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

Percentage Accurate: 94.3% → 94.3%

Time: 863.0ms

Alternatives: 4

Speedup: 1.0×

• 24.8% 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: 94.3% 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: 94.3% 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 94.6%

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

Alternative 2: 49.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_0 \leq -2000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;y \cdot y - 3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y y))))
   (if (<= t_0 -2000.0) t_0 (if (<= t_0 1.0) (- (* y y) 3.0) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (y * y);
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = t_0;
	} else if (t_0 <= 1.0) {
		tmp = (y * y) - 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 <= (-2000.0d0)) then
        tmp = t_0
    else if (t_0 <= 1.0d0) then
        tmp = (y * y) - 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 <= -2000.0) {
		tmp = t_0;
	} else if (t_0 <= 1.0) {
		tmp = (y * y) - 3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * y)
	tmp = 0
	if t_0 <= -2000.0:
		tmp = t_0
	elif t_0 <= 1.0:
		tmp = (y * y) - 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 <= -2000.0)
		tmp = t_0;
	elseif (t_0 <= 1.0)
		tmp = Float64(Float64(y * y) - 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 <= -2000.0)
		tmp = t_0;
	elseif (t_0 <= 1.0)
		tmp = (y * y) - 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, -2000.0], t$95$0, If[LessEqual[t$95$0, 1.0], N[(N[(y * y), $MachinePrecision] - 3.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y y)) < -2e3 or 1 < (/.f64 x (*.f64 y y))

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{x}{{y}^{2}} - 3} \]

   5. Applied rewrites 87.6%

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

   if -2e3 < (/.f64 x (*.f64 y y)) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} - 3 \]

   5. Applied rewrites 13.1%

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

Alternative 3: 7.1% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} - 3 \]

5. Applied rewrites 7.8%

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

Alternative 4: 1.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ y \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y y))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y * y

Julia

function code(x, y)
	return Float64(y * y)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{x}{{y}^{2}} - 3} \]

5. Applied rewrites 46.1%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 1.8%

   \[\leadsto y \cdot \color{blue}{y} \]
9. 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 2024313 
(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))