Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 13

Speedup: 1.0×

• 50.6% 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: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\sinh y}{y} \leq 2:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (sinh y) y) 2.0) (cos x) (* (sinh y) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((sinh(y) / y) <= 2.0) {
		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 ((sinh(y) / y) <= 2.0d0) 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 ((Math.sinh(y) / y) <= 2.0) {
		tmp = Math.cos(x);
	} else {
		tmp = Math.sinh(y) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.sinh(y) / y) <= 2.0:
		tmp = math.cos(x)
	else:
		tmp = math.sinh(y) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(sinh(y) / y) <= 2.0)
		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 ((sinh(y) / y) <= 2.0)
		tmp = cos(x);
	else
		tmp = sinh(y) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision], 2.0], N[Cos[x], $MachinePrecision], N[(N[Sinh[y], $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (sinh.f64 y) y) < 2

   1. Initial program 100.0%

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

      1. associate-*r/ 99.8%

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

      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 99.1%

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

   if 2 < (/.f64 (sinh.f64 y) 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 77.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sinh y}{y} \leq 2:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\sinh y \cdot \frac{1}{y}\\ \end{array} \]

Alternative 3: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sinh y}{y}\\ \mathbf{if}\;t_0 \leq 2:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sinh y) y))) (if (<= t_0 2.0) (cos x) t_0)))

C

double code(double x, double y) {
	double t_0 = sinh(y) / y;
	double tmp;
	if (t_0 <= 2.0) {
		tmp = cos(x);
	} 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 = sinh(y) / y
    if (t_0 <= 2.0d0) then
        tmp = cos(x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sinh(y) / y;
	double tmp;
	if (t_0 <= 2.0) {
		tmp = Math.cos(x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sinh(y) / y
	tmp = 0
	if t_0 <= 2.0:
		tmp = math.cos(x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sinh(y) / y)
	tmp = 0.0
	if (t_0 <= 2.0)
		tmp = cos(x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sinh(y) / y;
	tmp = 0.0;
	if (t_0 <= 2.0)
		tmp = cos(x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sinh[y], $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, 2.0], N[Cos[x], $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (sinh.f64 y) y) < 2

   1. Initial program 100.0%

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

      1. associate-*r/ 99.8%

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

      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 99.1%

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

   if 2 < (/.f64 (sinh.f64 y) 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 77.5%

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

   5. Taylor expanded in y around inf 77.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{e^{y} - \frac{1}{e^{y}}}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 77.5%

         \[\leadsto \color{blue}{\frac{e^{y} - \frac{1}{e^{y}}}{y} \cdot 0.5} \]

      2. associate-/r/ 77.5%

         \[\leadsto \color{blue}{\frac{e^{y} - \frac{1}{e^{y}}}{\frac{y}{0.5}}} \]

      3. metadata-eval 77.5%

         \[\leadsto \frac{e^{y} - \frac{1}{e^{y}}}{\frac{y}{\color{blue}{\frac{1}{2}}}} \]

      4. associate-/l* 77.5%

         \[\leadsto \frac{e^{y} - \frac{1}{e^{y}}}{\color{blue}{\frac{y \cdot 2}{1}}} \]

      5. *-commutative 77.5%

         \[\leadsto \frac{e^{y} - \frac{1}{e^{y}}}{\frac{\color{blue}{2 \cdot y}}{1}} \]

      6. /-rgt-identity 77.5%

         \[\leadsto \frac{e^{y} - \frac{1}{e^{y}}}{\color{blue}{2 \cdot y}} \]

      7. associate-/r* 77.5%

         \[\leadsto \color{blue}{\frac{\frac{e^{y} - \frac{1}{e^{y}}}{2}}{y}} \]

      8. rec-exp 77.5%

         \[\leadsto \frac{\frac{e^{y} - \color{blue}{e^{-y}}}{2}}{y} \]

      9. sinh-def 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sinh y}{y} \leq 2:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;\frac{\sinh y}{y}\\ \end{array} \]

Alternative 4: 49.9% 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 50.8%

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

5. Final simplification 50.8%

   \[\leadsto \cos x \]

Alternative 5: 3.2% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ -6 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -6.0)

C

double code(double x, double y) {
	return -6.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -6.0d0
end function

