Details

analyze2.3s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
18.7%	81.1%	0.2%	12
18.7%	81.1%	0.2%	13
20.5%	79.3%	0.2%	14

sample47.0ms

Algorithm

intervals

Results

25.0ms	248×	body	80	valid
2.0ms	4×	body	640	valid
2.0ms	4×	body	640	invalid
1.0ms	7×	body	80	invalid
1.0ms	1×	body	1280	invalid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	invalid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid
0.0ms	1×	body	160	invalid

simplify86.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5054	43

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.7b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64`
6×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `sub-neg_binary64` `diff-log_binary64`
2×	`flip3--_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `associate--r+_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `cos-sum_binary64` `times-frac_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 63

Calls

4 calls:

20.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
11.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.4s

Counts

4 → 12

Calls

4 calls:

403.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
246.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
335.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
450.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (180.0ms)

Iter	Nodes	Cost
0	470	483
1	470	483
0	61	71
1	61	71
0	470	483
1	470	483
0	61	71
1	61	71
0	4885	3
1	4885	3
0	436	543
1	436	543
0	72	57
1	72	57
0	436	543
1	436	543
0	72	57
1	72	57
0	4451	3
1	4451	3
0	381	333
1	381	333
0	42	39
1	42	39
0	381	333
1	381	333
0	42	39
1	42	39
0	10	18
1	10	18
0	509	1325
1	509	1325
0	4316	675
1	4316	675
0	509	1325
1	509	1325
0	4316	675
1	4316	675
0	47	8
1	47	8

simplify120.0ms

Counts

75 → 75

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5004	1518

prune103.0ms

Filtered

55 candidates to 75 candidates (-36.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Merged error: 1.6b

Counts

76 → 5

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
6×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`diff-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

2 → 39

Calls

2 calls:

20.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series733.0ms

Counts

2 → 6

Calls

2 calls:

396.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
337.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	436	543
1	436	543
0	72	57
1	72	57
0	436	543
1	436	543
0	72	57
1	72	57
0	4451	3
1	4451	3
0	509	1325
1	509	1325
0	4316	675
1	4316	675
0	509	1325
1	509	1325
0	4316	675
1	4316	675
0	47	8
1	47	8

simplify99.0ms

Counts

45 → 45

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5003	980

prune47.0ms

Filtered

30 candidates to 45 candidates (-50.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	45	5	50

Merged error: 1.6b

Counts

50 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
32.9b	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
34.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `difference-of-squares_binary64`
2×	`sub-neg_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `flip3--_binary64` `diff-log_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `cos-sum_binary64` `remove-posit16` `times-frac_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 55

Calls

4 calls:

12.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
1.0ms	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.4s

Counts

4 → 12

Calls

4 calls:

243.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
331.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
437.0ms	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
437.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	470	483
1	470	483
0	61	71
1	61	71
0	470	483
1	470	483
0	61	71
1	61	71
0	4885	3
1	4885	3
0	84	4605
1	84	4605
0	4698	1461
1	4698	1461
0	84	4605
1	84	4605
0	4698	1461
1	4698	1461
0	1	3
1	1	3
0	436	543
1	436	543
0	72	57
1	72	57
0	436	543
1	436	543
0	72	57
1	72	57
0	4451	3
1	4451	3
0	381	333
1	381	333
0	42	39
1	42	39
0	381	333
1	381	333
0	42	39
1	42	39
0	10	18
1	10	18

simplify102.0ms

Counts

67 → 67

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4947	1075
1	4947	1075

prune88.0ms

Filtered

49 candidates to 67 candidates (-36.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	66	6	72

Merged error: 1.6b

Counts

72 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
25.7b	(posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))
32.9b	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
34.9b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-unpow_binary64`
2×	`difference-of-squares_binary64` `remove-posit16`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `cos-sum_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `pow-exp_binary64`

Counts

4 → 50

Calls

4 calls:

13.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
1.0ms	(posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))
1.0ms	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
11.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series1.5s

Counts

4 → 12

Calls

4 calls:

337.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
291.0ms	(posit16->binary64 (binary64->posit16 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)))
433.0ms	(posit16->binary64 (binary64->posit16 (cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))))
440.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	470	483
1	470	483
0	61	71
1	61	71
0	470	483
1	470	483
0	61	71
1	61	71
0	4885	3
1	4885	3
0	84	4605
1	84	4605
0	4698	1461
1	4698	1461
0	84	4605
1	84	4605
0	4698	1461
1	4698	1461
0	1	3
1	1	3
0	74	3636
1	74	3636
0	5102	3564
0	74	3636
1	74	3636
0	5102	3564
0	1	3
1	1	3
0	436	543
1	436	543
0	72	57
1	72	57
0	436	543
1	436	543
0	72	57
1	72	57
0	4451	3
1	4451	3

simplify168.0ms

Counts

62 → 62

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4850	898
1	4850	898

prune78.0ms

Filtered

44 candidates to 62 candidates (-40.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	62	6	68

Merged error: 1.6b

Counts

68 → 6

regimes110.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	26
1	63	26

end0.0ms

sample1.4s

Algorithm

intervals

Results

836.0ms	7820×	body	80	valid
38.0ms	54×	body	1280	valid
37.0ms	65×	body	1280	invalid
35.0ms	84×	body	640	invalid
30.0ms	59×	body	640	valid
25.0ms	248×	body	80	invalid
20.0ms	64×	body	320	invalid
16.0ms	48×	body	320	valid
8.0ms	36×	body	160	invalid
4.0ms	19×	body	160	valid
4.0ms	4×	body	2560	invalid

Details

analyze2.3s

sample47.0ms

simplify86.0ms

prune10.0ms

localize21.0ms

rewrite58.0ms

series1.4s

simplify120.0ms

prune103.0ms

localize14.0ms

rewrite35.0ms

series733.0ms

simplify99.0ms

prune47.0ms

localize22.0ms

rewrite38.0ms

series1.4s

simplify102.0ms

prune88.0ms

localize26.0ms

rewrite27.0ms

series1.5s

simplify168.0ms

prune78.0ms

regimes110.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample1.4s

Profiling