Details

sample79.0ms

Algorithm

intervals

Results

39.0ms	821×	body	80	nan
14.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	16	13
done	16	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`times-frac`
24×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
16×	`sqrt-prod`
7×	`associate-/l*`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `add-log-exp` `difference-of-squares`
3×	`associate-/r*` `div-inv`
2×	`pow1` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-out` `flip3--` `frac-2neg` `flip3-+` `div-exp` `frac-add` `clear-num` `sum-log` `flip--` `flip-+`

Counts

2 → 62

Calls

2 calls:

44.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
14.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series354.0ms

Counts

2 → 6

Calls

2 calls:

166.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
189.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify1.7s

Counts

68 → 68

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	152	1133
1	327	1052
2	820	994
3	2399	983
done	5001	975

prune249.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (- 1.0 (* x x))))
0.3b	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.3b	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.5b	(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

950×	`sqrt-prod`
671×	`add-sqr-sqrt`
580×	`times-frac`
284×	`add-cube-cbrt` `*-un-lft-identity`
132×	`swap-sqr`
64×	`associate-r` `associate-l`
49×	`unswap-sqr`
43×	`difference-of-squares`
20×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
13×	`pow1`
12×	`sqrt-div` `associate-/r*`
6×	`cbrt-undiv` `sqrt-undiv` `div-exp` `div-inv`
4×	`sqrt-pow1` `prod-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `pow1/2` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 539

Calls

4 calls:

15.0ms	(sqrt (sqrt (- 1.0 (* x x))))
29.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
31.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
168.0ms	(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

series832.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(sqrt (sqrt (- 1.0 (* x x))))
166.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
190.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
190.0ms	(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

simplify2.8s

Counts

551 → 551

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	425	17088
1	1240	15204
2	3776	12226
done	5000	11608

prune1.5s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	26
1	13	26
done	13	26

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.9s	23838×	body	80	nan
699.0ms	8000×	body	80	valid