Java

public static double code(double x, double y) {
	return -6.0;
}

Python

def code(x, y):
	return -6.0

Julia

function code(x, y)
	return -6.0
end

MATLAB

function tmp = code(x, y)
	tmp = -6.0;
end

Wolfram

code[x_, y_] := -6.0

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 3.6%

   \[\leadsto \color{blue}{-6} \]

8. Final simplification 3.6%

   \[\leadsto -6 \]

Alternative 6: 3.8% 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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 4.2%

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

8. Final simplification 4.2%

   \[\leadsto -1 \]

Alternative 7: 7.5% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.1111111111111111 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.1111111111111111)

C

double code(double x, double y) {
	return 0.1111111111111111;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.1111111111111111d0
end function

Java

public static double code(double x, double y) {
	return 0.1111111111111111;
}

Python

def code(x, y):
	return 0.1111111111111111

Julia

function code(x, y)
	return 0.1111111111111111
end

MATLAB

function tmp = code(x, y)
	tmp = 0.1111111111111111;
end

Wolfram

code[x_, y_] := 0.1111111111111111

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 7.2%

   \[\leadsto \color{blue}{0.1111111111111111} \]

8. Final simplification 7.2%

   \[\leadsto 0.1111111111111111 \]

Alternative 8: 7.7% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.16666666666666666 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.16666666666666666)

C

double code(double x, double y) {
	return 0.16666666666666666;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.16666666666666666d0
end function

Java

public static double code(double x, double y) {
	return 0.16666666666666666;
}

Python

def code(x, y):
	return 0.16666666666666666

Julia

function code(x, y)
	return 0.16666666666666666
end

MATLAB

function tmp = code(x, y)
	tmp = 0.16666666666666666;
end

Wolfram

code[x_, y_] := 0.16666666666666666

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 7.4%

   \[\leadsto \color{blue}{0.16666666666666666} \]

8. Final simplification 7.4%

   \[\leadsto 0.16666666666666666 \]

Alternative 9: 8.0% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.25 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.25)

C

double code(double x, double y) {
	return 0.25;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.25d0
end function

Java

public static double code(double x, double y) {
	return 0.25;
}

Python

def code(x, y):
	return 0.25

Julia

function code(x, y)
	return 0.25
end

MATLAB

function tmp = code(x, y)
	tmp = 0.25;
end

Wolfram

code[x_, y_] := 0.25

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 7.6%

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

8. Final simplification 7.6%

   \[\leadsto 0.25 \]

Alternative 10: 8.1% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.3333333333333333)

C

double code(double x, double y) {
	return 0.3333333333333333;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.3333333333333333d0
end function

Java

public static double code(double x, double y) {
	return 0.3333333333333333;
}

Python

def code(x, y):
	return 0.3333333333333333

Julia

function code(x, y)
	return 0.3333333333333333
end

MATLAB

function tmp = code(x, y)
	tmp = 0.3333333333333333;
end

Wolfram

code[x_, y_] := 0.3333333333333333

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 7.8%

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

8. Final simplification 7.8%

   \[\leadsto 0.3333333333333333 \]

Alternative 11: 8.5% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.5)

C

double code(double x, double y) {
	return 0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0
end function

Java

public static double code(double x, double y) {
	return 0.5;
}

Python

def code(x, y):
	return 0.5

Julia

function code(x, y)
	return 0.5
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5;
end

Wolfram

code[x_, y_] := 0.5

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 8.1%

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

8. Final simplification 8.1%

   \[\leadsto 0.5 \]

Alternative 12: 8.8% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0.6666666666666666 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.6666666666666666)

C

double code(double x, double y) {
	return 0.6666666666666666;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.6666666666666666d0
end function

Java

public static double code(double x, double y) {
	return 0.6666666666666666;
}

Python

def code(x, y):
	return 0.6666666666666666

Julia

function code(x, y)
	return 0.6666666666666666
end

MATLAB

function tmp = code(x, y)
	tmp = 0.6666666666666666;
end

Wolfram

code[x_, y_] := 0.6666666666666666

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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

7. Applied egg-rr 8.3%

   \[\leadsto \color{blue}{0.6666666666666666} \]

8. Final simplification 8.3%

   \[\leadsto 0.6666666666666666 \]

Alternative 13: 28.4% 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 64.2%

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

5. Taylor expanded in y around 0 26.5%

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

6. Final simplification 26.5%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))