Linear.Quaternion:$csin from linear-1.19.1.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.8s

Alternatives: 7

Speedup: 1.0×

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

Specification

Math

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

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sinh y}{y}\\ \mathbf{if}\;t\_0 \leq 1:\\ \;\;\;\;\cos x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (sinh y) y))) (if (<= t_0 1.0) (cos x) t_0)))

C

double code(double x, double y) {
	double t_0 = sinh(y) / y;
	double tmp;
	if (t_0 <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		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 <= 1.0:
		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 <= 1.0)
		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 <= 1.0)
		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, 1.0], N[Cos[x], $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (sinh.f64 y) y) < 1

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

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

   if 1 < (/.f64 (sinh.f64 y) y)

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.6%

      \[\leadsto \color{blue}{1} \cdot \frac{\sinh y}{y} \]
   4. Step-by-step derivation

      1. *-un-lft-identity 72.6%

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

      2. add-log-exp 71.0%

         \[\leadsto \color{blue}{\log \left(e^{\frac{\sinh y}{y}}\right)} \]

      3. *-un-lft-identity 71.0%

         \[\leadsto \log \color{blue}{\left(1 \cdot e^{\frac{\sinh y}{y}}\right)} \]

      4. log-prod 71.0%

         \[\leadsto \color{blue}{\log 1 + \log \left(e^{\frac{\sinh y}{y}}\right)} \]

      5. metadata-eval 71.0%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{\sinh y}{y}}\right) \]

      6. add-log-exp 72.6%

         \[\leadsto 0 + \color{blue}{\frac{\sinh y}{y}} \]

   5. Applied egg-rr 72.6%

      \[\leadsto \color{blue}{0 + \frac{\sinh y}{y}} \]
   6. Step-by-step derivation

      1. +-lft-identity 72.6%

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

   7. Simplified 72.6%

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

Alternative 3: 62.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 330:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+138}:\\ \;\;\;\;\frac{y + y \cdot \left(-0.5 \cdot \left(x \cdot x\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 330.0)
   (cos x)
   (if (<= y 1.45e+138)
     (/ (+ y (* y (* -0.5 (* x x)))) y)
     (+ 1.0 (* 0.16666666666666666 (* y y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 330.0) {
		tmp = cos(x);
	} else if (y <= 1.45e+138) {
		tmp = (y + (y * (-0.5 * (x * x)))) / y;
	} else {
		tmp = 1.0 + (0.16666666666666666 * (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 <= 330.0d0) then
        tmp = cos(x)
    else if (y <= 1.45d+138) then
        tmp = (y + (y * ((-0.5d0) * (x * x)))) / y
    else
        tmp = 1.0d0 + (0.16666666666666666d0 * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 330.0) {
		tmp = Math.cos(x);
	} else if (y <= 1.45e+138) {
		tmp = (y + (y * (-0.5 * (x * x)))) / y;
	} else {
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 330.0:
		tmp = math.cos(x)
	elif y <= 1.45e+138:
		tmp = (y + (y * (-0.5 * (x * x)))) / y
	else:
		tmp = 1.0 + (0.16666666666666666 * (y * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 330.0)
		tmp = cos(x);
	elseif (y <= 1.45e+138)
		tmp = Float64(Float64(y + Float64(y * Float64(-0.5 * Float64(x * x)))) / y);
	else
		tmp = Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 330.0)
		tmp = cos(x);
	elseif (y <= 1.45e+138)
		tmp = (y + (y * (-0.5 * (x * x)))) / y;
	else
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 330.0], N[Cos[x], $MachinePrecision], If[LessEqual[y, 1.45e+138], N[(N[(y + N[(y * N[(-0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 330

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.5%

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

   if 330 < y < 1.45000000000000005e138

   1. Initial program 100.0%

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

      1. add-log-exp 97.1%

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

      2. *-un-lft-identity 97.1%

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

      3. log-prod 97.1%

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

      4. metadata-eval 97.1%

         \[\leadsto \color{blue}{0} + \log \left(e^{\cos x \cdot \frac{\sinh y}{y}}\right) \]

