Statistics.Sample:$skurtosis from math-functions-0.1.5.2

Percentage Accurate: 94.1% → 99.7%

Time: 4.1s

Alternatives: 5

Speedup: 1.0×

• 24.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot y} - 3 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x / (y * y)) - 3.0

Julia

function code(x, y)
	return Float64(Float64(x / Float64(y * y)) - 3.0)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]

Initial Program: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot y} - 3 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x / (y * y)) - 3.0

Julia

function code(x, y)
	return Float64(Float64(x / Float64(y * y)) - 3.0)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 5.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{y\_m}}{y\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y\_m \cdot y\_m} - 3\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m)
 :precision binary64
 (if (<= y_m 5.2e-160) (/ (/ x y_m) y_m) (- (/ x (* y_m y_m)) 3.0)))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double tmp;
	if (y_m <= 5.2e-160) {
		tmp = (x / y_m) / y_m;
	} else {
		tmp = (x / (y_m * y_m)) - 3.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8) :: tmp
    if (y_m <= 5.2d-160) then
        tmp = (x / y_m) / y_m
    else
        tmp = (x / (y_m * y_m)) - 3.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	double tmp;
	if (y_m <= 5.2e-160) {
		tmp = (x / y_m) / y_m;
	} else {
		tmp = (x / (y_m * y_m)) - 3.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	tmp = 0
	if y_m <= 5.2e-160:
		tmp = (x / y_m) / y_m
	else:
		tmp = (x / (y_m * y_m)) - 3.0
	return tmp

Julia

y_m = abs(y)
function code(x, y_m)
	tmp = 0.0
	if (y_m <= 5.2e-160)
		tmp = Float64(Float64(x / y_m) / y_m);
	else
		tmp = Float64(Float64(x / Float64(y_m * y_m)) - 3.0);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m)
	tmp = 0.0;
	if (y_m <= 5.2e-160)
		tmp = (x / y_m) / y_m;
	else
		tmp = (x / (y_m * y_m)) - 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := If[LessEqual[y$95$m, 5.2e-160], N[(N[(x / y$95$m), $MachinePrecision] / y$95$m), $MachinePrecision], N[(N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.20000000000000007e-160

   1. Initial program 94.8%

      \[\frac{x}{y \cdot y} - 3 \]
   2. Add Preprocessing

   4. Applied rewrites 32.5%

      \[\leadsto \color{blue}{\sqrt{\frac{x}{y}} \cdot \sqrt{\frac{\frac{x}{y}}{y \cdot y}}} - 3 \]

   5. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot {\left(\sqrt{-1}\right)}^{2}}{{y}^{2}}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right)}{{y}^{2}}} \]

      2. unpow2 N/A

         \[\leadsto \frac{-1 \cdot \left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right)}{\color{blue}{y \cdot y}} \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{-1 \cdot \left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right)}{y}}{y}} \]

      4. mul-1-neg N/A

         \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right)}}{y}}{y} \]

      5. *-commutative N/A

         \[\leadsto \frac{\frac{\mathsf{neg}\left(\color{blue}{{\left(\sqrt{-1}\right)}^{2} \cdot x}\right)}{y}}{y} \]

      6. unpow2 N/A

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

      7. rem-square-sqrt N/A

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

      8. distribute-frac-neg N/A

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

      9. distribute-frac-neg2 N/A

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

      10. mul-1-neg N/A

          \[\leadsto \frac{\frac{\color{blue}{\mathsf{neg}\left(x\right)}}{\mathsf{neg}\left(y\right)}}{y} \]

      11. distribute-frac-neg N/A

          \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(\frac{x}{\mathsf{neg}\left(y\right)}\right)}}{y} \]

      12. distribute-neg-frac N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{\frac{x}{\mathsf{neg}\left(y\right)}}{y}\right)} \]

      13. distribute-frac-neg2 N/A

          \[\leadsto \color{blue}{\frac{\frac{x}{\mathsf{neg}\left(y\right)}}{\mathsf{neg}\left(y\right)}} \]

