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

Percentage Accurate: 94.5% → 99.9%

Time: 4.8s

Alternatives: 4

Speedup: 1.0×

• 24.1% 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: 94.5% 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: 99.9% accurate, 1.0× 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 92.0%

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

   1. sub-neg N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

   3. associate-/r* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{y}\right), y\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), \left(\mathsf{neg}\left(3\right)\right)\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), -3\right) \]

3. Simplified 99.9%

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

Alternative 2: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot y}\\ t_1 := \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;t\_0 \leq -4:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.2:\\ \;\;\;\;-3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y y))) (t_1 (/ (/ x y) y)))
   (if (<= t_0 -4.0) t_1 (if (<= t_0 0.2) -3.0 t_1))))

C

double code(double x, double y) {
	double t_0 = x / (y * y);
	double t_1 = (x / y) / y;
	double tmp;
	if (t_0 <= -4.0) {
		tmp = t_1;
	} else if (t_0 <= 0.2) {
		tmp = -3.0;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x / (y * y)
    t_1 = (x / y) / y
    if (t_0 <= (-4.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.2d0) then
        tmp = -3.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * y);
	double t_1 = (x / y) / y;
	double tmp;
	if (t_0 <= -4.0) {
		tmp = t_1;
	} else if (t_0 <= 0.2) {
		tmp = -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * y)
	t_1 = (x / y) / y
	tmp = 0
	if t_0 <= -4.0:
		tmp = t_1
	elif t_0 <= 0.2:
		tmp = -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * y))
	t_1 = Float64(Float64(x / y) / y)
	tmp = 0.0
	if (t_0 <= -4.0)
		tmp = t_1;
	elseif (t_0 <= 0.2)
		tmp = -3.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * y);
	t_1 = (x / y) / y;
	tmp = 0.0;
	if (t_0 <= -4.0)
		tmp = t_1;
	elseif (t_0 <= 0.2)
		tmp = -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t$95$0, -4.0], t$95$1, If[LessEqual[t$95$0, 0.2], -3.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y y)) < -4 or 0.20000000000000001 < (/.f64 x (*.f64 y y))

   1. Initial program 84.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{y}\right), y\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), \left(\mathsf{neg}\left(3\right)\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), -3\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 82.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   7. Simplified 82.6%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 98.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right) \]

   9. Applied egg-rr 98.3%

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

   if -4 < (/.f64 x (*.f64 y y)) < 0.20000000000000001

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{y}\right), y\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), \left(\mathsf{neg}\left(3\right)\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), -3\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 97.8%

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

Alternative 3: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_0 \leq -4:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0.2:\\ \;\;\;\;-3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y y))))
   (if (<= t_0 -4.0) t_0 (if (<= t_0 0.2) -3.0 t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * y);
	double tmp;
	if (t_0 <= -4.0) {
		tmp = t_0;
	} else if (t_0 <= 0.2) {
		tmp = -3.0;
	} 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 = x / (y * y)
    if (t_0 <= (-4.0d0)) then
        tmp = t_0
    else if (t_0 <= 0.2d0) then
        tmp = -3.0d0
    else
        tmp = t_0
    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 <= -4.0) {
		tmp = t_0;
	} else if (t_0 <= 0.2) {
		tmp = -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * y)
	tmp = 0
	if t_0 <= -4.0:
		tmp = t_0
	elif t_0 <= 0.2:
		tmp = -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * y))
	tmp = 0.0
	if (t_0 <= -4.0)
		tmp = t_0;
	elseif (t_0 <= 0.2)
		tmp = -3.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * y);
	tmp = 0.0;
	if (t_0 <= -4.0)
		tmp = t_0;
	elseif (t_0 <= 0.2)
		tmp = -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4.0], t$95$0, If[LessEqual[t$95$0, 0.2], -3.0, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y y)) < -4 or 0.20000000000000001 < (/.f64 x (*.f64 y y))

   1. Initial program 84.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{y}\right), y\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), \left(\mathsf{neg}\left(3\right)\right)\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), -3\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({y}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 82.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right) \]

   7. Simplified 82.6%

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

   if -4 < (/.f64 x (*.f64 y y)) < 0.20000000000000001

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{y}\right), y\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), \left(\mathsf{neg}\left(3\right)\right)\right) \]

      6. metadata-eval 100.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), -3\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 97.8%

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

Alternative 4: 51.7% accurate, 7.0× 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 92.0%

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

   1. sub-neg N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y \cdot y}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

   3. associate-/r* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{\frac{x}{y}}{y}\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(\frac{x}{y}\right), y\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), \left(\mathsf{neg}\left(3\right)\right)\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), y\right), -3\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in x around 0

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

7. Simplified 50.2%

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

Developer Target 1: 99.9% accurate, 1.0× 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 2024161 
(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))