Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 10

Speedup: 1.0×

• 48.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 69.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.1e-8) (cos x) (* (sinh y) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.1e-8) {
		tmp = cos(x);
	} else {
		tmp = sinh(y) * (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.1d-8) then
        tmp = cos(x)
    else
        tmp = sinh(y) * (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.1e-8) {
		tmp = Math.cos(x);
	} else {
		tmp = Math.sinh(y) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.1e-8:
		tmp = math.cos(x)
	else:
		tmp = math.sinh(y) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.1e-8)
		tmp = cos(x);
	else
		tmp = Float64(sinh(y) * Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.1e-8)
		tmp = cos(x);
	else
		tmp = sinh(y) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.1e-8], N[Cos[x], $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.09999999999999994e-8

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 70.4%

      \[\leadsto \color{blue}{\cos x} \]

   if 2.09999999999999994e-8 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 76.5%

      \[\leadsto \color{blue}{\frac{1}{y}} \cdot \sinh y \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-8}:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \frac{1}{y}\\ \end{array} \]

Alternative 3: 54.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 55000:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot {x}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 55000.0) (cos x) (* -0.5 (pow x 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 55000.0) {
		tmp = cos(x);
	} else {
		tmp = -0.5 * pow(x, 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 55000.0d0) then
        tmp = cos(x)
    else
        tmp = (-0.5d0) * (x ** 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 55000.0) {
		tmp = Math.cos(x);
	} else {
		tmp = -0.5 * Math.pow(x, 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 55000.0:
		tmp = math.cos(x)
	else:
		tmp = -0.5 * math.pow(x, 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 55000.0)
		tmp = cos(x);
	else
		tmp = Float64(-0.5 * (x ^ 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 55000.0)
		tmp = cos(x);
	else
		tmp = -0.5 * (x ^ 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 55000.0], N[Cos[x], $MachinePrecision], N[(-0.5 * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 55000

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 69.9%

      \[\leadsto \color{blue}{\cos x} \]

   if 55000 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{\cos x \cdot \left(e^{y} - \frac{1}{e^{y}}\right)}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(\cos x \cdot \left(e^{y} - \frac{1}{e^{y}}\right)\right)}{y}} \]

      2. *-commutative 100.0%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(\left(e^{y} - \frac{1}{e^{y}}\right) \cdot \cos x\right)}}{y} \]

      3. rec-exp 100.0%

         \[\leadsto \frac{0.5 \cdot \left(\left(e^{y} - \color{blue}{e^{-y}}\right) \cdot \cos x\right)}{y} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{0.5 \cdot \left(\left(e^{y} - e^{-y}\right) \cdot \cos x\right)}{y}} \]

   7. Taylor expanded in y around 0 3.1%

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

   8. Taylor expanded in x around 0 21.7%

      \[\leadsto \frac{\color{blue}{y + -0.5 \cdot \left({x}^{2} \cdot y\right)}}{y} \]

   9. Taylor expanded in x around inf 14.6%

      \[\leadsto \color{blue}{-0.5 \cdot {x}^{2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 55000:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot {x}^{2}\\ \end{array} \]

Alternative 4: 51.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \cos x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (cos x))

C

double code(double x, double y) {
	return cos(x);
}

Fortran

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

Java

public static double code(double x, double y) {
	return Math.cos(x);
}

Python

def code(x, y):
	return math.cos(x)

Julia

function code(x, y)
	return cos(x)
end

MATLAB

function tmp = code(x, y)
	tmp = cos(x);
end

Wolfram

code[x_, y_] := N[Cos[x], $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

   2. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 54.0%

   \[\leadsto \color{blue}{\cos x} \]

5. Final simplification 54.0%

   \[\leadsto \cos x \]

Alternative 5: 8.3% accurate, 66.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+21}:\\ \;\;\;\;0.25\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 5.8e+21) 0.25 -1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5.8e+21) {
		tmp = 0.25;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 5.8d+21) then
        tmp = 0.25d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 5.8e+21) {
		tmp = 0.25;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5.8e+21:
		tmp = 0.25
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5.8e+21)
		tmp = 0.25;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5.8e+21)
		tmp = 0.25;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5.8e+21], 0.25, -1.0]

Derivation

1. Split input into 2 regimes

2. if x < 5.8e21

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 73.0%

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

   6. Applied egg-rr 8.4%

      \[\leadsto \color{blue}{0.25} \]

   if 5.8e21 < x

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 28.8%

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

   6. Applied egg-rr 6.6%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 8.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+21}:\\ \;\;\;\;0.25\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 8.4% accurate, 66.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+21}:\\ \;\;\;\;0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 5.8e+21) 0.3333333333333333 -1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5.8e+21) {
		tmp = 0.3333333333333333;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 5.8d+21) then
        tmp = 0.3333333333333333d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 5.8e+21) {
		tmp = 0.3333333333333333;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5.8e+21:
		tmp = 0.3333333333333333
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5.8e+21)
		tmp = 0.3333333333333333;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5.8e+21)
		tmp = 0.3333333333333333;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5.8e+21], 0.3333333333333333, -1.0]

Derivation

1. Split input into 2 regimes

2. if x < 5.8e21

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 73.0%

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

   6. Applied egg-rr 8.6%

      \[\leadsto \color{blue}{0.3333333333333333} \]

   if 5.8e21 < x

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 28.8%

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

   6. Applied egg-rr 6.6%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 8.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.8 \cdot 10^{+21}:\\ \;\;\;\;0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 8.8% accurate, 66.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{+78}:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 3.1e+78) 0.5 -1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.1e+78) {
		tmp = 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 3.1d+78) then
        tmp = 0.5d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.1e+78) {
		tmp = 0.5;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.1e+78:
		tmp = 0.5
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.1e+78)
		tmp = 0.5;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.1e+78)
		tmp = 0.5;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.1e+78], 0.5, -1.0]

Derivation

1. Split input into 2 regimes

2. if x < 3.1e78

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 70.1%

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

   6. Applied egg-rr 9.2%

      \[\leadsto \color{blue}{0.5} \]

   if 3.1e78 < x

   1. Initial program 100.0%

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

      1. associate-*r/ 99.9%

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

      2. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 29.7%

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

   6. Applied egg-rr 7.2%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 8.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{+78}:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 3.4% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ -3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -3.0)

C

double code(double x, double y) {
	return -3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -3.0d0
end function

Java

public static double code(double x, double y) {
	return -3.0;
}

Python

def code(x, y):
	return -3.0

Julia

function code(x, y)
	return -3.0
end

MATLAB

function tmp = code(x, y)
	tmp = -3.0;
end

Wolfram

code[x_, y_] := -3.0

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

   2. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 61.8%

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

6. Applied egg-rr 4.1%

   \[\leadsto \color{blue}{-3} \]

7. Final simplification 4.1%

   \[\leadsto -3 \]

Alternative 9: 4.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

   2. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 61.8%

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

6. Applied egg-rr 5.0%

   \[\leadsto \color{blue}{-1} \]

7. Final simplification 5.0%

   \[\leadsto -1 \]

Alternative 10: 28.9% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

   1. associate-*r/ 99.9%

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

   2. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 61.8%

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

5. Taylor expanded in y around 0 28.6%

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

6. Final simplification 28.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023302 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))