      14. associate-/r* N/A

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

      15. sqr-neg-rev N/A

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

      16. unpow2 N/A

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

      17. unpow2 N/A

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

      18. associate-/r* N/A

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

      19. lower-/.f64 N/A

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

      20. lower-/.f64 59.6

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

   7. Applied rewrites 59.6%

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

   if 5.20000000000000007e-160 < y

   1. Initial program 99.9%

      \[\frac{x}{y \cdot y} - 3 \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 92.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \frac{x}{y\_m \cdot y\_m}\\ t_1 := t\_0 - 3\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+14} \lor \neg \left(t\_1 \leq -2\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-3\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m)
 :precision binary64
 (let* ((t_0 (/ x (* y_m y_m))) (t_1 (- t_0 3.0)))
   (if (or (<= t_1 -1e+14) (not (<= t_1 -2.0))) t_0 -3.0)))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double t_0 = x / (y_m * y_m);
	double t_1 = t_0 - 3.0;
	double tmp;
	if ((t_1 <= -1e+14) || !(t_1 <= -2.0)) {
		tmp = t_0;
	} else {
		tmp = -3.0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (y_m * y_m)
    t_1 = t_0 - 3.0d0
    if ((t_1 <= (-1d+14)) .or. (.not. (t_1 <= (-2.0d0)))) then
        tmp = t_0
    else
        tmp = -3.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	double t_0 = x / (y_m * y_m);
	double t_1 = t_0 - 3.0;
	double tmp;
	if ((t_1 <= -1e+14) || !(t_1 <= -2.0)) {
		tmp = t_0;
	} else {
		tmp = -3.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	t_0 = x / (y_m * y_m)
	t_1 = t_0 - 3.0
	tmp = 0
	if (t_1 <= -1e+14) or not (t_1 <= -2.0):
		tmp = t_0
	else:
		tmp = -3.0
	return tmp

Julia

y_m = abs(y)
function code(x, y_m)
	t_0 = Float64(x / Float64(y_m * y_m))
	t_1 = Float64(t_0 - 3.0)
	tmp = 0.0
	if ((t_1 <= -1e+14) || !(t_1 <= -2.0))
		tmp = t_0;
	else
		tmp = -3.0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m)
	t_0 = x / (y_m * y_m);
	t_1 = t_0 - 3.0;
	tmp = 0.0;
	if ((t_1 <= -1e+14) || ~((t_1 <= -2.0)))
		tmp = t_0;
	else
		tmp = -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := Block[{t$95$0 = N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - 3.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+14], N[Not[LessEqual[t$95$1, -2.0]], $MachinePrecision]], t$95$0, -3.0]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64)) < -1e14 or -2 < (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64))

   1. Initial program 93.6%

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

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y \cdot y}} - 3 \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{x}{\color{blue}{y \cdot y}} - 3 \]

      3. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3 \]

      4. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3 \]

      5. lower-/.f64 99.8

         \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{y} - 3 \]

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y} - 3} \]

   6. Applied rewrites 3.1%

      \[\leadsto \color{blue}{\frac{{\left(\frac{\sqrt{x}}{y}\right)}^{6} - 27}{{\left(\frac{\sqrt{x}}{y}\right)}^{8} - {\left(\mathsf{fma}\left(\frac{\frac{x}{y}}{y}, 3, 9\right)\right)}^{2}} \cdot \left({\left(\frac{\sqrt{x}}{y}\right)}^{4} - \mathsf{fma}\left(\frac{\frac{x}{y}}{y}, 3, 9\right)\right)} \]

   7. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot {\left(\sqrt{-1}\right)}^{2}}{{y}^{2}}} \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x \cdot {\left(\sqrt{-1}\right)}^{2}}{{y}^{2}} \cdot -1} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(x \cdot {\left(\sqrt{-1}\right)}^{2}\right) \cdot -1}{{y}^{2}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left({\left(\sqrt{-1}\right)}^{2} \cdot x\right)} \cdot -1}{{y}^{2}} \]

