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

Percentage Accurate: 94.1% → 99.9%

Time: 6.9s

Alternatives: 6

Speedup: 1.0×

• 25.5% 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, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1}{y}}{\frac{y}{x}} - 3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ (/ 1.0 y) (/ y x)) 3.0))

C

double code(double x, double y) {
	return ((1.0 / y) / (y / x)) - 3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 / y) / (y / x)) - 3.0d0
end function

Java

public static double code(double x, double y) {
	return ((1.0 / y) / (y / x)) - 3.0;
}

Python

def code(x, y):
	return ((1.0 / y) / (y / x)) - 3.0

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 / y) / Float64(y / x)) - 3.0)
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 / y) / (y / x)) - 3.0;
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 / y), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]

Derivation

1. Initial program 96.2%

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

   1. associate-/r* 99.9%

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

   2. clear-num 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3 \]

   3. inv-pow 99.9%

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

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{{\left(\frac{y}{\frac{x}{y}}\right)}^{-1}} - 3 \]
5. Step-by-step derivation

   1. unpow-1 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3 \]

   2. associate-/r/ 99.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot y}} - 3 \]

   3. *-commutative 99.9%

      \[\leadsto \frac{1}{\color{blue}{y \cdot \frac{y}{x}}} - 3 \]

   4. associate-/r* 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1}{y}}{\frac{y}{x}}} - 3 \]

6. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\frac{\frac{1}{y}}{\frac{y}{x}}} - 3 \]
7. Add Preprocessing

Alternative 2: 98.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot y}\\ \mathbf{if}\;t\_0 \leq -200000000000 \lor \neg \left(t\_0 \leq 10^{-16}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;-3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y y))))
   (if (or (<= t_0 -200000000000.0) (not (<= t_0 1e-16))) (/ (/ x y) y) -3.0)))

C

double code(double x, double y) {
	double t_0 = x / (y * y);
	double tmp;
	if ((t_0 <= -200000000000.0) || !(t_0 <= 1e-16)) {
		tmp = (x / y) / y;
	} 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 <= (-200000000000.0d0)) .or. (.not. (t_0 <= 1d-16))) then
        tmp = (x / y) / y
    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 <= -200000000000.0) || !(t_0 <= 1e-16)) {
		tmp = (x / y) / y;
	} else {
		tmp = -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * y)
	tmp = 0
	if (t_0 <= -200000000000.0) or not (t_0 <= 1e-16):
		tmp = (x / y) / y
	else:
		tmp = -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * y))
	tmp = 0.0
	if ((t_0 <= -200000000000.0) || !(t_0 <= 1e-16))
		tmp = Float64(Float64(x / y) / y);
	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 <= -200000000000.0) || ~((t_0 <= 1e-16)))
		tmp = (x / y) / y;
	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, -200000000000.0], N[Not[LessEqual[t$95$0, 1e-16]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision], -3.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 y y)) < -2e11 or 9.9999999999999998e-17 < (/.f64 x (*.f64 y y))

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 91.5%

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

      1. *-lft-identity 91.5%

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

      2. associate-*l/ 90.1%

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

      3. unpow2 90.1%

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

      4. associate-/r* 90.2%

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

      5. *-rgt-identity 90.2%

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

      6. associate-/l* 90.0%

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

      7. unpow-1 90.0%

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

      8. unpow-1 90.0%

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

      9. pow-sqr 90.2%

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

      10. metadata-eval 90.2%

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

      11. *-commutative 90.2%

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

   5. Simplified 90.2%

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

      1. metadata-eval 90.2%

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

      2. pow-flip 90.1%

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

      3. unpow2 90.1%

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

      4. associate-/r* 90.2%

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

   7. Applied egg-rr 90.2%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 98.0%

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

      2. div-inv 98.1%

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

   9. Applied egg-rr 98.1%

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

   if -2e11 < (/.f64 x (*.f64 y y)) < 9.9999999999999998e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot y} \leq -200000000000 \lor \neg \left(\frac{x}{y \cdot y} \leq 10^{-16}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;-3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.0% accurate, 0.3× speedup

Math

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

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 93.2%

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

   3. Taylor expanded in y around 0 93.2%

      \[\leadsto \color{blue}{\frac{x + -3 \cdot {y}^{2}}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in x around inf 91.5%

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

   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 99.5%

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

4. Final simplification 95.1%

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

Alternative 4: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot y \leq 2 \cdot 10^{-222}:\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* y y) 2e-222) (/ (/ x y) y) (- (/ x (* y y)) 3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y * y) <= 2e-222) {
		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) <= 2d-222) 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) <= 2e-222) {
		tmp = (x / y) / y;
	} else {
		tmp = (x / (y * y)) - 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y * y) <= 2e-222:
		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) <= 2e-222)
		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) <= 2e-222)
		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], 2e-222], 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) < 2.0000000000000001e-222

   1. Initial program 89.5%

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

   3. Taylor expanded in x around inf 89.5%

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

      1. *-lft-identity 89.5%

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

      2. associate-*l/ 87.3%

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

      3. unpow2 87.3%

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

      4. associate-/r* 87.4%

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

      5. *-rgt-identity 87.4%

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

      6. associate-/l* 87.3%

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

      7. unpow-1 87.3%

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

      8. unpow-1 87.3%

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

      9. pow-sqr 87.4%

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

      10. metadata-eval 87.4%

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

      11. *-commutative 87.4%

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

   5. Simplified 87.4%

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

      1. metadata-eval 87.4%

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

      2. pow-flip 87.3%

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

      3. unpow2 87.3%

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

      4. associate-/r* 87.4%

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

   7. Applied egg-rr 87.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.8%

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

      2. div-inv 99.9%

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

   9. Applied egg-rr 99.9%

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

   if 2.0000000000000001e-222 < (*.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: 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 96.2%

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

   1. associate-/r* 99.9%

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

   2. clear-num 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3 \]

   3. inv-pow 99.9%

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

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{{\left(\frac{y}{\frac{x}{y}}\right)}^{-1}} - 3 \]
5. Step-by-step derivation

   1. unpow-1 99.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{\frac{x}{y}}}} - 3 \]

   2. clear-num 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 6: 50.3% 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 96.2%

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

3. Taylor expanded in x around 0 45.9%

   \[\leadsto \color{blue}{-3} \]
4. 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 2024139 
(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))