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evalr

evaluate an expression using range arithmetic

shake

compute a bounding interval Calling Sequence evalr(expr) shake(expr, ampl) Parameters

 expr - expression ampl - (optional) positive integer Description

 • The evalr(expr) function evaluates an expression containing ranges written INTERVAL(a..b) with a<=b, sequences of ranges written INTERVAL(a..b, c..d, ...), or bounded variables written INTERVAL(x, a..b). By default a variable x is converted to INTERVAL(x, -infinity ..infinity). The result of evalr in this case can be a sequence of ranges, or an expression if both sides of the resulting range are equal. The imprecise variables INTERVAL(x, -infinity..infinity) are converted back to x if the result is the same for all values of x.
 • The function evalr can be called with an expression without a range. In this case, the decision functions min, max, abs and Signum are evaluated using range arithmetic. Thus, evalr(Signum(expr)) can return FAIL.
 • The shake(expr, ampl) function replaces the constants at the leaves of the expression tree by an interval of width Float(10, -ampl), then uses evalr to propagate these intervals bottom-up. If ampl is not specified, the current value of Digits is used. Examples

 > $\mathrm{evalr}\left(\mathrm{min}\left(2,\mathrm{sqrt}\left(3\right)\right)\right)$
 $\sqrt{{3}}$ (1)
 > $\mathrm{evalr}\left(\mathrm{sin}\left(\mathrm{INTERVAL}\left(2..7\right)\right)\right)$
 ${\mathrm{INTERVAL}}{}\left({-1}{..}{\mathrm{sin}}{}\left({2}\right)\right)$ (2)
 > $\mathrm{evalr}\left(\mathrm{abs}\left(x\right)\right)$
 ${\mathrm{INTERVAL}}{}\left({\mathrm{INTERVAL}}{}\left({x}{,}{0}{..}{\mathrm{\infty }}\right){,}{-}{\mathrm{INTERVAL}}{}\left({x}{,}{-}{\mathrm{\infty }}{..}{0}\right)\right)$ (3)
 > $\mathrm{shake}\left(\mathrm{\pi },3\right)$
 ${\mathrm{INTERVAL}}{}\left({3.1102}{..}{3.1730}\right)$ (4)