Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample99.0ms

Algorithm

intervals

Results

57.0ms	156×	body	1280	valid
16.0ms	17×	body	2560	valid
11.0ms	50×	body	640	valid
7.0ms	22×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	4×	body	80	valid

simplify26.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

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: 39.3b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

1.7b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.8b	(cos.f64 (+.f64 x eps))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64` `insert-posit16`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 25

Calls

2 calls:

9.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
6.0ms	(cos.f64 (+.f64 x eps))

series284.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
138.0ms	(cos.f64 (+.f64 x eps))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	653	2556
1	653	2556
0	43	9
1	43	9
0	653	2556
1	653	2556
0	43	9
1	43	9
0	1	3
1	1	3
0	717	2619
1	717	2619
0	73	9
1	73	9
0	717	2619
1	717	2619
0	73	9
1	73	9
0	1	3
1	1	3

simplify146.0ms

Counts

31 → 31

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4889	390
1	4889	390

prune37.0ms

Filtered

25 candidates to 31 candidates (-24.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	6	32

Merged error: 0.3b

Counts

32 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.8b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`distribute-lft-out_binary64` `times-frac_binary64`
9×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`associate-/l*_binary64`
4×	`insert-posit16`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `flip-+_binary64` `sum-log_binary64`
2×	`associate-/l/_binary64` `consolidate-/-/-b_binary64_1`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

8.0ms	(+.f64 x (+.f64 x eps))
11.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
16.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

281.0ms	(+.f64 x (+.f64 x eps))
293.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
304.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
292.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4968	2592
1	4968	2592
0	86	9
1	86	9
0	4968	2592
1	4968	2592
0	86	9
1	86	9
0	1	3
1	1	3
0	4789	2664
1	4789	2664
0	129	9
1	129	9
0	4789	2664
1	4789	2664
0	129	9
1	129	9
0	1	3
1	1	3
0	4965	2574
1	4965	2574
0	74	9
1	74	9
0	4965	2574
1	4965	2574
0	74	9
1	74	9
0	1	3
1	1	3
0	4821	2547
1	4821	2547
0	50	9
1	50	9
0	4821	2547
1	4821	2547
0	50	9
1	50	9
0	1	3
1	1	3

simplify191.0ms

Counts

96 → 96

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4834	967
1	4834	967

prune78.0ms

Filtered

69 candidates to 96 candidates (-39.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 0.3b

Counts

102 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (+.f64 (+.f64 x x) eps) 2)
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 (+.f64 x x) eps) 2)))
4.8b	(sin.f64 (/.f64 (+.f64 (+.f64 x x) eps) 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
12×	`distribute-lft-out_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `associate-/l*_binary64`
4×	`flip3-+_binary64` `associate-/l/_binary64` `consolidate-+-/-l_binary64` `consolidate-/-/-b_binary64_1` `flip-+_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r_binary64` `associate-l*_binary64` `insert-posit16`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 72

Calls

3 calls:

15.0ms	(/.f64 (+.f64 (+.f64 x x) eps) 2)
17.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 (+.f64 x x) eps) 2)))
12.0ms	(sin.f64 (/.f64 (+.f64 (+.f64 x x) eps) 2))

series755.0ms

Counts

3 → 9

Calls

3 calls:

245.0ms	(/.f64 (+.f64 (+.f64 x x) eps) 2)
259.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 (+.f64 x x) eps) 2)))
251.0ms	(sin.f64 (/.f64 (+.f64 (+.f64 x x) eps) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4874	2592
1	4874	2592
0	71	9
1	71	9
0	4874	2592
1	4874	2592
0	71	9
1	71	9
0	1	3
1	1	3
0	5001	2664
0	123	9
1	123	9
0	5001	2664
0	123	9
1	123	9
0	1	3
1	1	3
0	4871	2574
1	4871	2574
0	59	9
1	59	9
0	4871	2574
1	4871	2574
0	59	9
1	59	9
0	1	3
1	1	3

simplify166.0ms

Counts

81 → 81

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4756	1089
1	4756	1089

prune60.0ms

Filtered

55 candidates to 81 candidates (-47.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	81	6	87

Merged error: 0.3b

Counts

87 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))
0.1b	(*.f64 (cos.f64 x) (cos.f64 eps))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
2.4b	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
10×	`*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`diff-log_binary64` `insert-posit16`
3×	`sub-neg_binary64` `cos-mult_binary64` `sin-mult_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`associate--l-_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `sub-div_binary64` `frac-sub_binary64` `associate--l+_binary64`

Counts

4 → 71

Calls

4 calls:

7.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))
6.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
6.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
12.0ms	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))

series673.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps)))
111.0ms	(*.f64 (cos.f64 x) (cos.f64 eps))
113.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
259.0ms	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	901	2727
1	901	2727
0	161	9
1	161	9
0	901	2727
1	901	2727
0	161	9
1	161	9
0	1	3
1	1	3
0	67	2574
1	67	2574
0	76	9
1	76	9
0	67	2574
1	67	2574
0	76	9
1	76	9
0	1	3
1	1	3
0	67	2574
1	67	2574
0	82	9
1	82	9
0	67	2574
1	67	2574
0	82	9
1	82	9
0	1	3
1	1	3
0	517	2700
1	517	2700
0	146	9
1	146	9
0	517	2700
1	517	2700
0	146	9
1	146	9
0	1	3
1	1	3

simplify79.0ms

Counts

83 → 83

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5608	1317

prune60.0ms

Filtered

61 candidates to 83 candidates (-36.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	79	10	89

Merged error: 0.2b

Counts

89 → 10

regimes84.0ms

Accuracy

91.9% (0.5b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 6.5b

bsearch117.0ms

Steps

Iters	Range		Point
8	4.176678541163516e-56	7.677016792647431e-52	7.492679465452055e-52
10	-3.650512965565952e+19	-3956.286836737309	-4009.334003099285

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	94	104
1	94	104

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4427×	body	1280	valid
582.0ms	632×	body	2560	valid
438.0ms	1886×	body	640	valid
110.0ms	688×	body	320	valid
31.0ms	282×	body	160	valid
5.0ms	85×	body	80	valid

Details

analyze2.0ms

sample99.0ms

simplify26.0ms

prune1.0ms

localize12.0ms

rewrite15.0ms

series284.0ms

simplify146.0ms

prune37.0ms

localize13.0ms

rewrite48.0ms

series1.2s

simplify191.0ms

prune78.0ms

localize13.0ms

rewrite47.0ms

series755.0ms

simplify166.0ms

prune60.0ms

localize13.0ms

rewrite34.0ms

series673.0ms

simplify79.0ms

prune60.0ms

regimes84.0ms

bsearch117.0ms

simplify8.0ms

end0.0ms

sample3.0s

Profiling