Details

sample144.0ms

Algorithm

intervals

Results

56.0ms	255×	body	160	nan
41.0ms	558×	body	80	nan
23.0ms	256×	body	80	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
9	3422
8	1055
7	442
6	232
5	95
4	58
3	33
2	17
1	14
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1)))
29.2b	(sqrt (- (* x x) 1))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `sqrt-prod`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

12.0ms	(+ x (sqrt (- (* x x) 1)))
16.0ms	(sqrt (- (* x x) 1))

series116.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ x (sqrt (- (* x x) 1)))
49.0ms	(sqrt (- (* x x) 1))

simplify1.6s

Counts

38 → 38

Iterations

Iter	Nodes
4	2458
3	999
2	438
1	206
0	91

prune293.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
10×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 56

Calls

2 calls:

4.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
34.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series177.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
89.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify3.3s

Counts

62 → 62

Iterations

Iter	Nodes
4	5346
3	1730
2	660
1	293
0	132

prune543.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	9

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	7763×	body	160	nan
1.5s	16351×	body	80	nan
733.0ms	8000×	body	80	valid