Linear.Quaternion:$ccosh from linear-1.19.1.3

Percentage Accurate: 89.4% → 99.9%

Time: 8.5s

Alternatives: 11

Speedup: 1.0×

• 49.6% 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: 89.4% 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 88.6%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 86.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 1:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 1.0) (* (/ (sin x) x) y) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -((double) INFINITY)) {
		tmp = sinh(y);
	} else if (sinh(y) <= 1.0) {
		tmp = (sin(x) / x) * y;
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -Inf)
		tmp = sinh(y);
	elseif (sinh(y) <= 1.0)
		tmp = (sin(x) / x) * y;
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], (-Infinity)], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 1.0], N[(N[(N[Sin[x], $MachinePrecision] / x), $MachinePrecision] * y), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -inf.0 or 1 < (sinh.f64 y)

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 75.1%

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

   if -inf.0 < (sinh.f64 y) < 1

   1. Initial program 76.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 98.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 1:\\ \;\;\;\;\frac{\sin x}{x} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 4 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (sinh y) (- INFINITY))
   (sinh y)
   (if (<= (sinh y) 4e-12)
     (/ y (+ 1.0 (* (* x x) 0.16666666666666666)))
     (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (sinh(y) <= -((double) INFINITY)) {
		tmp = sinh(y);
	} else if (sinh(y) <= 4e-12) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else {
		tmp = sinh(y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (Math.sinh(y) <= -Double.POSITIVE_INFINITY) {
		tmp = Math.sinh(y);
	} else if (Math.sinh(y) <= 4e-12) {
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if math.sinh(y) <= -math.inf:
		tmp = math.sinh(y)
	elif math.sinh(y) <= 4e-12:
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (sinh(y) <= Float64(-Inf))
		tmp = sinh(y);
	elseif (sinh(y) <= 4e-12)
		tmp = Float64(y / Float64(1.0 + Float64(Float64(x * x) * 0.16666666666666666)));
	else
		tmp = sinh(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (sinh(y) <= -Inf)
		tmp = sinh(y);
	elseif (sinh(y) <= 4e-12)
		tmp = y / (1.0 + ((x * x) * 0.16666666666666666));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[Sinh[y], $MachinePrecision], (-Infinity)], N[Sinh[y], $MachinePrecision], If[LessEqual[N[Sinh[y], $MachinePrecision], 4e-12], N[(y / N[(1.0 + N[(N[(x * x), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (sinh.f64 y) < -inf.0 or 3.99999999999999992e-12 < (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 74.9%

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

   if -inf.0 < (sinh.f64 y) < 3.99999999999999992e-12

   1. Initial program 75.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 75.3%

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

      1. associate-/l* 99.3%

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

   6. Simplified 99.3%

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

   7. Taylor expanded in x around 0 76.7%

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

      1. *-commutative 76.7%

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

      2. unpow2 76.7%

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

   9. Simplified 76.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\sinh y \leq -\infty:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;\sinh y \leq 4 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{1 + \left(x \cdot x\right) \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 4: 86.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \mathbf{if}\;y \leq -1800000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+139}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (+ 1.0 (* -0.16666666666666666 (* x x))) (sinh y))))
   (if (<= y -1800000.0)
     t_0
     (if (<= y 0.62) (/ y (/ x (sin x))) (if (<= y 1.3e+139) (sinh y) t_0)))))

