Details

analyze262.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

sample47.0ms

Algorithm

intervals

Results

14.0ms	75×	body	2560	nan
10.0ms	256×	body	80	valid
9.0ms	60×	body	1280	nan
3.0ms	28×	body	640	nan
2.0ms	21×	body	320	nan
0.0ms	7×	body	160	nan
0.0ms	10×	body	80	nan

simplify259.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (242.0ms)

Iter	Nodes	Cost
0	5151	14

prune1.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
31.6b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64`
2×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `insert-posit16` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

2 → 32

Calls

2 calls:

9.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
6.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series555.0ms

Counts

2 → 6

Calls

2 calls:

272.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
282.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	320	612
1	320	612
0	41	42
1	41	42
0	320	612
1	320	612
0	41	42
1	41	42
0	5141	62
0	352	657
1	352	657
0	30	42
1	30	42
0	352	657
1	352	657
0	30	42
1	30	42
0	5141	62

simplify107.0ms

Counts

38 → 38

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5082	554

prune28.0ms

Filtered

31 candidates to 38 candidates (-22.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	1	39

Merged error: 0b

Counts

39 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`sqrt-prod_binary64`
12×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `difference-of-squares_binary64` `insert-posit16` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 56

Calls

2 calls:

4.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
16.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

series887.0ms

Counts

2 → 6

Calls

2 calls:

330.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
557.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	489	903
1	489	903
0	4872	647
1	4872	647
0	489	903
1	489	903
0	4872	647
1	4872	647
0	4889	137
1	4889	137
0	521	948
1	521	948
0	33	267
1	33	267
0	521	948
1	521	948
0	33	267
1	33	267
0	4969	39
1	4969	39

simplify107.0ms

Counts

62 → 62

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4959	1239
1	4959	1239

prune53.0ms

Filtered

47 candidates to 62 candidates (-31.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	1	63

Merged error: 0b

Counts

63 → 1

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms

sample1.7s

Algorithm

intervals

Results

541.0ms	2938×	body	2560	nan
378.0ms	2455×	body	1280	nan
310.0ms	8000×	body	80	valid
151.0ms	1233×	body	640	nan
65.0ms	660×	body	320	nan
19.0ms	303×	body	160	nan
10.0ms	310×	body	80	nan

Details

analyze262.0ms

sample47.0ms

simplify259.0ms

prune1.0ms

localize7.0ms

rewrite16.0ms

series555.0ms

simplify107.0ms

prune28.0ms

localize9.0ms

rewrite22.0ms

series887.0ms

simplify107.0ms

prune53.0ms

simplify6.0ms

end0.0ms

sample1.7s

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