Details

analyze805.0ms (13.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample92.0ms (1.5%)

Algorithm

1×

intervals

Results

49.0ms	112×	body	1280	valid
17.0ms	20×	body	2560	valid
11.0ms	50×	body	640	valid
4.0ms	27×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	12×	body	160	valid

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms (0.1%)

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: 36.1b

Counts

2 → 1

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.5b	(tan.f64 (+.f64 x eps))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `tan-quot_binary64`
2×	`tan-sum_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series52.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
21.0ms	(tan.f64 (+.f64 x eps))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune54.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 15.6b

Counts

31 → 8

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`tan-quot_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

12.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series235.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
66.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
26.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
24.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5109	1560

prune158.0ms (2.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	85	12	97
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	91	14	105

Merged error: 15.5b

Counts

105 → 14

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
3.4b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`pow1_binary64`
45×	`tan-quot_binary64`
21×	`frac-times_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64`
15×	`associate-*r/_binary64`
14×	`associate-*l/_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
5×	`frac-sub_binary64`
4×	`pow-prod-up_binary64` `pow-sqr_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate--l+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `swap-sqr_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 109

Calls

4 calls:

15.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
12.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series540.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

451.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
39.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
25.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
25.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4984	1908
1	4984	1908

prune182.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	120	15	135

Merged error: 15.5b

Counts

135 → 15

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 eps) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
3.4b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 eps) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64` `add-sqr-sqrt_binary64`
17×	`tan-quot_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64`
5×	`associate-*r/_binary64` `frac-sub_binary64` `frac-times_binary64`
4×	`associate-*l/_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `associate--l+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`

Counts

4 → 95

Calls

4 calls:

13.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 eps) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 eps) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series487.0ms (8%)

Counts

4 → 12

Calls

4 calls:

442.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 eps) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
25.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
10.0ms	(*.f64 (tan.f64 eps) (tan.f64 eps))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4975	1501
1	4975	1501

prune119.0ms (2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	106	16	122

Merged error: 15.5b

Counts

122 → 16

regimes210.0ms (3.4%)

Accuracy

Total 0.9b remaining (6%)

Threshold costs 0.9b (6%)

bsearch73.0ms (1.2%)

Steps

Iters	Range		Point
10	1.8668904184323883e-58	2.576071762552961e-47	1.3314514851199195e-51
8	-3.624131594184871e-35	-2.520610488139427e-38	-2.3047993601266133e-36

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	581	123
1	581	123

end0.0ms (0%)

sample2.7s (44.7%)

Algorithm

1×

intervals

Results

1.3s	3334×	body	1280	valid
597.0ms	686×	body	2560	valid
398.0ms	1765×	body	640	valid
117.0ms	791×	body	320	valid
54.0ms	1089×	body	80	valid
36.0ms	335×	body	160	valid

Details

analyze805.0ms (13.2%)

sample92.0ms (1.5%)

simplify7.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite12.0ms (0.2%)

series52.0ms (0.8%)

simplify54.0ms (0.9%)

prune54.0ms (0.9%)

localize11.0ms (0.2%)

rewrite34.0ms (0.6%)

series235.0ms (3.8%)

simplify52.0ms (0.8%)

prune158.0ms (2.6%)

localize15.0ms (0.2%)

rewrite43.0ms (0.7%)

series540.0ms (8.8%)

simplify33.0ms (0.5%)

prune182.0ms (3%)

localize17.0ms (0.3%)

rewrite34.0ms (0.5%)

series487.0ms (8%)

simplify33.0ms (0.5%)

prune119.0ms (2%)

regimes210.0ms (3.4%)

bsearch73.0ms (1.2%)

simplify15.0ms (0.2%)

end0.0ms (0%)

sample2.7s (44.7%)

Profiling