C

double code(double x, double y) {
	double t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * sinh(y);
	double tmp;
	if (y <= -1800000.0) {
		tmp = t_0;
	} else if (y <= 0.62) {
		tmp = y / (x / sin(x));
	} else if (y <= 1.3e+139) {
		tmp = sinh(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 + ((-0.16666666666666666d0) * (x * x))) * sinh(y)
    if (y <= (-1800000.0d0)) then
        tmp = t_0
    else if (y <= 0.62d0) then
        tmp = y / (x / sin(x))
    else if (y <= 1.3d+139) then
        tmp = sinh(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * Math.sinh(y);
	double tmp;
	if (y <= -1800000.0) {
		tmp = t_0;
	} else if (y <= 0.62) {
		tmp = y / (x / Math.sin(x));
	} else if (y <= 1.3e+139) {
		tmp = Math.sinh(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * math.sinh(y)
	tmp = 0
	if y <= -1800000.0:
		tmp = t_0
	elif y <= 0.62:
		tmp = y / (x / math.sin(x))
	elif y <= 1.3e+139:
		tmp = math.sinh(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))) * sinh(y))
	tmp = 0.0
	if (y <= -1800000.0)
		tmp = t_0;
	elseif (y <= 0.62)
		tmp = Float64(y / Float64(x / sin(x)));
	elseif (y <= 1.3e+139)
		tmp = sinh(y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * sinh(y);
	tmp = 0.0;
	if (y <= -1800000.0)
		tmp = t_0;
	elseif (y <= 0.62)
		tmp = y / (x / sin(x));
	elseif (y <= 1.3e+139)
		tmp = sinh(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1800000.0], t$95$0, If[LessEqual[y, 0.62], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+139], N[Sinh[y], $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e6 or 1.30000000000000011e139 < 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 84.1%

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

      1. unpow2 84.1%

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

   6. Simplified 84.1%

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

   if -1.8e6 < y < 0.619999999999999996

   1. Initial program 76.7%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 74.6%

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

      1. associate-/l* 97.9%

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

   6. Simplified 97.9%

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

   if 0.619999999999999996 < y < 1.30000000000000011e139

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{1} \cdot \sinh y \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1800000:\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+139}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \end{array} \]

Alternative 5: 85.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \mathbf{if}\;y \leq -1800000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;\frac{\sin x}{-0.16666666666666666 \cdot \left(x \cdot y\right) + \frac{x}{y}}\\ \mathbf{elif}\;y \leq 10^{+137}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (+ 1.0 (* -0.16666666666666666 (* x x))) (sinh y))))
   (if (<= y -1800000.0)
     t_0
     (if (<= y 0.62)
       (/ (sin x) (+ (* -0.16666666666666666 (* x y)) (/ x y)))
       (if (<= y 1e+137) (sinh y) t_0)))))

C

double code(double x, double y) {
	double t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * sinh(y);
	double tmp;
	if (y <= -1800000.0) {
		tmp = t_0;
	} else if (y <= 0.62) {
		tmp = sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y));
	} else if (y <= 1e+137) {
		tmp = sinh(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 + ((-0.16666666666666666d0) * (x * x))) * sinh(y)
    if (y <= (-1800000.0d0)) then
        tmp = t_0
    else if (y <= 0.62d0) then
        tmp = sin(x) / (((-0.16666666666666666d0) * (x * y)) + (x / y))
    else if (y <= 1d+137) then
        tmp = sinh(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * Math.sinh(y);
	double tmp;
	if (y <= -1800000.0) {
		tmp = t_0;
	} else if (y <= 0.62) {
		tmp = Math.sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y));
	} else if (y <= 1e+137) {
		tmp = Math.sinh(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * math.sinh(y)
	tmp = 0
	if y <= -1800000.0:
		tmp = t_0
	elif y <= 0.62:
		tmp = math.sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y))
	elif y <= 1e+137:
		tmp = math.sinh(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))) * sinh(y))
	tmp = 0.0
	if (y <= -1800000.0)
		tmp = t_0;
	elseif (y <= 0.62)
		tmp = Float64(sin(x) / Float64(Float64(-0.16666666666666666 * Float64(x * y)) + Float64(x / y)));
	elseif (y <= 1e+137)
		tmp = sinh(y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 + (-0.16666666666666666 * (x * x))) * sinh(y);
	tmp = 0.0;
	if (y <= -1800000.0)
		tmp = t_0;
	elseif (y <= 0.62)
		tmp = sin(x) / ((-0.16666666666666666 * (x * y)) + (x / y));
	elseif (y <= 1e+137)
		tmp = sinh(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sinh[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1800000.0], t$95$0, If[LessEqual[y, 0.62], N[(N[Sin[x], $MachinePrecision] / N[(N[(-0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+137], N[Sinh[y], $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e6 or 1e137 < 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 84.1%

