Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2

Percentage Accurate: 100.0% → 100.0%

Time: 981.0ms

Alternatives: 3

Speedup: 1.0×

• 75.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[e^{\left(x \cdot y\right) \cdot y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (exp (* (* x y) y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return math.exp(((x * y) * y))

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	exp(((x * y) * y))
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[e^{\left(x \cdot y\right) \cdot y} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (exp (* (* x y) y)))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return math.exp(((x * y) * y))

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	exp(((x * y) * y))
END code

Alternative 1: 75.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\left(x \cdot y\right) \cdot y \leq -143750390.52798983:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  (if (<= (* (* x y) y) -143750390.52798983) 0.0 1.0))

C

double code(double x, double y) {
	double tmp;
	if (((x * y) * y) <= -143750390.52798983) {
		tmp = 0.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x * y) * y) <= (-143750390.52798983d0)) then
        tmp = 0.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x * y) * y) <= -143750390.52798983) {
		tmp = 0.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x * y) * y) <= -143750390.52798983:
		tmp = 0.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x * y) * y) <= -143750390.52798983)
		tmp = 0.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x * y) * y) <= -143750390.52798983)
		tmp = 0.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision], -143750390.52798983], 0.0, 1.0]

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	LET tmp = IF (((x * y) * y) <= (-1437503905279898345470428466796875e-25)) THEN (0) ELSE (1) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x y) y) < -143750390.52798983

   1. Initial program 100.0%

      \[e^{\left(x \cdot y\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

      \[\leadsto 1 \]

   5. Taylor expanded in undef-var around zero

      \[\leadsto 0 \]
   6. Step-by-step derivation

   7. Applied rewrites 27.1%

      \[\leadsto 0 \]

   if -143750390.52798983 < (*.f64 (*.f64 x y) y)

   1. Initial program 100.0%

      \[e^{\left(x \cdot y\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto 1 \]
   3. Step-by-step derivation

   4. Applied rewrites 51.4%

      \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 51.4% accurate, 18.0× speedup

Math

\[1 \]

FPCore

(FPCore (x y)
  :precision binary64
  :pre TRUE
  1.0)

C

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

Fortran

real(8) function code(x, y)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

ReFlow

f(x, y):
	x in [-inf, +inf],
	y in [-inf, +inf]
code: THEORY
BEGIN
f(x, y: real): real =
	1
END code

Derivation

1. Initial program 100.0%

   \[e^{\left(x \cdot y\right) \cdot y} \]

2. Taylor expanded in x around 0

   \[\leadsto 1 \]
3. Step-by-step derivation

4. Applied rewrites 51.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))