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

Percentage Accurate: 94.1% → 99.8%

Time: 4.3s

Alternatives: 5

Speedup: 1.0×

• 25.9% 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: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 5 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 5e-289) (/ (/ x y) y) (- (/ x (* y y)) 3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5e-289) {
		tmp = (x / y) / y;
	} else {
		tmp = (x / (y * y)) - 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y * y) <= 5d-289) then
        tmp = (x / y) / y
    else
        tmp = (x / (y * y)) - 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y * y) <= 5e-289) {
		tmp = (x / y) / y;
	} else {
		tmp = (x / (y * y)) - 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 5e-289:
		tmp = (x / y) / y
	else:
		tmp = (x / (y * y)) - 3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y * y) <= 5e-289)
		tmp = Float64(Float64(x / y) / y);
	else
		tmp = Float64(Float64(x / Float64(y * y)) - 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y * y) <= 5e-289)
		tmp = (x / y) / y;
	else
		tmp = (x / (y * y)) - 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y * y), $MachinePrecision], 5e-289], N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y y) < 5.00000000000000029e-289

   1. Initial program 78.4%

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

      1. unpow1 N/A

         \[\leadsto \color{blue}{{\left(\frac{x}{y \cdot y}\right)}^{1}} - 3 \]

      2. metadata-eval N/A

         \[\leadsto {\left(\frac{x}{y \cdot y}\right)}^{\color{blue}{\left(\frac{2}{2}\right)}} - 3 \]

      3. sqrt-pow1 N/A

         \[\leadsto \color{blue}{\sqrt{{\left(\frac{x}{y \cdot y}\right)}^{2}}} - 3 \]

      4. pow2 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. sqrt-prod N/A

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

      9. rem-square-sqrt N/A

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

      10. sqrt-unprod N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\sqrt{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}}}} - 3 \]

      11. rem-sqrt-square-rev N/A

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

      12. neg-fabs N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\left|\mathsf{neg}\left(y \cdot y\right)\right|}}} - 3 \]

      13. rem-sqrt-square N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\sqrt{\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \left(\mathsf{neg}\left(y \cdot y\right)\right)}}}} - 3 \]

      14. sqrt-prod N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\sqrt{\mathsf{neg}\left(y \cdot y\right)} \cdot \sqrt{\mathsf{neg}\left(y \cdot y\right)}}}} - 3 \]

      15. rem-square-sqrt N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

      16. lower-*.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

      17. lower-sqrt.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x}} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}} - 3 \]

      18. lower-sqrt.f64 N/A

          \[\leadsto \sqrt{x} \cdot \color{blue}{\sqrt{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

      19. lower-/.f64 N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\color{blue}{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

   4. Applied rewrites 37.5%

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

   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. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. unpow2 N/A

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

      5. rem-square-sqrt N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. unpow2 N/A

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

      9. associate-/r* N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.9

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

   7. Applied rewrites 99.9%

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

   if 5.00000000000000029e-289 < (*.f64 y 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: 93.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_0 \leq -3 \lor \neg \left(t\_0 \leq 3\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y y))))
   (if (or (<= t_0 -3.0) (not (<= t_0 3.0))) t_0 -3.0)))

C

double code(double x, double y) {
	double t_0 = x / (y * y);
	double tmp;
	if ((t_0 <= -3.0) || !(t_0 <= 3.0)) {
		tmp = t_0;
	} else {
		tmp = -3.0;
	}
	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 = x / (y * y)
    if ((t_0 <= (-3.0d0)) .or. (.not. (t_0 <= 3.0d0))) then
        tmp = t_0
    else
        tmp = -3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * y);
	double tmp;
	if ((t_0 <= -3.0) || !(t_0 <= 3.0)) {
		tmp = t_0;
	} else {
		tmp = -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * y)
	tmp = 0
	if (t_0 <= -3.0) or not (t_0 <= 3.0):
		tmp = t_0
	else:
		tmp = -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * y))
	tmp = 0.0
	if ((t_0 <= -3.0) || !(t_0 <= 3.0))
		tmp = t_0;
	else
		tmp = -3.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * y);
	tmp = 0.0;
	if ((t_0 <= -3.0) || ~((t_0 <= 3.0)))
		tmp = t_0;
	else
		tmp = -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -3.0], N[Not[LessEqual[t$95$0, 3.0]], $MachinePrecision]], t$95$0, -3.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y y)) < -3 or 3 < (/.f64 x (*.f64 y y))

   1. Initial program 88.0%

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

      1. unpow1 N/A

         \[\leadsto \color{blue}{{\left(\frac{x}{y \cdot y}\right)}^{1}} - 3 \]

      2. metadata-eval N/A

         \[\leadsto {\left(\frac{x}{y \cdot y}\right)}^{\color{blue}{\left(\frac{2}{2}\right)}} - 3 \]

      3. sqrt-pow1 N/A

         \[\leadsto \color{blue}{\sqrt{{\left(\frac{x}{y \cdot y}\right)}^{2}}} - 3 \]

      4. pow2 N/A

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

      5. lift-/.f64 N/A

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

      6. associate-*l/ N/A

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

      7. associate-/l* N/A

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

      8. sqrt-prod N/A

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

      9. rem-square-sqrt N/A

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

      10. sqrt-unprod N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\sqrt{\left(y \cdot y\right) \cdot \left(y \cdot y\right)}}}} - 3 \]

      11. rem-sqrt-square-rev N/A

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

      12. neg-fabs N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\left|\mathsf{neg}\left(y \cdot y\right)\right|}}} - 3 \]

      13. rem-sqrt-square N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\sqrt{\left(\mathsf{neg}\left(y \cdot y\right)\right) \cdot \left(\mathsf{neg}\left(y \cdot y\right)\right)}}}} - 3 \]

      14. sqrt-prod N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\sqrt{\mathsf{neg}\left(y \cdot y\right)} \cdot \sqrt{\mathsf{neg}\left(y \cdot y\right)}}}} - 3 \]

      15. rem-square-sqrt N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\color{blue}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

      16. lower-*.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

      17. lower-sqrt.f64 N/A

          \[\leadsto \color{blue}{\sqrt{x}} \cdot \sqrt{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}} - 3 \]

      18. lower-sqrt.f64 N/A

          \[\leadsto \sqrt{x} \cdot \color{blue}{\sqrt{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

      19. lower-/.f64 N/A

          \[\leadsto \sqrt{x} \cdot \sqrt{\color{blue}{\frac{\frac{x}{y \cdot y}}{\mathsf{neg}\left(y \cdot y\right)}}} - 3 \]

   4. Applied rewrites 34.5%

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

   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. mul-1-neg N/A

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

      3. *-commutative N/A

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

      4. unpow2 N/A

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

      5. rem-square-sqrt N/A

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

      6. mul-1-neg N/A

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

      7. remove-double-neg N/A

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

      8. unpow2 N/A

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

      9. associate-/r* N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 99.0

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

   7. Applied rewrites 99.0%

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

   9. Applied rewrites 87.2%

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

   if -3 < (/.f64 x (*.f64 y y)) < 3

   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 99.2%

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

4. Final simplification 93.1%

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

Alternative 3: 99.9% accurate, 0.8× speedup

Math

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

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]

Derivation

1. Initial program 93.9%

   \[\frac{x}{y \cdot y} - 3 \]
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

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

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]

Derivation

1. Initial program 93.9%

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

Alternative 5: 49.6% accurate, 20.0× 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 93.9%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 50.2%

   \[\leadsto \color{blue}{-3} \]
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 2024320 
(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))