Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.1% → 99.8%

Time: 8.6s

Alternatives: 12

Speedup: 1.0×

• 49.5% 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: 89.1% 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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. associate-*r/ 99.5%

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

3. Simplified 99.5%

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

   1. associate-*r/ 87.7%

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

   2. *-commutative 87.7%

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

   3. associate-/l* 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{\sin x}{-0.16666666666666666 \cdot \left(y \cdot x\right) + \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -0.002)
   (sinh y)
   (if (<= (sinh y) 0.0005)
     (/ (sin x) (+ (* -0.16666666666666666 (* y x)) (/ x y)))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -0.002) {
		tmp = sinh(y);
	} else if (sinh(y) <= 0.0005) {
		tmp = sin(x) / ((-0.16666666666666666 * (y * 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) <= (-0.002d0)) then
        tmp = sinh(y)
    else if (sinh(y) <= 0.0005d0) then
        tmp = sin(x) / (((-0.16666666666666666d0) * (y * 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) <= -0.002) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 0.0005) {
		tmp = Math.sin(x) / ((-0.16666666666666666 * (y * x)) + (x / y));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -0.002:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 0.0005:
		tmp = math.sin(x) / ((-0.16666666666666666 * (y * x)) + (x / y))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = Float64(sin(x) / Float64(Float64(-0.16666666666666666 * Float64(y * x)) + Float64(x / y)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = sin(x) / ((-0.16666666666666666 * (y * x)) + (x / y));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -0.002], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], N[(N[Sin[x], $MachinePrecision] / N[(N[(-0.16666666666666666 * N[(y * x), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -2e-3 or 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.6%

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

   if -2e-3 < (sinh.f64 y) < 5.0000000000000001e-4

   1. Initial program 73.4%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 99.4%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{\sin x}{-0.16666666666666666 \cdot \left(y \cdot x\right) + \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 3: 87.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -0.002)
   (sinh y)
   (if (<= (sinh y) 0.0005) (* (sin x) (/ y x)) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -0.002) {
		tmp = sinh(y);
	} else if (sinh(y) <= 0.0005) {
		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) <= (-0.002d0)) then
        tmp = sinh(y)
    else if (sinh(y) <= 0.0005d0) 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) <= -0.002) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 0.0005) {
		tmp = Math.sin(x) * (y / x);
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -0.002:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 0.0005:
		tmp = math.sin(x) * (y / x)
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		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) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = sin(x) * (y / x);
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -0.002], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], 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) < -2e-3 or 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.6%

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

   if -2e-3 < (sinh.f64 y) < 5.0000000000000001e-4

   1. Initial program 73.4%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 72.7%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 99.1%

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

   6. Simplified 99.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\sin x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 4: 87.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -0.002)
   (sinh y)
   (if (<= (sinh y) 0.0005) (/ y (/ x (sin x))) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -0.002) {
		tmp = sinh(y);
	} else if (sinh(y) <= 0.0005) {
		tmp = y / (x / sin(x));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (sinh(y) <= (-0.002d0)) then
        tmp = sinh(y)
    else if (sinh(y) <= 0.0005d0) then
        tmp = y / (x / sin(x))
    else
        tmp = sinh(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -0.002) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 0.0005) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -0.002:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 0.0005:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = Float64(y / Float64(x / sin(x)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = y / (x / sin(x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -0.002], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -2e-3 or 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.6%

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

   if -2e-3 < (sinh.f64 y) < 5.0000000000000001e-4

   1. Initial program 73.4%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 72.7%

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

      1. associate-/l* 99.2%

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

   6. Simplified 99.2%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 5: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{y}{1 + 0.16666666666666666 \cdot \left(x \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) -0.002)
   (sinh y)
   (if (<= (sinh y) 0.0005)
     (/ y (+ 1.0 (* 0.16666666666666666 (* x x))))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -0.002) {
		tmp = sinh(y);
	} else if (sinh(y) <= 0.0005) {
		tmp = y / (1.0 + (0.16666666666666666 * (x * 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) <= (-0.002d0)) then
        tmp = sinh(y)
    else if (sinh(y) <= 0.0005d0) then
        tmp = y / (1.0d0 + (0.16666666666666666d0 * (x * 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) <= -0.002) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 0.0005) {
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -0.002:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 0.0005:
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = Float64(y / Float64(1.0 + Float64(0.16666666666666666 * Float64(x * x))));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -0.002)
		tmp = sinh(y);
	elseif (sinh(y) <= 0.0005)
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], -0.002], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 0.0005], N[(y / N[(1.0 + N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -2e-3 or 5.0000000000000001e-4 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*r/ 99.3%

