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

Percentage Accurate: 94.2% → 99.9%

Time: 1.7s

Alternatives: 5

Speedup: 1.0×

• 25.2% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y)
use fmin_fmax_functions
    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: 94.2% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y)
use fmin_fmax_functions
    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, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y\_m \leq 2 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{y\_m}}{y\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y\_m \cdot y\_m} - 3\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m)
 :precision binary64
 (if (<= y_m 2e-153) (/ (/ x y_m) y_m) (- (/ x (* y_m y_m)) 3.0)))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double tmp;
	if (y_m <= 2e-153) {
		tmp = (x / y_m) / y_m;
	} else {
		tmp = (x / (y_m * y_m)) - 3.0;
	}
	return tmp;
}

Fortran

y_m =     private
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8) :: tmp
    if (y_m <= 2d-153) then
        tmp = (x / y_m) / y_m
    else
        tmp = (x / (y_m * y_m)) - 3.0d0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	double tmp;
	if (y_m <= 2e-153) {
		tmp = (x / y_m) / y_m;
	} else {
		tmp = (x / (y_m * y_m)) - 3.0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	tmp = 0
	if y_m <= 2e-153:
		tmp = (x / y_m) / y_m
	else:
		tmp = (x / (y_m * y_m)) - 3.0
	return tmp

Julia

y_m = abs(y)
function code(x, y_m)
	tmp = 0.0
	if (y_m <= 2e-153)
		tmp = Float64(Float64(x / y_m) / y_m);
	else
		tmp = Float64(Float64(x / Float64(y_m * y_m)) - 3.0);
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m)
	tmp = 0.0;
	if (y_m <= 2e-153)
		tmp = (x / y_m) / y_m;
	else
		tmp = (x / (y_m * y_m)) - 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := If[LessEqual[y$95$m, 2e-153], N[(N[(x / y$95$m), $MachinePrecision] / y$95$m), $MachinePrecision], N[(N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.00000000000000008e-153

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 45.3

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

   4. Applied rewrites 45.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 51.0

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

   6. Applied rewrites 51.0%

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

   if 2.00000000000000008e-153 < y

   1. Initial program 94.2%

      \[\frac{x}{y \cdot y} - 3 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \frac{\frac{x}{y\_m}}{y\_m} - 3 \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 (- (/ (/ x y_m) y_m) 3.0))

C

y_m = fabs(y);
double code(double x, double y_m) {
	return ((x / y_m) / y_m) - 3.0;
}

Fortran

y_m =     private
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    code = ((x / y_m) / y_m) - 3.0d0
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	return ((x / y_m) / y_m) - 3.0;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	return ((x / y_m) / y_m) - 3.0

Julia

y_m = abs(y)
function code(x, y_m)
	return Float64(Float64(Float64(x / y_m) / y_m) - 3.0)
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := N[(N[(N[(x / y$95$m), $MachinePrecision] / y$95$m), $MachinePrecision] - 3.0), $MachinePrecision]

Derivation

1. Initial program 94.2%

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

   1. lift-*.f64 N/A

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

   2. lift-/.f64 N/A

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

   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

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

3. Applied rewrites 99.9%

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

Alternative 3: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \frac{x}{y\_m \cdot y\_m} - 3\\ t_1 := \frac{\frac{x}{y\_m}}{y\_m}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -2:\\ \;\;\;\;-3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m)
 :precision binary64
 (let* ((t_0 (- (/ x (* y_m y_m)) 3.0)) (t_1 (/ (/ x y_m) y_m)))
   (if (<= t_0 -1e+17) t_1 (if (<= t_0 -2.0) -3.0 t_1))))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double t_0 = (x / (y_m * y_m)) - 3.0;
	double t_1 = (x / y_m) / y_m;
	double tmp;
	if (t_0 <= -1e+17) {
		tmp = t_1;
	} else if (t_0 <= -2.0) {
		tmp = -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

