Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample21.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify168.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	166	17
1	166	17

prune3.0ms

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 3 expressions with local error:

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

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64` `insert-posit16`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 103

Calls

3 calls:

1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
210.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

series1.6s

Counts

3 → 9

Calls

3 calls:

495.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
504.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
575.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	630	1031
1	630	1031
0	4812	640
1	4812	640
0	630	1031
1	630	1031
0	4812	640
1	4812	640
0	5432	21
0	744	1590
1	744	1590
0	4909	1496
1	4909	1496
0	744	1590
1	744	1590
0	4909	1496
1	4909	1496
0	1	3
1	1	3
0	78	1784
1	78	1784
0	4984	1739
1	4984	1739
0	78	1784
1	78	1784
0	4984	1739
1	4984	1739
0	1	3
1	1	3

simplify163.0ms

Counts

112 → 112

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4937	1991
1	4937	1991

prune97.0ms

Filtered

72 candidates to 112 candidates (-55.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	1	113

Merged error: 0b

Counts

113 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

167×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
148×	`times-frac_binary64`
92×	`sqrt-prod_binary64`
76×	`add-cube-cbrt_binary64`
48×	`associate-r_binary64`
32×	`add-exp-log_binary64`
30×	`difference-of-squares_binary64`
27×	`associate-l_binary64`
20×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
15×	`unswap-sqr_binary64` `distribute-lft-out--_binary64`
14×	`associate-/r*_binary64`
11×	`pow1_binary64` `div-exp_binary64` `sqrt-div_binary64`
9×	`associate-/l*_binary64`
8×	`associate-/r/_binary64` `prod-exp_binary64`
6×	`cbrt-undiv_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `div-inv_binary64` `insert-posit16` `flip-+_binary64`
3×	`1-exp_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `pow-flip_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `inv-pow_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 255

Calls

4 calls:

49.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
21.0ms	(sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
12.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))

series2.3s

Counts

4 → 12

Calls

4 calls:

622.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))))
628.0ms	(sqrt.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))))
519.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
578.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	732	1389
1	732	1389
0	4815	927
1	4815	927
0	732	1389
1	732	1389
0	4815	927
1	4815	927
0	1	3
1	1	3
0	738	1226
1	738	1226
0	4901	710
1	4901	710
0	738	1226
1	738	1226
0	4901	710
1	4901	710
0	1	3
1	1	3
0	1204	1949
1	1204	1949
0	5196	1781
0	1204	1949
1	1204	1949
0	5196	1781
0	1	3
1	1	3
0	1090	1821
1	1090	1821
0	4939	1448
1	4939	1448
0	1090	1821
1	1090	1821
0	4939	1448
1	4939	1448
0	1	3
1	1	3

simplify200.0ms

Counts

267 → 267

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4947	4818
1	4947	4818

prune224.0ms

Filtered

137 candidates to 267 candidates (-94.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	267	1	268

Merged error: 0b

Counts

268 → 1

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	30
1	27	30

end0.0ms

sample494.0ms

Algorithm

intervals

Results

390.0ms

8000×

body

valid

Details

analyze12.0ms

sample21.0ms

simplify168.0ms

prune3.0ms

localize9.0ms

rewrite229.0ms

series1.6s

simplify163.0ms

prune97.0ms

localize11.0ms

rewrite107.0ms

series2.3s

simplify200.0ms

prune224.0ms

simplify6.0ms

end0.0ms

sample494.0ms

Profiling