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

   3. Simplified 99.3%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 79.6%

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

   if -2e-3 < (sinh.f64 y) < 5.0000000000000001e-4

   1. Initial program 73.4%

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

      1. associate-*r/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 72.7%

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

      1. associate-/l* 99.2%

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

      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. Step-by-step derivation

      1. associate-/r/ 99.2%

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

      2. div-inv 99.1%

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

      3. associate-/r* 98.9%

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

   8. Applied egg-rr 98.9%

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

   9. Taylor expanded in x around 0 79.5%

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

   10. Taylor expanded in y around 0 79.6%

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

       1. *-commutative 79.6%

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

       2. +-commutative 79.6%

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

       3. *-commutative 79.6%

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

       4. distribute-lft-in 79.6%

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

       5. rgt-mult-inverse 79.8%

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

       6. associate-*r* 79.8%

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

       7. *-commutative 79.8%

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

   12. Simplified 79.8%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -0.002:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 0.0005:\\ \;\;\;\;\frac{y}{1 + 0.16666666666666666 \cdot \left(x \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

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 87.7%

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

   1. associate-*r/ 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 7: 60.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -300:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;\frac{y}{1 + 0.16666666666666666 \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+198}:\\ \;\;\;\;\frac{y \cdot 6}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -300.0)
   (* (/ y x) (/ 6.0 x))
   (if (<= y 330.0)
     (/ y (+ 1.0 (* 0.16666666666666666 (* x x))))
     (if (<= y 2.7e+198) (/ (* y 6.0) (* x x)) (sqrt (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -300.0) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 330.0) {
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	} else if (y <= 2.7e+198) {
		tmp = (y * 6.0) / (x * 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 <= (-300.0d0)) then
        tmp = (y / x) * (6.0d0 / x)
    else if (y <= 330.0d0) then
        tmp = y / (1.0d0 + (0.16666666666666666d0 * (x * x)))
    else if (y <= 2.7d+198) then
        tmp = (y * 6.0d0) / (x * 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 <= -300.0) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 330.0) {
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	} else if (y <= 2.7e+198) {
		tmp = (y * 6.0) / (x * x);
	} else {
		tmp = Math.sqrt((y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -300.0:
		tmp = (y / x) * (6.0 / x)
	elif y <= 330.0:
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)))
	elif y <= 2.7e+198:
		tmp = (y * 6.0) / (x * x)
	else:
		tmp = math.sqrt((y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -300.0)
		tmp = Float64(Float64(y / x) * Float64(6.0 / x));
	elseif (y <= 330.0)
		tmp = Float64(y / Float64(1.0 + Float64(0.16666666666666666 * Float64(x * x))));
	elseif (y <= 2.7e+198)
		tmp = Float64(Float64(y * 6.0) / Float64(x * x));
	else
		tmp = sqrt(Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -300.0)
		tmp = (y / x) * (6.0 / x);
	elseif (y <= 330.0)
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	elseif (y <= 2.7e+198)
		tmp = (y * 6.0) / (x * x);
	else
		tmp = sqrt((y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -300.0], N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 330.0], N[(y / N[(1.0 + N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+198], N[(N[(y * 6.0), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -300

   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%

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

      2. associate-/r/ 37.3%

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

   6. Simplified 37.3%

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

      1. associate-/r/ 4.9%

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

      2. div-inv 4.9%

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

      3. associate-/r* 37.3%

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

   8. Applied egg-rr 37.3%

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

   9. Taylor expanded in x around 0 36.5%

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

   10. Taylor expanded in x around inf 52.8%

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

       1. unpow2 52.8%

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

       2. associate-*r/ 52.8%

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

       3. times-frac 52.8%

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

   12. Simplified 52.8%

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

   if -300 < y < 330

   1. Initial program 74.1%

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

      1. associate-*r/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. associate-/l* 97.4%

