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

Percentage Accurate: 94.1% → 99.9%

Time: 5.4s

Alternatives: 5

Speedup: 1.0×

• 25.0% 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: 99.9% 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 91.0%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot y}\\ t_1 := \frac{\frac{x}{y}}{y}\\ \mathbf{if}\;t\_0 \leq -500:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.05:\\ \;\;\;\;-3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y y))) (t_1 (/ (/ x y) y)))
   (if (<= t_0 -500.0) t_1 (if (<= t_0 0.05) -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 <= -500.0) {
		tmp = t_1;
	} else if (t_0 <= 0.05) {
		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 <= (-500.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.05d0) 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 <= -500.0) {
		tmp = t_1;
	} else if (t_0 <= 0.05) {
		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 <= -500.0:
		tmp = t_1
	elif t_0 <= 0.05:
		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 <= -500.0)
		tmp = t_1;
	elseif (t_0 <= 0.05)
		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 <= -500.0)
		tmp = t_1;
	elseif (t_0 <= 0.05)
		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, -500.0], t$95$1, If[LessEqual[t$95$0, 0.05], -3.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y y)) < -500 or 0.050000000000000003 < (/.f64 x (*.f64 y y))

   1. Initial program 81.4%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -500 < (/.f64 x (*.f64 y y)) < 0.050000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 93.0% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y):
	t_0 = x / (y * y)
	tmp = 0
	if t_0 <= -3.0:
		tmp = t_0
	elif t_0 <= 3.0:
		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 <= -3.0)
		tmp = t_0;
	elseif (t_0 <= 3.0)
		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 <= -3.0)
		tmp = t_0;
	elseif (t_0 <= 3.0)
		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, -3.0], t$95$0, If[LessEqual[t$95$0, 3.0], -3.0, t$95$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 81.4%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   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 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 4 \cdot 10^{-309}:\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 4e-309) (/ (/ x y) y) (- (/ x (* y y)) 3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 4e-309) {
		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) <= 4d-309) 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) <= 4e-309) {
		tmp = (x / y) / y;
	} else {
		tmp = (x / (y * y)) - 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 4e-309:
		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) <= 4e-309)
		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) <= 4e-309)
		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], 4e-309], 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) < 3.9999999999999977e-309

   1. Initial program 68.3%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if 3.9999999999999977e-309 < (*.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 5: 50.7% 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 91.0%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Developer target: 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 2024110 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (- (/ (/ x y) y) 3.0)

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