1.0 / x)));
	else
		tmp = sqrt(Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -280000000000.0)
		tmp = 6.0 * (y / (x * x));
	elseif (y <= 4.6e+142)
		tmp = (y / x) / ((x * 0.16666666666666666) + (1.0 / x));
	else
		tmp = sqrt((y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -280000000000.0], N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+142], N[(N[(y / x), $MachinePrecision] / N[(N[(x * 0.16666666666666666), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8e11

   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%

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

   6. Simplified 5.0%

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

   7. Taylor expanded in x around 0 4.7%

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

      1. *-commutative 4.7%

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

      2. unpow2 4.7%

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

   9. Simplified 4.7%

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

   10. Taylor expanded in x around inf 53.5%

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

       1. associate-*r/ 53.5%

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

       2. unpow2 53.5%

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

   12. Simplified 53.5%

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

       1. *-un-lft-identity 53.5%

          \[\leadsto \frac{6 \cdot y}{\color{blue}{1 \cdot \left(x \cdot x\right)}} \]

       2. times-frac 53.5%

          \[\leadsto \color{blue}{\frac{6}{1} \cdot \frac{y}{x \cdot x}} \]

       3. metadata-eval 53.5%

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

   14. Applied egg-rr 53.5%

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

   if -2.8e11 < y < 4.60000000000000004e142

   1. Initial program 80.3%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 60.2%

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

      1. associate-/l* 79.8%

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

      2. associate-/r/ 82.7%

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

   6. Simplified 82.7%

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

      1. associate-/r/ 79.8%

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

      2. div-inv 79.7%

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

      3. associate-/r* 82.6%

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

   8. Applied egg-rr 82.6%

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

   9. Taylor expanded in x around 0 63.8%

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

   if 4.60000000000000004e142 < 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 6.0%

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

   5. Taylor expanded in x around 0 13.0%

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

      1. *-commutative 13.0%

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

   7. Simplified 13.0%

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

      1. div-inv 13.0%

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

      2. associate-*l* 4.8%

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

      3. div-inv 4.8%

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

      4. *-inverses 4.8%

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

      5. *-commutative 4.8%

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

      6. *-un-lft-identity 4.8%

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

      7. add-sqr-sqrt 4.8%

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

      8. sqrt-unprod 59.1%

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

   9. Applied egg-rr 59.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -280000000000:\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{y}{x}}{x \cdot 0.16666666666666666 + \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \]

Alternative 8: 56.5% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -280000000000 \lor \neg \left(y \leq 220\right):\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -280000000000.0) (not (<= y 220.0)))
   (* 6.0 (/ y (* x x)))
   (/ y (+ 1.0 (* x (* x 0.16666666666666666))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -280000000000.0) || !(y <= 220.0)) {
		tmp = 6.0 * (y / (x * x));
	} else {
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-280000000000.0d0)) .or. (.not. (y <= 220.0d0))) then
        tmp = 6.0d0 * (y / (x * x))
    else
        tmp = y / (1.0d0 + (x * (x * 0.16666666666666666d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -280000000000.0) || !(y <= 220.0)) {
		tmp = 6.0 * (y / (x * x));
	} else {
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -280000000000.0) or not (y <= 220.0):
		tmp = 6.0 * (y / (x * x))
	else:
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -280000000000.0) || !(y <= 220.0))
		tmp = Float64(6.0 * Float64(y / Float64(x * x)));
	else
		tmp = Float64(y / Float64(1.0 + Float64(x * Float64(x * 0.16666666666666666))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -280000000000.0) || ~((y <= 220.0)))
		tmp = 6.0 * (y / (x * x));
	else
		tmp = y / (1.0 + (x * (x * 0.16666666666666666)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -280000000000.0], N[Not[LessEqual[y, 220.0]], $MachinePrecision]], N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(1.0 + N[(x * N[(x * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e11 or 220 < 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 4.9%

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

      1. associate-/l* 4.9%

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

   6. Simplified 4.9%

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

   7. Taylor expanded in x around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. unpow2 4.2%

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

   9. Simplified 4.2%

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

   10. Taylor expanded in x around inf 46.7%

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

       1. associate-*r/ 46.7%

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

       2. unpow2 46.7%

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

   12. Simplified 46.7%

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

       1. *-un-lft-identity 46.7%

          \[\leadsto \frac{6 \cdot y}{\color{blue}{1 \cdot \left(x \cdot x\right)}} \]

