Name Argument(s) Formula or meaning Argument Constraints Result constraints
abs x Absolute value of x.
acos, arccos x Arccosine of x in radians. –1.0 ≤ x ≤ 1.0 0 ≤ acos(x) ≤ π
acosh, arccosh x Hyperbolic arccosine of x in radians.
acot, arccot x Arccotangent of x in radians.
acoth, arccoth x Hyperbolic arccotangent of x in radians.
acsc, arccsc x Arccosecant of x in radians.
acsch, arccsch x Hyperbolic arccosecant of x in radians.
asec, arcsec x Arcsecant of x in radians.
asech, arcsech x Hyperbolic arcsecant of x in radians.
asin, arcsin xArcsine of x in radians. –1.0 ≤ x ≤ 1.0 0 ≤ asin(x) ≤ π
atan, arctan x Arctangent of x in radians. 0 ≤ atan(x) ≤ π
atanh, arctanh x Hyperbolic arctangent of x in radians.
ceil, ceiling x Smallest number not less than x whose value is an exact integer.
cos x Cosine of x
cosh x Hyperbolic cosine of x.
cot x Cotangent of x.
coth x Hyperbolic cotangent of x.
csc x Cosecant of x.
csch x Hyperbolic cosecant of x.
delay x, y The value of x at y time units in the past.
factorial n The factorial of n. Factorials are defined by n! = n*(n–1)* ... * 1. n must be an integer.
exp x e x, where e is the base of the natural logarithm.
floor x The largest number not greater than x whose value is an exact integer.
ln x Natural logarithm of x. x > 0
log x By default, the base 10 logarithm of x, but can be set to be the natural logarithm of x, or to be an illegal construct. x > 0
log x, y The base x logarithm of y. y > 0
log10 x Base 10 logarithm of x. x > 0
piecewise x1, y1, [x2, y2,] [...] [z] A piecewise function: if (y1), x1. Otherwise, if (y2), x2, etc. Otherwise, z. y1, y2, y3 [etc] must be Boolean
pow, power x, y x y.
root b, x The root base b of x.
sec x Secant of x.
sech x Hyperbolic secant of x.
sqr x x2.
sqrt x x. x > 0 sqrt(x) ≥ 0
sin x Sine of x.
sinh x Hyperbolic sine of x.
tan x Tangent of x. x ≠ n*π/2, for odd integer n
tanh x Hyperbolic tangent of x.
and x, y, z... Boolean and(x, y, z...): returns true if all of its arguments are true. Note that and is an n-ary function, taking 0 or more arguments, and that and() returns true. All arguments must be Boolean
not x Boolean not(x) x must be Boolean
or x, y, z... Boolean or(x, y, z...): returns true if at least one of its arguments is true. Note that or is an n-ary function, taking 0 or more arguments, and that or() returns false. All arguments must be Boolean
xor x, y, z... Boolean xor(x, y, z...): returns true if an odd number of its arguments is true. Note that xor is an n-ary function, taking 0 or more arguments, and that xor() returns false. All arguments must be Boolean
eq x, y, z... Boolean eq(x, y, z...): returns true if all arguments are equal. Note that eq is an n-ary function, but must take 2 or more arguments.
geq x, y, z... Boolean geq(x, y, z...): returns true if each argument is greater than or equal to the argument following it. Note that geq is an n-ary function, but must take 2 or more arguments.
gt x, y, z... Boolean gt(x, y, z...): returns true if each argument is greater than the argument following it. Note that gt is an n-ary function, but must take 2 or more arguments.
leq x, y, z... Boolean leq(x, y, z...): returns true if each argument is less than or equal to the argument following it. Note that leq is an n-ary function, but must take 2 or more arguments.
lt x, y, z... Boolean lt(x, y, z...): returns true if each argument is less than the argument following it. Note that lt is an n-ary function, but must take 2 or more arguments.
neq x, y Boolean x != y: returns true unless x and y are equal.
plus x, y, z... x + y + z + ...: The sum of the arguments of the function. Note that plus is an n-ary function taking 0 or more arguments, and that plus() returns 0.
times x, y, z... x * y * z * ...: The product of the arguments of the function. Note that times is an n-ary function taking 0 or more arguments, and that times() returns 1.
minus x, y xy.
divide x, y x / y.
Mathematical functions defined in the "Level 3" text-string formula syntax.