Building Blocks

Formulize searches for formula by combining mathematical building-blocks (e.g. add, subtract, multiply, divide). The list below describes all of the standard building blocks available.

Arithmetic

Name	Usage	Comments
constant	1.234	Allows solutions to use real-valued constants
integer	7	Allows solutions to use integer constants
add	x + y or add(x,y)
subtract	x - y or sub(x,y)
multiply	x * y or mul(x,y)
divide	x / y or div(x,y)	y must be non-zero
negation	-x

Trigonometric

Name	Usage	Comments
sine	sin(x)	The angle is in radians
cosine	cos(x)	The angle is in radians
tangent	tan(x)	The angle is in radians

Exponential

Name	Usage	Comments
exponential	exp(x)	Returns e^x
logarithm	log(x)	This is the natural logaritm (base e)
factorial	factorial(x) or x!	Computes the real valued factorial as gamma(x+1)
power	x ^ y or pow(x,y)	x and y could be any expression
sqrt	sqrt(x)	x must be positive

History Functions

Name	Usage	Comments
Delayed Variable	delay(x,num_rows)	Returns the value of the x variable num_rows prior to the current row
Simple Moving Average	smm(x,num_rows)	Returns the average value of the last num_rows values of the x variable
Weighted Moving Average	wma(x,num_rows)	Returns the arithmetically weighted average value of the last num_rows values of the x variable
Modified Moving Average	mma(x,num_rows)	Returns the modified average value of the last num_rows values of the x variable
Simple Moving Median	smm(x,num_rows)	Returns the median value of the last num_rows values of the x variable

Squashing Functions

Name	Usage	Comments
logistic function	logistic(x)	This is a common sigmoid squashing function. Returns 1/(1+ exp(-x))
step function	step(x)	Returns 1 if x is positive, zero otherwise
sign function	sgn(x)	Returns -1 if x is negative, +1 if x is positive, and 0 if x is zero
gaussian function	gauss(x)	This is a bell-shaped squashing function. Returns exp(-x^2)
hyperbolic tangent	tanh(x)	This is a common squashing function. Returns a value between -1 and +1
Error Function	erf(x)	Integral of the normal distribution. Returns a value between -1 and +1
Error Function Compliment	erfc(x)	Returns 1.0 - erf(x)

Boolean

Name	Usage	Comments
equal to	equal(x,y)	Returns 1 if x equals y numerically, 0 otherwise
less than	less(x,y)	Returns 1 if x < y, 0 otherwise
less than or equal to	less_or_equal(x,y)	Returns 1 if x <= y, 0 otherwise
greater than	greater(x,y)	Returns 1 if x > y, 0 otherwise
greater than or equal to	greater_or_equal(x,y)	Returns 1 if x >= y, 0 otherwise
if-then-else	if(x,y,z)	Returns y if x is greater than 0, z otherwise
logical and	and(x,y)	Returns 1 if both x and y are greater than 0, 0 otherwise
logical or	or(x,y)	Returns 1 if either x or y are greater than 0, 0 otherwise
logical xor	xor(x,y)	Returns 1 if (x <= 0 and y > 0) or (x > 0 and y <= 0), 0 otherwise
logical not	not(x)	Returns 0 if x is greater than 0, 1 otherwise

Other

Name	Usage	Comments
minimum	min(x,y)	Returns the minimum (signed) result of x and y for the data point
maximum	max(x,y)	Returns the maximum (signed) result of x and y for the data point
modulo	mod(x,y)	Returns the remainder of x/y
floor	floor(x)	Returns an integer of x rounded down toward -infinity
ceiling	ceil(x)	Returns an integer of x rounded up toward +infinite
round	round(x)	Returns an integer of x rounded to the nearest integer
absolute value	abs(x)	Returns the positive value of x

Inverse Trigonometry

Name	Usage	Comments
Arcsine	asin(x)	The inverse of the sine function
Arccosine	acos(x)	The inverse of the cosine function
Arctangent	atan(x)	The inverse of the tangent function
Two-argument Arctangent	atan2(x,y)	The inverse of the tangent function