Adding Inverse Rules #1016
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Adding Inverse Rules #1016
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| (when (flag-set? 'localize 'costs) | ||
| #| (when (flag-set? 'localize 'costs) |
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Why did you disable this?
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| (let loop ([prog prog] | ||
| [loc loc]) | ||
| (let loop ([prog prog] [loc loc]) |
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You gotta update your raco fmt version. Run raco pkg update fmt.
| @@ -225,6 +235,13 @@ | |||
| [difference-of-sqr--1 (+ (* a a) -1) (* (+ a 1) (- a 1))] | |||
| [pow-sqr (* (pow a b) (pow a b)) (pow a (* 2 b))]) | |||
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| (define-ruleset* difference-of-squares-canonicalize-revv | |||
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Suggested change
| (define-ruleset* difference-of-squares-canonicalize-revv | |
| (define-ruleset* difference-of-squares-canonicalize-rev |
| [difference-of-sqr-1-rev (* (+ a 1) (- a 1)) (- (* a a) 1)] | ||
| [difference-of-sqr--1-rev (* (+ a 1) (- a 1)) (+ (* a a) -1)] | ||
| [difference-of-squares-rev (* (+ a b) (- a b)) (- (* a a) (* b b))] | ||
| [pow-sqr-rev (pow a (* 2 b)) (* (pow a b) (pow a b))]) |
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Is the pow-sqr-rev rule true? Consider (pow -1 (* 2 1/2)) = (pow -1 1) = -1 but (* (pow -1 1/2) (pow -1 1/2)) is illegal because (pow -1 1/2) does not exist.
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| ; Specialized numerical functions | ||
| ; TODO: These are technically rules over impls | ||
| ; | ||
| ; (define-ruleset* special-numerical-reduce | ||
| ; (numerics simplify) | ||
| ; #:type ([x real] [y real] [z real]) | ||
| ; [log1p-expm1 (log1p (expm1 x)) x] | ||
| ; [hypot-1-def (sqrt (+ 1 (* y y))) (hypot 1 y)] | ||
| ; [fmm-def (- (* x y) z) (fma x y (neg z))] | ||
| ; [fmm-undef (fma x y (neg z)) (- (* x y) z)]) | ||
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| ; (define-ruleset* special-numerical-expand | ||
| ; (numerics) | ||
| ; #:type ([x real] [y real]) | ||
| ; [log1p-expm1-u x (log1p (expm1 x))] | ||
| ; [expm1-log1p-u x (expm1 (log1p x))]) | ||
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| ; (define-ruleset* numerics-papers | ||
| ; (numerics) | ||
| ; #:type ([a real] [b real] [c real] [d real]) | ||
| ; ; "Further Analysis of Kahan's Algorithm for | ||
| ; ; the Accurate Computation of 2x2 Determinants" | ||
| ; ; Jeannerod et al., Mathematics of Computation, 2013 | ||
| ; ; | ||
| ; ; a * b - c * d ===> fma(a, b, -(d * c)) + fma(-d, c, d * c) | ||
| ; [prod-diff (- (* a b) (* c d)) (+ (fma a b (neg (* d c))) (fma (neg d) c (* d c)))]) | ||
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Any reason to add this comment back?
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| (arithmetic sound) | ||
| (arithmetic) |
| (define-ruleset* log2-factor | ||
| (exponents sound) | ||
| #:type ([a real] [b real]) | ||
| [log2-expand (log x 2) (/ (log x) (log 2))] |
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You want (log2 x) not (log x 2).
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| [acos-cos-rev (fabs (remainder x (* 2 (PI)))) (acos (cos x))] | ||
| [asin-sin-rev (- (fabs (remainder (+ x (/ (PI) 2)) (* 2 (PI)))) (/ (PI) 2)) (asin (sin x))] | ||
| [atan-tan-rev (remainder x (PI)) (atan (tan x))]) |
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I really doubt that these rules help but I guess they probably don't hurt either.
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| [hang-m0-tan-rev (tan (/ (neg a) 2)) (/ (- 1 (cos a)) (neg (sin a)))] | ||
| [hang-p0-tan-rev (tan (/ a 2)) (/ (- 1 (cos a)) (sin a))] | ||
| [hang-0m-tan-rev (tan (/ (neg a) 2)) (/ (neg (sin a)) (+ 1 (cos a)))] | ||
| [hang-0p-tan-rev (tan (/ a 2)) (/ (sin a) (+ 1 (cos a)))]) |
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I suspect these aren't sound
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| (define-ruleset* trig-expand-sound | ||
| (trigonometry sound) | ||
| #:type ([x real] [y real] [a real] [b real]) | ||
| [sin-sum (sin (+ x y)) (+ (* (sin x) (cos y)) (* (cos x) (sin y)))] | ||
| [cos-sum (cos (+ x y)) (- (* (cos x) (cos y)) (* (sin x) (sin y)))] | ||
| [cos-sum-rev (- (* (cos x) (cos y)) (* (sin x) (sin y))) (cos (+ x y))] |
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Why isn't this in the block below?
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Description:
This PR introduces the implementation of all inverse rules. The inverse rules allow the system to reverse operations in order to achieve a few goals. By adding inverse rules we hope to prove more expressions equal to one another so that they are in the same eclass. We also hope to further improve results as the quality of our rulesets improve with missing rules.
This pr has improved results overall but there are a few benchmarks that have gotten worse which is expected.