      5. add-log-exp 100.0%

         \[\leadsto 0 + \color{blue}{\cos x \cdot \frac{\sinh y}{y}} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0 + \cos x \cdot \frac{\sinh y}{y}} \]
   5. Step-by-step derivation

      1. +-lft-identity 100.0%

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

      2. associate-*r/ 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 3.2%

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

   8. Taylor expanded in x around 0 8.6%

      \[\leadsto \frac{\color{blue}{y + -0.5 \cdot \left({x}^{2} \cdot y\right)}}{y} \]
   9. Step-by-step derivation

      1. associate-*r* 8.6%

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

   10. Simplified 8.6%

       \[\leadsto \frac{\color{blue}{y + \left(-0.5 \cdot {x}^{2}\right) \cdot y}}{y} \]
   11. Step-by-step derivation

       1. unpow2 8.6%

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

   12. Applied egg-rr 8.6%

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

   if 1.45000000000000005e138 < y

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 71.0%

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

   4. Taylor expanded in y around 0 62.2%

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

      1. unpow2 62.2%

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

   6. Applied egg-rr 62.2%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 330:\\ \;\;\;\;\cos x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+138}:\\ \;\;\;\;\frac{y + y \cdot \left(-0.5 \cdot \left(x \cdot x\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.1% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.9 \cdot 10^{+50}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y + y \cdot \left(-0.5 \cdot \left(x \cdot x\right)\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 5.9e+50)
   (+ 1.0 (* 0.16666666666666666 (* y y)))
   (/ (+ y (* y (* -0.5 (* x x)))) y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5.9e+50) {
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	} else {
		tmp = (y + (y * (-0.5 * (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 <= 5.9d+50) then
        tmp = 1.0d0 + (0.16666666666666666d0 * (y * y))
    else
        tmp = (y + (y * ((-0.5d0) * (x * x)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 5.9e+50) {
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	} else {
		tmp = (y + (y * (-0.5 * (x * x)))) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5.9e+50:
		tmp = 1.0 + (0.16666666666666666 * (y * y))
	else:
		tmp = (y + (y * (-0.5 * (x * x)))) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5.9e+50)
		tmp = Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y)));
	else
		tmp = Float64(Float64(y + Float64(y * Float64(-0.5 * Float64(x * x)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5.9e+50)
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	else
		tmp = (y + (y * (-0.5 * (x * x)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5.9e+50], N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + N[(y * N[(-0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.8999999999999998e50

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.7%

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

   4. Taylor expanded in y around 0 54.6%

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

      1. unpow2 54.6%

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

   6. Applied egg-rr 54.6%

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

   if 5.8999999999999998e50 < x

   1. Initial program 100.0%

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

      1. add-log-exp 99.7%

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

      2. *-un-lft-identity 99.7%

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

      3. log-prod 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \color{blue}{0} + \log \left(e^{\cos x \cdot \frac{\sinh y}{y}}\right) \]

      5. add-log-exp 100.0%

         \[\leadsto 0 + \color{blue}{\cos x \cdot \frac{\sinh y}{y}} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0 + \cos x \cdot \frac{\sinh y}{y}} \]
   5. Step-by-step derivation

      1. +-lft-identity 100.0%

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

      2. associate-*r/ 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 53.6%

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

   8. Taylor expanded in x around 0 18.6%

      \[\leadsto \frac{\color{blue}{y + -0.5 \cdot \left({x}^{2} \cdot y\right)}}{y} \]
   9. Step-by-step derivation

      1. associate-*r* 18.6%

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

   10. Simplified 18.6%

       \[\leadsto \frac{\color{blue}{y + \left(-0.5 \cdot {x}^{2}\right) \cdot y}}{y} \]
   11. Step-by-step derivation