      4. unpow2 N/A

         \[\leadsto \frac{\left(\color{blue}{\left(\sqrt{-1} \cdot \sqrt{-1}\right)} \cdot x\right) \cdot -1}{{y}^{2}} \]

      5. rem-square-sqrt N/A

         \[\leadsto \frac{\left(\color{blue}{-1} \cdot x\right) \cdot -1}{{y}^{2}} \]

      6. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot -1}{{y}^{2}} \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(x \cdot -1\right)}}{{y}^{2}} \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \frac{\color{blue}{x \cdot \left(\mathsf{neg}\left(-1\right)\right)}}{{y}^{2}} \]

      9. metadata-eval N/A

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

      10. *-rgt-identity N/A

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

      11. lower-/.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 92.5

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

   9. Applied rewrites 92.5%

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

   if -1e14 < (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64)) < -2

   1. Initial program 100.0%

      \[\frac{x}{y \cdot y} - 3 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-3} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.8%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot y} - 3 \leq -1 \cdot 10^{+14} \lor \neg \left(\frac{x}{y \cdot y} - 3 \leq -2\right):\\ \;\;\;\;\frac{x}{y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;-3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \frac{\frac{x}{y\_m}}{y\_m} - 3 \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 (- (/ (/ x y_m) y_m) 3.0))

C

y_m = fabs(y);
double code(double x, double y_m) {
	return ((x / y_m) / y_m) - 3.0;
}

Fortran

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

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	return ((x / y_m) / y_m) - 3.0;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	return ((x / y_m) / y_m) - 3.0

Julia

y_m = abs(y)
function code(x, y_m)
	return Float64(Float64(Float64(x / y_m) / y_m) - 3.0)
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := N[(N[(N[(x / y$95$m), $MachinePrecision] / y$95$m), $MachinePrecision] - 3.0), $MachinePrecision]

Derivation

1. Initial program 96.7%

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

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x}{y \cdot y}} - 3 \]

   2. lift-*.f64 N/A

      \[\leadsto \frac{x}{\color{blue}{y \cdot y}} - 3 \]

   3. associate-/r* N/A

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3 \]

   4. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3 \]

   5. lower-/.f64 99.9

      \[\leadsto \frac{\color{blue}{\frac{x}{y}}}{y} - 3 \]

4. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y} - 3} \]
5. Add Preprocessing

Alternative 4: 94.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \frac{x}{y\_m \cdot y\_m} - 3 \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 (- (/ x (* y_m y_m)) 3.0))

C

y_m = fabs(y);
double code(double x, double y_m) {
	return (x / (y_m * y_m)) - 3.0;
}

Fortran

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

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	return (x / (y_m * y_m)) - 3.0;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	return (x / (y_m * y_m)) - 3.0

Julia

y_m = abs(y)
function code(x, y_m)
	return Float64(Float64(x / Float64(y_m * y_m)) - 3.0)
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m)
	tmp = (x / (y_m * y_m)) - 3.0;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := N[(N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]

Derivation

1. Initial program 96.7%

   \[\frac{x}{y \cdot y} - 3 \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 5: 51.1% accurate, 20.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ -3 \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 -3.0)

C

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

Fortran

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

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	return -3.0;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	return -3.0

Julia

y_m = abs(y)
function code(x, y_m)
	return -3.0
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := -3.0

Derivation

1. Initial program 96.7%

   \[\frac{x}{y \cdot y} - 3 \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-3} \]
4. Step-by-step derivation

5. Applied rewrites 50.0%

   \[\leadsto \color{blue}{-3} \]
6. Add Preprocessing

Developer Target 1: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y}}{y} - 3 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x / y) / y) - 3.0

Julia

function code(x, y)
	return Float64(Float64(Float64(x / y) / y) - 3.0)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] - 3.0), $MachinePrecision]

Reproduce

herbie shell --seed 2024342 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (/ x y) y) 3))

  (- (/ x (* y y)) 3.0))