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Initially, neural network based evaluation functions generally consisted of one neural network for the entire evaluation function, with input features selected from the board and whose output is an integer, normalized to the centipawn scale so that a value of 100 is roughly equivalent to a material advantage of a pawn.
Horner's method evaluates a polynomial using repeated bracketing: + + + + + = + (+ (+ (+ + (+)))). This method reduces the number of multiplications and additions to just Horner's method is so common that a computer instruction "multiply–accumulate operation" has been added to many computer processors, which allow doing the addition and multiplication operations in one combined step.
Quantile functions are used in both statistical applications and Monte Carlo methods. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function.
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When the function is evaluated for a given value, as in f(3): or, y = f(3) = 3 + 2 = 5, 3 is the actual parameter (the argument) for evaluation by the defined function; it is a given value (actual value) that is substituted for the formal parameter of the defined function.
The practical motivation for partial application is that very often the functions obtained by supplying some but not all of the arguments to a function are useful; for example, many languages have a function or operator similar to plus_one. Partial application makes it easy to define these functions, for example by creating a function that ...
A modular function is a function that is invariant with respect to the modular group, but without the condition that it be holomorphic in the upper half-plane (among other requirements). Instead, modular functions are meromorphic: they are holomorphic on the complement of a set of isolated points, which are poles of the function.
This consists in using the last computed approximate values of the root for approximating the function by a polynomial of low degree, which takes the same values at these approximate roots. Then the root of the polynomial is computed and used as a new approximate value of the root of the function, and the process is iterated.