       2. times-frac 46.7%

          \[\leadsto \color{blue}{\frac{6}{1} \cdot \frac{y}{x \cdot x}} \]

       3. metadata-eval 46.7%

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

   14. Applied egg-rr 46.7%

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

   if -2.8e11 < y < 220

   1. Initial program 76.2%

      \[\frac{\sin x \cdot \sinh y}{x} \]
   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 72.2%

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

      1. associate-/l* 95.9%

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

   6. Simplified 95.9%

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

   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. *-commutative 73.2%

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

      2. unpow2 73.2%

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

   9. Simplified 73.2%

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

   10. Taylor expanded in x around 0 73.2%

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

       1. *-commutative 73.2%

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

       2. unpow2 73.2%

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

       3. associate-*r* 73.2%

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

   12. Simplified 73.2%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -280000000000 \lor \neg \left(y \leq 220\right):\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{1 + x \cdot \left(x \cdot 0.16666666666666666\right)}\\ \end{array} \]

Alternative 9: 56.3% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3100 \lor \neg \left(y \leq 250\right):\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3100.0) (not (<= y 250.0)))
   (* 6.0 (/ y (* x x)))
   (/ x (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3100.0) || !(y <= 250.0)) {
		tmp = 6.0 * (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 <= (-3100.0d0)) .or. (.not. (y <= 250.0d0))) then
        tmp = 6.0d0 * (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 <= -3100.0) || !(y <= 250.0)) {
		tmp = 6.0 * (y / (x * x));
	} else {
		tmp = x / (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3100.0) or not (y <= 250.0):
		tmp = 6.0 * (y / (x * x))
	else:
		tmp = x / (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3100.0) || !(y <= 250.0))
		tmp = Float64(6.0 * 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 <= -3100.0) || ~((y <= 250.0)))
		tmp = 6.0 * (y / (x * x));
	else
		tmp = x / (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3100.0], N[Not[LessEqual[y, 250.0]], $MachinePrecision]], N[(6.0 * N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3100 or 250 < 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 4.8%

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

      1. associate-/l* 4.8%

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

   6. Simplified 4.8%

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

   7. Taylor expanded in x around 0 4.2%

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

      1. *-commutative 4.2%

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

      2. unpow2 4.2%

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

   9. Simplified 4.2%

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

   10. Taylor expanded in x around inf 45.6%

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

       1. associate-*r/ 45.6%

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

       2. unpow2 45.6%

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

   12. Simplified 45.6%

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

       1. *-un-lft-identity 45.6%

          \[\leadsto \frac{6 \cdot y}{\color{blue}{1 \cdot \left(x \cdot x\right)}} \]

       2. times-frac 45.6%

          \[\leadsto \color{blue}{\frac{6}{1} \cdot \frac{y}{x \cdot x}} \]

       3. metadata-eval 45.6%

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

   14. Applied egg-rr 45.6%

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

   if -3100 < y < 250

   1. Initial program 75.6%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 73.8%

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

   5. Taylor expanded in x around 0 27.6%

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

      1. *-commutative 27.6%

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

   7. Simplified 27.6%

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

      1. associate-/l* 51.8%

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

      2. associate-/r/ 73.0%

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

   9. Applied egg-rr 73.0%

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

       1. *-commutative 73.0%

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

       2. clear-num 73.8%

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

       3. un-div-inv 73.9%

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

   11. Applied egg-rr 73.9%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3100 \lor \neg \left(y \leq 250\right):\\ \;\;\;\;6 \cdot \frac{y}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \]

Alternative 10: 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 87.5%

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

   1. associate-*r/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 40.1%

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

5. Taylor expanded in x around 0 20.0%

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

   1. *-commutative 20.0%

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

7. Simplified 20.0%

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

   1. associate-/l* 28.7%

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

   2. associate-/r/ 52.6%

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

9. Applied egg-rr 52.6%

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

10. Final simplification 52.6%

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

Alternative 11: 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 87.5%

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

   1. associate-*r/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 40.1%

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

   1. associate-/l* 52.5%

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

   2. associate-/r/ 65.5%

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

6. Simplified 65.5%

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

7. Taylor expanded in x around 0 28.7%

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

8. Final simplification 28.7%

   \[\leadsto y \]

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 2023297 
(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))