err-propagation

A collection of functions for differentiation and propagation of error on formulas with arbitrary variables.

So far, it has only been tested with GNU Guile Scheme 2.2.6.

Credits:

The derivation procedure used in this program is adapted from the book "Structure and Interpretation of Computer Programs, Second Edition" by H. Abelson, G.J. Sussman and J. Sussman.

Usage:

To start the Guile REPL with the functions loaded, run:

guile -l err-propagation.scm

Examples:

Propagation of error for formula 2 * f * dx-avg:

scheme@(guile-user)> (err-propagate '(* 2 (* f dx-avg)) '((dx-avg 0.1) (f 0.01)))
$1 = (sqrt (+ (^ (* (* 2 dx-avg) 0.01) 2) (^ (* (* 2 f) 0.1) 2)))

The result of err-propagate can also be evaluated:

scheme@(guile-user)> (define dx-avg 0.072)
scheme@(guile-user)> (define f 1200)
scheme@(guile-user)> (eval $1 (interaction-environment))
$2 = 240.00000000432

or turned into an Excel-compatible infix formula:

scheme@(guile-user)> (expr-to-infix-str $1)
$3 = "SQRT(((2 * dx-avg) * 0.01) ^ 2 + ((2 * f) * 0.1) ^ 2)"

License:

GNU General Public License version 3