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

      1. unpow2 84.1%

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

   6. Simplified 84.1%

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

   if -1.8e6 < y < 0.619999999999999996

   1. Initial program 76.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 98.0%

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

   if 0.619999999999999996 < y < 1e137

   1. Initial program 99.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 87.8%

      \[\leadsto \color{blue}{1} \cdot \sinh y \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1800000:\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;\frac{\sin x}{-0.16666666666666666 \cdot \left(x \cdot y\right) + \frac{x}{y}}\\ \mathbf{elif}\;y \leq 10^{+137}:\\ \;\;\;\;\sinh y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right) \cdot \sinh y\\ \end{array} \]

Alternative 6: 87.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0027:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0027) (sinh y) (if (<= y 0.62) (/ y (/ x (sin x))) (sinh y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0027) {
		tmp = sinh(y);
	} else if (y <= 0.62) {
		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 (y <= (-0.0027d0)) then
        tmp = sinh(y)
    else if (y <= 0.62d0) 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 (y <= -0.0027) {
		tmp = Math.sinh(y);
	} else if (y <= 0.62) {
		tmp = y / (x / Math.sin(x));
	} else {
		tmp = Math.sinh(y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0027:
		tmp = math.sinh(y)
	elif y <= 0.62:
		tmp = y / (x / math.sin(x))
	else:
		tmp = math.sinh(y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0027)
		tmp = sinh(y);
	elseif (y <= 0.62)
		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 (y <= -0.0027)
		tmp = sinh(y);
	elseif (y <= 0.62)
		tmp = y / (x / sin(x));
	else
		tmp = sinh(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0027], N[Sinh[y], $MachinePrecision], If[LessEqual[y, 0.62], N[(y / N[(x / N[Sin[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sinh[y], $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0027000000000000001 or 0.619999999999999996 < y

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 75.1%

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

   if -0.0027000000000000001 < y < 0.619999999999999996

   1. Initial program 76.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 75.2%

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

      1. associate-/l* 98.6%

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

   6. Simplified 98.6%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0027:\\ \;\;\;\;\sinh y\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;\frac{y}{\frac{x}{\sin x}}\\ \mathbf{else}:\\ \;\;\;\;\sinh y\\ \end{array} \]

Alternative 7: 54.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 1.35e+154) (* x (/ y x)) (sqrt (* y y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.35e+154) {
		tmp = x * (y / 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 <= 1.35d+154) then
        tmp = x * (y / 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 <= 1.35e+154) {
		tmp = x * (y / x);
	} else {
		tmp = Math.sqrt((y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.35e+154:
		tmp = x * (y / x)
	else:
		tmp = math.sqrt((y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.35e+154)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = sqrt(Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.35e+154)
		tmp = x * (y / x);
	else
		tmp = sqrt((y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.35e+154], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(y * y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.35000000000000003e154

   1. Initial program 86.8%

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

   2. Taylor expanded in y around 0 44.3%

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

   3. Taylor expanded in x around 0 21.9%

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

      1. *-commutative 21.9%

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

   5. Simplified 21.9%

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

      1. associate-/l* 32.5%

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

      2. associate-/r/ 56.7%

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

   7. Applied egg-rr 56.7%

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

   if 1.35000000000000003e154 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 5.2%

