Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

sample18.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify200.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	5575	20

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: 0.0b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`distribute-lft-out_binary64`
15×	`log-prod_binary64`
12×	`div-inv_binary64`
11×	`add-cube-cbrt_binary64`
6×	`distribute-rgt-out_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `log-div_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `add-cbrt-cube_binary64` `distribute-rgt1-in_binary64` `insert-posit16` `flip-+_binary64`
1×	`rem-log-exp_binary64` `log-pow_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 53

Calls

2 calls:

27.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
25.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

series903.0ms

Counts

2 → 6

Calls

2 calls:

436.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
466.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	651	1022
1	651	1022
0	55	723
1	55	723
0	651	1022
1	651	1022
0	55	723
1	55	723
0	4947	103
1	4947	103
0	716	1168
1	716	1168
0	63	755
1	63	755
0	716	1168
1	716	1168
0	63	755
1	63	755
0	5080	131

simplify106.0ms

Counts

59 → 59

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4947	1411
1	4947	1411

prune52.0ms

Filtered

46 candidates to 59 candidates (-28.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	1	60

Merged error: 0b

Counts

60 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`add-cube-cbrt_binary64` `times-frac_binary64`
8×	`pow1_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64`
6×	`log-div_binary64`
5×	`flip3-+_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `associate-l_binary64` `flip-+_binary64`
4×	`distribute-lft-out_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`unswap-sqr_binary64` `insert-posit16`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `associate-*r/_binary64` `log-pow_binary64` `rec-exp_binary64` `un-div-inv_binary64` `sqrt-prod_binary64`
1×	`log-prod_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 79

Calls

3 calls:

12.0ms	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
7.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
15.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))

series1.1s

Counts

3 → 9

Calls

3 calls:

453.0ms	(log.f64 (.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x)))
250.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
412.0ms	(.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) (/.f64 1 x))

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	538	1017
1	538	1017
0	58	723
1	58	723
0	538	1017
1	538	1017
0	58	723
1	58	723
0	4971	80
1	4971	80
0	323	565
1	323	565
0	77	108
1	77	108
0	323	565
1	323	565
0	77	108
1	77	108
0	94	22
1	94	22
0	611	1157
1	611	1157
0	79	755
1	79	755
0	611	1157
1	611	1157
0	79	755
1	79	755
0	4943	115
1	4943	115

simplify125.0ms

Counts

88 → 88

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5110	1629

prune73.0ms

Filtered

68 candidates to 88 candidates (-29.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	1	89

Merged error: 0b

Counts

89 → 1

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	20
1	31	20

end0.0ms

sample519.0ms

Algorithm

intervals

Results

422.0ms	8000×	body	80	valid
0.0ms	4×	body	80	nan

Details

analyze5.0ms

sample18.0ms

simplify200.0ms

prune1.0ms

localize9.0ms

rewrite55.0ms

series903.0ms

simplify106.0ms

prune52.0ms

localize10.0ms

rewrite37.0ms

series1.1s

simplify125.0ms

prune73.0ms

simplify6.0ms

end0.0ms

sample519.0ms

Profiling