Details

analyze742.0ms

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

sample91.0ms

Algorithm

intervals

Results

44.0ms	108×	body	1280	valid
22.0ms	20×	body	2560	valid
11.0ms	53×	body	640	valid
3.0ms	22×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	16×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

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: 38.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.7b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.2b	(tan.f64 (+.f64 x eps))

rewrite15.0ms

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` `insert-posit16` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

2 → 26

Calls

2 calls:

9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series644.0ms

Counts

2 → 6

Calls

2 calls:

394.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
250.0ms	(tan.f64 (+.f64 x eps))

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	257	189
1	257	189
0	34	63
1	34	63
0	257	189
1	257	189
0	34	63
1	34	63
0	4331	3
1	4331	3
0	366	318
1	366	318
0	42	81
1	42	81
0	366	318
1	366	318
0	42	81
1	42	81
0	4478	3
1	4478	3

simplify212.0ms

Counts

32 → 32

Iterations

Useful iterations: 0 (192.0ms)

Iter	Nodes	Cost
0	4874	454
1	4874	454

prune38.0ms

Filtered

26 candidates to 32 candidates (-23.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	20	12	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	12	33

Merged error: 22.7b

Counts

33 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
4.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite43.0ms

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` `insert-posit16`
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 → 89

Calls

4 calls:

6.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
11.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series983.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
283.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
201.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
312.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	631	1146
1	631	1146
0	10	9
1	10	9
0	631	1146
1	631	1146
0	10	9
1	10	9
0	1	3
1	1	3
0	351	342
1	351	342
0	8	9
1	8	9
0	351	342
1	351	342
0	8	9
1	8	9
0	1	3
1	1	3
0	584	1017
1	584	1017
0	10	9
1	10	9
0	584	1017
1	584	1017
0	10	9
1	10	9
0	1	3
1	1	3
0	310	258
1	310	258
0	10	9
1	10	9
0	310	258
1	310	258
0	10	9
1	10	9
0	1	3
1	1	3

simplify119.0ms

Counts

101 → 101

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5008	2269

prune121.0ms

Filtered

73 candidates to 101 candidates (-38.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	86	15	101
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	96	17	113

Merged error: 22.6b

Counts

113 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))))
0.2b	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
0.3b	(*.f64 (tan.f64 eps) (sin.f64 x))
4.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`difference-of-squares_binary64`
9×	`associate-/r*_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out--_binary64`
5×	`associate-/l*_binary64` `tan-quot_binary64`
4×	`associate-/l/_binary64` `insert-posit16`
3×	`associate-r_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))))
8.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
24.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

series1.2s

Counts

4 → 12

Calls

4 calls:

341.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))))
254.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
200.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
366.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	838	1535
1	838	1535
0	52	473
1	52	473
0	838	1535
1	838	1535
0	52	473
1	52	473
0	1	3
1	1	3
0	339	306
1	339	306
0	8	9
1	8	9
0	339	306
1	339	306
0	8	9
1	8	9
0	1	3
1	1	3
0	520	621
1	520	621
0	8	9
1	8	9
0	520	621
1	520	621
0	8	9
1	8	9
0	1	3
1	1	3
0	791	1422
1	791	1422
0	10	9
1	10	9
0	791	1422
1	791	1422
0	10	9
1	10	9
0	1	3
1	1	3

simplify144.0ms

Counts

123 → 123

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5778	3434

prune124.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	123	17	140

Merged error: 22.6b

Counts

140 → 17

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
0.3b	(exp.f64 (tan.f64 x))
3.4b	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
4.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64` `log-prod_binary64`
6×	`unpow-prod-down_binary64` `exp-prod_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow-pow_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `rem-log-exp_binary64`
2×	`pow-to-exp_binary64` `sqr-pow_binary64` `difference-of-squares_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `log-pow_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `flip--_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

4 → 68

Calls

4 calls:

5.0ms	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
3.0ms	(exp.f64 (tan.f64 x))
4.0ms	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
22.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))

series1.0s

Counts

4 → 12

Calls

4 calls:

233.0ms	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
199.0ms	(exp.f64 (tan.f64 x))
258.0ms	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
352.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	774	1534
1	774	1534
0	56	473
1	56	473
0	774	1534
1	774	1534
0	56	473
1	56	473
0	1	3
1	1	3
0	497	678
1	497	678
0	7	9
1	7	9
0	497	678
1	497	678
0	7	9
1	7	9
0	1	3
1	1	3
0	400	585
1	400	585
0	12	9
1	12	9
0	400	585
1	400	585
0	12	9
1	12	9
0	1	3
1	1	3
0	444	576
1	444	576
0	7	9
1	7	9
0	444	576
1	444	576
0	7	9
1	7	9
0	1	3
1	1	3

simplify181.0ms

Counts

80 → 80

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4928	1281
1	4928	1281

prune50.0ms

Filtered

52 candidates to 80 candidates (-53.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	80	17	97

Merged error: 22.6b

Counts

97 → 17

regimes90.0ms

Accuracy

0% (0.5b remaining)

Error of 21.7b against oracle of 21.2b and baseline of 21.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	30
1	33	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3314×	body	1280	valid
555.0ms	653×	body	2560	valid
399.0ms	1837×	body	640	valid
106.0ms	739×	body	320	valid
45.0ms	1076×	body	80	valid
38.0ms	381×	body	160	valid

Details

analyze742.0ms

sample91.0ms

simplify24.0ms

prune1.0ms

localize8.0ms

rewrite15.0ms

series644.0ms

simplify212.0ms

prune38.0ms

localize14.0ms

rewrite43.0ms

series983.0ms

simplify119.0ms

prune121.0ms

localize20.0ms

rewrite58.0ms

series1.2s

simplify144.0ms

prune124.0ms

localize16.0ms

rewrite35.0ms

series1.0s

simplify181.0ms

prune50.0ms

regimes90.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample2.6s

Profiling