Details

sample75.0ms

Algorithm

intervals

Results

35.0ms	728×	body	80	nan
15.0ms	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

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`div-inv` `difference-of-squares`
4×	`sqrt-div`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 98

Calls

4 calls:

43.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
57.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
18.0ms	(/ (sqrt (- 1.0 (* x x))) x)
6.0ms	(sqrt (- 1.0 (* x x)))

series880.0ms

Counts

4 → 12

Calls

4 calls:

434.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
143.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
197.0ms	(/ (sqrt (- 1.0 (* x x))) x)
106.0ms	(sqrt (- 1.0 (* x x)))

simplify1.6s

Counts

110 → 110

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	231	1946
1	540	1820
2	2326	1700
done	5001	1684

prune418.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt 1.0) x))
0.3b	(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
0.4b	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
0.5b	(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

289×	`sqrt-prod`
270×	`add-sqr-sqrt`
232×	`times-frac`
181×	`*-un-lft-identity`
127×	`add-cube-cbrt`
58×	`associate-r`
46×	`associate-l`
26×	`difference-of-squares`
25×	`unswap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
14×	`distribute-lft-out`
13×	`distribute-lft-out--`
12×	`associate-/r*`
7×	`pow1`
6×	`cbrt-undiv` `sqrt-div` `div-exp`
4×	`sqrt-undiv` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 320

Calls

4 calls:

13.0ms	(sqrt (+ (sqrt 1.0) x))
44.0ms	(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
42.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
160.0ms	(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(sqrt (+ (sqrt 1.0) x))
158.0ms	(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
166.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
288.0ms	(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

simplify665.0ms

Counts

332 → 332

Iterations

Useful iterations: done (648.0ms)

Iter	Nodes	Cost
0	358	6642
1	973	6103
done	5001	5903

prune1.3s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	22
1	17	22
done	17	22

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.2s	24032×	body	80	nan
714.0ms	8000×	body	80	valid