       1. unpow2 18.6%

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

   12. Applied egg-rr 18.6%

       \[\leadsto \frac{y + \left(-0.5 \cdot \color{blue}{\left(x \cdot x\right)}\right) \cdot y}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.9 \cdot 10^{+50}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y + y \cdot \left(-0.5 \cdot \left(x \cdot x\right)\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.1% accurate, 17.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.6 \cdot 10^{+151}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + -0.5 \cdot \left(x \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 8.6e+151)
   (+ 1.0 (* 0.16666666666666666 (* y y)))
   (+ 1.0 (* -0.5 (* x x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 8.6e+151) {
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	} else {
		tmp = 1.0 + (-0.5 * (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 (x <= 8.6d+151) then
        tmp = 1.0d0 + (0.16666666666666666d0 * (y * y))
    else
        tmp = 1.0d0 + ((-0.5d0) * (x * x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 8.6e+151) {
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	} else {
		tmp = 1.0 + (-0.5 * (x * x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 8.6e+151:
		tmp = 1.0 + (0.16666666666666666 * (y * y))
	else:
		tmp = 1.0 + (-0.5 * (x * x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 8.6e+151)
		tmp = Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y)));
	else
		tmp = Float64(1.0 + Float64(-0.5 * Float64(x * x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 8.6e+151)
		tmp = 1.0 + (0.16666666666666666 * (y * y));
	else
		tmp = 1.0 + (-0.5 * (x * x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 8.6e+151], N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-0.5 * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 8.59999999999999965e151

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 70.3%

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

   4. Taylor expanded in y around 0 50.5%

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

      1. unpow2 50.5%

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

   6. Applied egg-rr 50.5%

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

   if 8.59999999999999965e151 < x

   1. Initial program 100.0%

      \[\cos x \cdot \frac{\sinh y}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 53.5%

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

   4. Taylor expanded in x around 0 24.7%

      \[\leadsto \color{blue}{1 + -0.5 \cdot {x}^{2}} \]
   5. Step-by-step derivation

      1. *-commutative 24.7%

         \[\leadsto 1 + \color{blue}{{x}^{2} \cdot -0.5} \]

   6. Simplified 24.7%

      \[\leadsto \color{blue}{1 + {x}^{2} \cdot -0.5} \]
   7. Step-by-step derivation

      1. unpow2 24.7%

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

   8. Applied egg-rr 24.7%

      \[\leadsto 1 + \color{blue}{\left(x \cdot x\right)} \cdot -0.5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.6 \cdot 10^{+151}:\\ \;\;\;\;1 + 0.16666666666666666 \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + -0.5 \cdot \left(x \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.4% accurate, 29.3× speedup

Math

\[\begin{array}{l} \\ 1 + 0.16666666666666666 \cdot \left(y \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ 1.0 (* 0.16666666666666666 (* y y))))

C

double code(double x, double y) {
	return 1.0 + (0.16666666666666666 * (y * y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 + (0.16666666666666666d0 * (y * y))
end function

Java

public static double code(double x, double y) {
	return 1.0 + (0.16666666666666666 * (y * y));
}

Python

def code(x, y):
	return 1.0 + (0.16666666666666666 * (y * y))

Julia

function code(x, y)
	return Float64(1.0 + Float64(0.16666666666666666 * Float64(y * y)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 + (0.16666666666666666 * (y * y));
end

Wolfram

code[x_, y_] := N[(1.0 + N[(0.16666666666666666 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\cos x \cdot \frac{\sinh y}{y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 66.5%

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

4. Taylor expanded in y around 0 47.1%

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

   1. unpow2 47.1%

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

6. Applied egg-rr 47.1%

   \[\leadsto 1 + 0.16666666666666666 \cdot \color{blue}{\left(y \cdot y\right)} \]
7. Add Preprocessing

Alternative 7: 28.6% 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. Add Preprocessing

3. Taylor expanded in x around 0 66.5%

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

4. Taylor expanded in y around 0 34.7%

   \[\leadsto \color{blue}{1} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024191 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))