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

   3. Taylor expanded in x around 0 22.0%

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

      1. *-commutative 22.0%

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

   5. Simplified 22.0%

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

      1. associate-/l* 4.0%

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

      2. *-inverses 4.0%

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

      3. /-rgt-identity 4.0%

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

      4. add-sqr-sqrt 4.0%

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

      5. sqrt-unprod 61.1%

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

   7. Applied egg-rr 61.1%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{y \cdot y}\\ \end{array} \]

Alternative 8: 50.0% accurate, 18.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \lor \neg \left(x \leq 2.2 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(x \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x 3.1) (not (<= x 2.2e+145)))
   (* x (/ y x))
   (* -0.16666666666666666 (* x (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= 3.1) || !(x <= 2.2e+145)) {
		tmp = x * (y / x);
	} else {
		tmp = -0.16666666666666666 * (x * (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= 3.1d0) .or. (.not. (x <= 2.2d+145))) then
        tmp = x * (y / x)
    else
        tmp = (-0.16666666666666666d0) * (x * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= 3.1) || !(x <= 2.2e+145)) {
		tmp = x * (y / x);
	} else {
		tmp = -0.16666666666666666 * (x * (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= 3.1) or not (x <= 2.2e+145):
		tmp = x * (y / x)
	else:
		tmp = -0.16666666666666666 * (x * (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= 3.1) || !(x <= 2.2e+145))
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(-0.16666666666666666 * Float64(x * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= 3.1) || ~((x <= 2.2e+145)))
		tmp = x * (y / x);
	else
		tmp = -0.16666666666666666 * (x * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, 3.1], N[Not[LessEqual[x, 2.2e+145]], $MachinePrecision]], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(-0.16666666666666666 * N[(x * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.10000000000000009 or 2.20000000000000009e145 < x

   1. Initial program 86.9%

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

   2. Taylor expanded in y around 0 38.5%

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

   3. Taylor expanded in x around 0 24.2%

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

      1. *-commutative 24.2%

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

   5. Simplified 24.2%

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

      1. associate-/l* 32.2%

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

      2. associate-/r/ 58.9%

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

   7. Applied egg-rr 58.9%

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

   if 3.10000000000000009 < x < 2.20000000000000009e145

   1. Initial program 99.8%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 42.7%

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

      1. unpow2 42.7%

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

   6. Simplified 42.7%

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

   7. Taylor expanded in y around 0 37.3%

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

   8. Taylor expanded in x around inf 37.3%

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

      1. unpow2 37.3%

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

      2. associate-*l* 37.3%

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

      3. *-commutative 37.3%

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

   10. Simplified 37.3%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.1 \lor \neg \left(x \leq 2.2 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(x \cdot \left(x \cdot y\right)\right)\\ \end{array} \]

Alternative 9: 48.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2e+185)
   (* x (/ y x))
   (* y (+ 1.0 (* -0.16666666666666666 (* x x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2e+185) {
		tmp = x * (y / x);
	} else {
		tmp = y * (1.0 + (-0.16666666666666666 * (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 <= 2d+185) then
        tmp = x * (y / x)
    else
        tmp = y * (1.0d0 + ((-0.16666666666666666d0) * (x * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2e+185) {
		tmp = x * (y / x);
	} else {
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2e+185:
		tmp = x * (y / x)
	else:
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2e+185)
		tmp = Float64(x * Float64(y / x));
	else
		tmp = Float64(y * Float64(1.0 + Float64(-0.16666666666666666 * Float64(x * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2e+185)
		tmp = x * (y / x);
	else
		tmp = y * (1.0 + (-0.16666666666666666 * (x * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2e+185], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 + N[(-0.16666666666666666 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2e185

   1. Initial program 87.2%

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

   2. Taylor expanded in y around 0 42.9%

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

   3. Taylor expanded in x around 0 21.2%

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

      1. *-commutative 21.2%

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

   5. Simplified 21.2%

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

      1. associate-/l* 31.5%

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

      2. associate-/r/ 57.0%

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

   7. Applied egg-rr 57.0%

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

   if 2e185 < 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 71.4%

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

      1. unpow2 71.4%

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

   6. Simplified 71.4%

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

   7. Taylor expanded in y around 0 41.6%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + -0.16666666666666666 \cdot \left(x \cdot x\right)\right)\\ \end{array} \]

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 88.6%

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

2. Taylor expanded in y around 0 38.8%

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

3. Taylor expanded in x around 0 21.9%

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

   1. *-commutative 21.9%

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

5. Simplified 21.9%

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

   1. associate-/l* 28.5%

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

   2. associate-/r/ 53.3%

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

7. Applied egg-rr 53.3%

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

8. Final simplification 53.3%

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

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 88.6%

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

   1. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 38.8%

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

   1. associate-/l* 50.1%

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

6. Simplified 50.1%

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

7. Taylor expanded in x around 0 28.5%

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

8. Final simplification 28.5%

   \[\leadsto y \]

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 2023290 
(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))