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

      2. associate-/r/ 97.2%

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

   6. Simplified 97.2%

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

      1. associate-/r/ 97.4%

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

      2. div-inv 97.2%

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

      3. associate-/r* 97.0%

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

   8. Applied egg-rr 97.0%

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

   9. Taylor expanded in x around 0 78.1%

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

   10. Taylor expanded in y around 0 78.2%

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

       1. *-commutative 78.2%

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

       2. +-commutative 78.2%

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

       3. *-commutative 78.2%

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

       4. distribute-lft-in 78.2%

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

       5. rgt-mult-inverse 78.4%

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

       6. associate-*r* 78.4%

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

       7. *-commutative 78.4%

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

   12. Simplified 78.4%

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

   if 330 < y < 2.6999999999999999e198

   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 3.7%

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

      1. associate-/l* 3.7%

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

      2. associate-/r/ 29.6%

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

   6. Simplified 29.6%

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

      1. associate-/r/ 3.7%

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

      2. div-inv 3.7%

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

      3. associate-/r* 29.6%

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

   8. Applied egg-rr 29.6%

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

   9. Taylor expanded in x around 0 29.1%

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

   10. Taylor expanded in x around inf 57.4%

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

       1. unpow2 57.4%

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

       2. associate-*r/ 57.4%

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

   12. Simplified 57.4%

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

   if 2.6999999999999999e198 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 5.8%

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

   3. Taylor expanded in x around 0 19.6%

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

      1. div-inv 19.6%

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

      2. associate-*l* 5.8%

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

      3. div-inv 5.8%

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

      4. *-inverses 5.8%

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

      5. *-commutative 5.8%

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

      6. *-un-lft-identity 5.8%

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

      7. add-sqr-sqrt 5.8%

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

      8. sqrt-unprod 80.0%

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

   5. Applied egg-rr 80.0%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;\frac{y}{1 + 0.16666666666666666 \cdot \left(x \cdot x\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+198}:\\ \;\;\;\;\frac{y \cdot 6}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \]

Alternative 8: 57.5% accurate, 15.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -300:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;\frac{y}{1 + 0.16666666666666666 \cdot \left(x \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 6}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -300.0)
   (* (/ y x) (/ 6.0 x))
   (if (<= y 330.0)
     (/ y (+ 1.0 (* 0.16666666666666666 (* x x))))
     (/ (* y 6.0) (* x x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -300.0) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 330.0) {
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	} else {
		tmp = (y * 6.0) / (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-300.0d0)) then
        tmp = (y / x) * (6.0d0 / x)
    else if (y <= 330.0d0) then
        tmp = y / (1.0d0 + (0.16666666666666666d0 * (x * x)))
    else
        tmp = (y * 6.0d0) / (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -300.0) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 330.0) {
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	} else {
		tmp = (y * 6.0) / (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -300.0:
		tmp = (y / x) * (6.0 / x)
	elif y <= 330.0:
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)))
	else:
		tmp = (y * 6.0) / (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -300.0)
		tmp = Float64(Float64(y / x) * Float64(6.0 / x));
	elseif (y <= 330.0)
		tmp = Float64(y / Float64(1.0 + Float64(0.16666666666666666 * Float64(x * x))));
	else
		tmp = Float64(Float64(y * 6.0) / Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -300.0)
		tmp = (y / x) * (6.0 / x);
	elseif (y <= 330.0)
		tmp = y / (1.0 + (0.16666666666666666 * (x * x)));
	else
		tmp = (y * 6.0) / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -300.0], N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 330.0], N[(y / N[(1.0 + N[(0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 6.0), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -300

