Details

analyze801.0ms

Algorithm

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

sample95.0ms

Algorithm

intervals

Results

46.0ms	112×	body	1280	valid
17.0ms	20×	body	2560	valid
16.0ms	50×	body	640	valid
4.0ms	27×	body	320	valid
2.0ms	35×	body	80	valid
1.0ms	12×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

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: 36.1b

Counts

2 → 1

localize8.0ms

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

Algorithm

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))

series49.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms	(tan.f64 (+.f64 x eps))

simplify56.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune53.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

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

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))

rewrite38.0ms

Algorithm

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:

10.0ms	(/.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))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
15.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
25.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
28.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
126.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5109	1560

prune137.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

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

localize14.0ms

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))

rewrite41.0ms

Algorithm

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:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
12.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
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))

series557.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
26.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
41.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
464.0ms	(-.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))

simplify32.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4984	1908
1	4984	1908

prune134.0ms

Filtered

74 candidates to 121 candidates (-63.5%)

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

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))

rewrite36.0ms

Algorithm

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:

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))
14.0ms	(-.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))

series511.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
11.0ms	(*.f64 (tan.f64 eps) (tan.f64 eps))
12.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
462.0ms	(-.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))

simplify31.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4975	1501
1	4975	1501

prune81.0ms

Filtered

68 candidates to 107 candidates (-57.4%)

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

regimes224.0ms

Accuracy

87.2% (0.9b remaining)

Error of 15.7b against oracle of 14.8b and baseline of 22.1b

bsearch73.0ms

Steps

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

simplify14.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	581	123
1	581	123

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	3334×	body	1280	valid
591.0ms	686×	body	2560	valid
386.0ms	1765×	body	640	valid
122.0ms	791×	body	320	valid
51.0ms	1089×	body	80	valid
35.0ms	335×	body	160	valid

Details

analyze801.0ms

sample95.0ms

simplify7.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series49.0ms

simplify56.0ms

prune53.0ms

localize11.0ms

rewrite38.0ms

series250.0ms

simplify52.0ms

prune137.0ms

localize14.0ms

rewrite41.0ms

series557.0ms

simplify32.0ms

prune134.0ms

localize17.0ms

rewrite36.0ms

series511.0ms

simplify31.0ms

prune81.0ms

regimes224.0ms

bsearch73.0ms

simplify14.0ms

end0.0ms

sample2.7s

Profiling