y_m =     private
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x / (y_m * y_m)) - 3.0d0
    t_1 = (x / y_m) / y_m
    if (t_0 <= (-1d+17)) then
        tmp = t_1
    else if (t_0 <= (-2.0d0)) then
        tmp = -3.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	double t_0 = (x / (y_m * y_m)) - 3.0;
	double t_1 = (x / y_m) / y_m;
	double tmp;
	if (t_0 <= -1e+17) {
		tmp = t_1;
	} else if (t_0 <= -2.0) {
		tmp = -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	t_0 = (x / (y_m * y_m)) - 3.0
	t_1 = (x / y_m) / y_m
	tmp = 0
	if t_0 <= -1e+17:
		tmp = t_1
	elif t_0 <= -2.0:
		tmp = -3.0
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m)
	t_0 = Float64(Float64(x / Float64(y_m * y_m)) - 3.0)
	t_1 = Float64(Float64(x / y_m) / y_m)
	tmp = 0.0
	if (t_0 <= -1e+17)
		tmp = t_1;
	elseif (t_0 <= -2.0)
		tmp = -3.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m)
	t_0 = (x / (y_m * y_m)) - 3.0;
	t_1 = (x / y_m) / y_m;
	tmp = 0.0;
	if (t_0 <= -1e+17)
		tmp = t_1;
	elseif (t_0 <= -2.0)
		tmp = -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := Block[{t$95$0 = N[(N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x / y$95$m), $MachinePrecision] / y$95$m), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+17], t$95$1, If[LessEqual[t$95$0, -2.0], -3.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64)) < -1e17 or -2 < (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64))

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 45.3

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

   4. Applied rewrites 45.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/l/ N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 51.0

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

   6. Applied rewrites 51.0%

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

   if -1e17 < (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64)) < -2

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.9%

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

Alternative 4: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \frac{x}{y\_m \cdot y\_m}\\ t_1 := t\_0 - 3\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq -2:\\ \;\;\;\;-3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m)
 :precision binary64
 (let* ((t_0 (/ x (* y_m y_m))) (t_1 (- t_0 3.0)))
   (if (<= t_1 -1e+17) t_0 (if (<= t_1 -2.0) -3.0 t_0))))

C

y_m = fabs(y);
double code(double x, double y_m) {
	double t_0 = x / (y_m * y_m);
	double t_1 = t_0 - 3.0;
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_0;
	} else if (t_1 <= -2.0) {
		tmp = -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

y_m =     private
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (y_m * y_m)
    t_1 = t_0 - 3.0d0
    if (t_1 <= (-1d+17)) then
        tmp = t_0
    else if (t_1 <= (-2.0d0)) then
        tmp = -3.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	double t_0 = x / (y_m * y_m);
	double t_1 = t_0 - 3.0;
	double tmp;
	if (t_1 <= -1e+17) {
		tmp = t_0;
	} else if (t_1 <= -2.0) {
		tmp = -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	t_0 = x / (y_m * y_m)
	t_1 = t_0 - 3.0
	tmp = 0
	if t_1 <= -1e+17:
		tmp = t_0
	elif t_1 <= -2.0:
		tmp = -3.0
	else:
		tmp = t_0
	return tmp

Julia

y_m = abs(y)
function code(x, y_m)
	t_0 = Float64(x / Float64(y_m * y_m))
	t_1 = Float64(t_0 - 3.0)
	tmp = 0.0
	if (t_1 <= -1e+17)
		tmp = t_0;
	elseif (t_1 <= -2.0)
		tmp = -3.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m)
	t_0 = x / (y_m * y_m);
	t_1 = t_0 - 3.0;
	tmp = 0.0;
	if (t_1 <= -1e+17)
		tmp = t_0;
	elseif (t_1 <= -2.0)
		tmp = -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := Block[{t$95$0 = N[(x / N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 - 3.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+17], t$95$0, If[LessEqual[t$95$1, -2.0], -3.0, t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64)) < -1e17 or -2 < (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64))

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf

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

      1. pow2 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 45.3

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

   4. Applied rewrites 45.3%

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

   if -1e17 < (-.f64 (/.f64 x (*.f64 y y)) #s(literal 3 binary64)) < -2

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 50.9%

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

Alternative 5: 50.9% accurate, 9.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ -3 \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m) :precision binary64 -3.0)

C

y_m = fabs(y);
double code(double x, double y_m) {
	return -3.0;
}

Fortran

y_m =     private
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y_m)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    code = -3.0d0
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m) {
	return -3.0;
}

Python

y_m = math.fabs(y)
def code(x, y_m):
	return -3.0

Julia

y_m = abs(y)
function code(x, y_m)
	return -3.0
end

MATLAB

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

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_] := -3.0

Derivation

1. Initial program 94.2%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 50.9%

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

Reproduce

herbie shell --seed 2025123 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64
  (- (/ x (* y y)) 3.0))