   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%

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

      2. associate-/r/ 37.3%

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

   6. Simplified 37.3%

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

      1. associate-/r/ 4.9%

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

      2. div-inv 4.9%

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

      3. associate-/r* 37.3%

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

   8. Applied egg-rr 37.3%

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

   9. Taylor expanded in x around 0 36.5%

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

   10. Taylor expanded in x around inf 52.8%

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

       1. unpow2 52.8%

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

       2. associate-*r/ 52.8%

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

       3. times-frac 52.8%

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

   12. Simplified 52.8%

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

   if -300 < y < 330

   1. Initial program 74.1%

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

      1. associate-*r/ 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around 0 71.5%

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

      1. associate-/l* 97.4%

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

      2. associate-/r/ 97.2%

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

   6. Simplified 97.2%

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

      1. associate-/r/ 97.4%

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

      2. div-inv 97.2%

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

      3. associate-/r* 97.0%

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

   8. Applied egg-rr 97.0%

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

   9. Taylor expanded in x around 0 78.1%

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

   10. Taylor expanded in y around 0 78.2%

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

       1. *-commutative 78.2%

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

       2. +-commutative 78.2%

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

       3. *-commutative 78.2%

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

       4. distribute-lft-in 78.2%

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

       5. rgt-mult-inverse 78.4%

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

       6. associate-*r* 78.4%

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

       7. *-commutative 78.4%

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

   12. Simplified 78.4%

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

   if 330 < 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 4.3%

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

      1. associate-/l* 4.3%

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

      2. associate-/r/ 34.9%

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

   6. Simplified 34.9%

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

      1. associate-/r/ 4.3%

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

      2. div-inv 4.3%

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

      3. associate-/r* 34.9%

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

   8. Applied egg-rr 34.9%

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

   9. Taylor expanded in x around 0 34.3%

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

   10. Taylor expanded in x around inf 54.3%

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

       1. unpow2 54.3%

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

       2. associate-*r/ 54.3%

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

   12. Simplified 54.3%

       \[\leadsto \color{blue}{\frac{6 \cdot y}{x \cdot x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 330:\\ \;\;\;\;\frac{y}{1 + 0.16666666666666666 \cdot \left(x \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 6}{x \cdot x}\\ \end{array} \]

Alternative 9: 57.0% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -250 \lor \neg \left(y \leq 270\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -250.0) (not (<= y 270.0)))
   (* (/ y x) (/ 6.0 x))
   (/ x (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -250.0) || !(y <= 270.0)) {
		tmp = (y / x) * (6.0 / 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 <= (-250.0d0)) .or. (.not. (y <= 270.0d0))) then
        tmp = (y / x) * (6.0d0 / 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 <= -250.0) || !(y <= 270.0)) {
		tmp = (y / x) * (6.0 / x);
	} else {
		tmp = x / (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -250.0) or not (y <= 270.0):
		tmp = (y / x) * (6.0 / x)
	else:
		tmp = x / (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -250.0) || !(y <= 270.0))
		tmp = Float64(Float64(y / x) * Float64(6.0 / x));
	else
		tmp = Float64(x / Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -250.0) || ~((y <= 270.0)))
		tmp = (y / x) * (6.0 / x);
	else
		tmp = x / (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -250.0], N[Not[LessEqual[y, 270.0]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -250 or 270 < 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 4.6%

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

      1. associate-/l* 4.6%

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

      2. associate-/r/ 36.0%

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

   6. Simplified 36.0%

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

      1. associate-/r/ 4.6%

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

      2. div-inv 4.6%

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

      3. associate-/r* 36.0%

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

   8. Applied egg-rr 36.0%

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

   9. Taylor expanded in x around 0 35.4%

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

   10. Taylor expanded in x around inf 53.5%

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

       1. unpow2 53.5%

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

       2. associate-*r/ 53.5%

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

       3. times-frac 53.5%

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

   12. Simplified 53.5%

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

   if -250 < y < 270

   1. Initial program 74.1%

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

   2. Taylor expanded in y around 0 71.5%

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

   3. Taylor expanded in x around 0 30.9%

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

      1. associate-/l* 56.7%

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

      2. associate-/r/ 76.6%

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

   5. Applied egg-rr 76.6%

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

      1. *-commutative 76.6%

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

      2. clear-num 77.6%

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

      3. un-div-inv 77.7%

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

   7. Applied egg-rr 77.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -250 \lor \neg \left(y \leq 270\right):\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \end{array} \]

Alternative 10: 57.0% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -290:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 300:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 6}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -290.0)
   (* (/ y x) (/ 6.0 x))
   (if (<= y 300.0) (/ x (/ x y)) (/ (* y 6.0) (* x x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -290.0) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 300.0) {
		tmp = x / (x / y);
	} else {
		tmp = (y * 6.0) / (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-290.0d0)) then
        tmp = (y / x) * (6.0d0 / x)
    else if (y <= 300.0d0) then
        tmp = x / (x / y)
    else
        tmp = (y * 6.0d0) / (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -290.0) {
		tmp = (y / x) * (6.0 / x);
	} else if (y <= 300.0) {
		tmp = x / (x / y);
	} else {
		tmp = (y * 6.0) / (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -290.0:
		tmp = (y / x) * (6.0 / x)
	elif y <= 300.0:
		tmp = x / (x / y)
	else:
		tmp = (y * 6.0) / (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -290.0)
		tmp = Float64(Float64(y / x) * Float64(6.0 / x));
	elseif (y <= 300.0)
		tmp = Float64(x / Float64(x / y));
	else
		tmp = Float64(Float64(y * 6.0) / Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -290.0)
		tmp = (y / x) * (6.0 / x);
	elseif (y <= 300.0)
		tmp = x / (x / y);
	else
		tmp = (y * 6.0) / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -290.0], N[(N[(y / x), $MachinePrecision] * N[(6.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 300.0], N[(x / N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(y * 6.0), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -290

   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%

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

      2. associate-/r/ 37.3%

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

   6. Simplified 37.3%

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

      1. associate-/r/ 4.9%

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

      2. div-inv 4.9%

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

      3. associate-/r* 37.3%

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

   8. Applied egg-rr 37.3%

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

   9. Taylor expanded in x around 0 36.5%

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

   10. Taylor expanded in x around inf 52.8%

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

       1. unpow2 52.8%

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

       2. associate-*r/ 52.8%

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

       3. times-frac 52.8%

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

   12. Simplified 52.8%

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

   if -290 < y < 300

   1. Initial program 74.1%

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

   2. Taylor expanded in y around 0 71.5%

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

   3. Taylor expanded in x around 0 30.9%

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

      1. associate-/l* 56.7%

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

      2. associate-/r/ 76.6%

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

   5. Applied egg-rr 76.6%

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

      1. *-commutative 76.6%

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

      2. clear-num 77.6%

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

      3. un-div-inv 77.7%

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

   7. Applied egg-rr 77.7%

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

   if 300 < 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 4.3%

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

      1. associate-/l* 4.3%

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

      2. associate-/r/ 34.9%

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

   6. Simplified 34.9%

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

      1. associate-/r/ 4.3%

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

      2. div-inv 4.3%

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

      3. associate-/r* 34.9%

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

   8. Applied egg-rr 34.9%

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

   9. Taylor expanded in x around 0 34.3%

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

   10. Taylor expanded in x around inf 54.3%

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

       1. unpow2 54.3%

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

       2. associate-*r/ 54.3%

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

   12. Simplified 54.3%

       \[\leadsto \color{blue}{\frac{6 \cdot y}{x \cdot x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -290:\\ \;\;\;\;\frac{y}{x} \cdot \frac{6}{x}\\ \mathbf{elif}\;y \leq 300:\\ \;\;\;\;\frac{x}{\frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 6}{x \cdot x}\\ \end{array} \]

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 87.7%

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

2. Taylor expanded in y around 0 36.5%

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

3. Taylor expanded in x around 0 21.0%

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

   1. associate-/l* 29.3%

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

   2. associate-/r/ 55.2%

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

5. Applied egg-rr 55.2%

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

6. Final simplification 55.2%

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

Alternative 12: 28.1% 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 87.7%

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

   1. associate-*r/ 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in y around 0 36.5%

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

   1. associate-/l* 48.8%

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

   2. associate-/r/ 65.2%

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

6. Simplified 65.2%

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

7. Taylor expanded in x around 0 29.3%

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

8. Final simplification 29.3%

   \[\leadsto y \]

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 2023173 
(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))