Details

analyze2.4s

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

sample48.0ms

Algorithm

intervals

Results

26.0ms	250×	body	80	valid
2.0ms	4×	body	1280	invalid
2.0ms	15×	body	80	invalid
1.0ms	3×	body	320	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	160	invalid
0.0ms	1×	body	320	invalid
0.0ms	1×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5233	43

prune5.0ms

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: 17.4b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 K (+.f64 m n)) 2)
0.0b	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
34.5b	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`times-frac_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `associate-/r*_binary64` `difference-of-squares_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cos-diff_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `cos-sum_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 70

Calls

4 calls:

9.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
11.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
12.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

series2.0s

Counts

4 → 12

Calls

4 calls:

398.0ms	(/.f64 (*.f64 K (+.f64 m n)) 2)
534.0ms	(-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M)
510.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
564.0ms	(cos.f64 (-.f64 (/.f64 (*.f64 K (+.f64 m n)) 2) M))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	2714	428
1	2714	428
0	2714	428
1	2714	428
0	1	3
1	1	3
0	4615	177
1	4615	177
0	4615	177
1	4615	177
0	1	3
1	1	3
0	2606	262
1	2606	262
0	2606	262
1	2606	262
0	1	3
1	1	3
0	1693	416
1	1693	416
0	1693	416
1	1693	416
0	1	3
1	1	3

simplify80.0ms

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4979	1197
1	4979	1197

prune105.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 1.2b

Counts

83 → 4

localize19.0ms

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)

rewrite36.0ms

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:

21.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

series1.3s

Counts

2 → 6

Calls

2 calls:

826.0ms	(-.f64 (fabs.f64 (-.f64 m n)) (+.f64 (pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2) l))
517.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4615	177
1	4615	177
0	4615	177
1	4615	177
0	1	3
1	1	3
0	3611	410
1	3611	410
0	3611	410
1	3611	410
0	1	3
1	1	3

simplify87.0ms

Counts

45 → 45

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5099	975

prune45.0ms

Filtered

29 candidates to 45 candidates (-55.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Merged error: 1.2b

Counts

49 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)
0.0b	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
0.2b	(/.f64 K (/.f64 2 (+.f64 m n)))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac_binary64`
85×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
12×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `difference-of-squares_binary64` `div-inv_binary64`
4×	`flip3-+_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_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` `clear-num_binary64` `frac-2neg_binary64` `cos-sum_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 139

Calls

4 calls:

31.0ms	(-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)
14.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
14.0ms	(/.f64 K (/.f64 2 (+.f64 m n)))
27.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

series1.8s

Counts

4 → 12

Calls

4 calls:

269.0ms	(-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)
516.0ms	(pow.f64 (-.f64 (/.f64 (+.f64 m n) 2) M) 2)
718.0ms	(/.f64 K (/.f64 2 (+.f64 m n)))
277.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4741	1120
1	4741	1120
0	4741	1120
1	4741	1120
0	1	3
1	1	3
0	4407	72
1	4407	72
0	4407	72
1	4407	72
0	1	3
1	1	3
0	4615	177
1	4615	177
0	4615	177
1	4615	177
0	1	3
1	1	3
0	4908	437
1	4908	437
0	4908	437
1	4908	437
0	1	3
1	1	3

simplify110.0ms

Counts

151 → 151

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5283	2920

prune185.0ms

Filtered

109 candidates to 151 candidates (-38.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	149	6	155

Merged error: 1.2b

Counts

155 → 6

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
34.5b	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`sub-neg_binary64` `cos-diff_binary64` `cos-sum_binary64` `cbrt-prod_binary64`
1×	`pow1/3_binary64`

Counts

4 → 42

Calls

4 calls:

2.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)))
31.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
28.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
28.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

series1.3s

Counts

4 → 12

Calls

4 calls:

492.0ms	(cbrt.f64 (cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M)))
266.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
270.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))
268.0ms	(cos.f64 (-.f64 (/.f64 K (/.f64 2 (+.f64 m n))) M))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4741	1120
1	4741	1120
0	4741	1120
1	4741	1120
0	1	3
1	1	3
0	4741	1120
1	4741	1120
0	4741	1120
1	4741	1120
0	1	3
1	1	3
0	4741	1120
1	4741	1120
0	4741	1120
1	4741	1120
0	1	3
1	1	3
0	4645	1653
1	4645	1653
0	4645	1653
1	4645	1653
0	1	3
1	1	3

simplify94.0ms

Counts

54 → 54

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4972	904
1	4972	904

prune112.0ms

Filtered

45 candidates to 54 candidates (-20.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	54	6	60

Merged error: 1.2b

Counts

60 → 6

regimes112.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	66	26
1	66	26

end0.0ms

sample1.4s

Algorithm

intervals

Results

861.0ms	7818×	body	80	valid
44.0ms	75×	body	1280	invalid
37.0ms	292×	body	80	invalid
33.0ms	51×	body	1280	valid
32.0ms	75×	body	640	invalid
26.0ms	58×	body	640	valid
22.0ms	69×	body	320	invalid
15.0ms	47×	body	320	valid
9.0ms	41×	body	160	invalid
6.0ms	26×	body	160	valid
5.0ms	6×	body	2560	invalid

Details

analyze2.4s

sample48.0ms

simplify88.0ms

prune5.0ms

localize23.0ms

rewrite47.0ms

series2.0s

simplify80.0ms

prune105.0ms

localize19.0ms

rewrite36.0ms

series1.3s

simplify87.0ms

prune45.0ms

localize23.0ms

rewrite95.0ms

series1.8s

simplify110.0ms

prune185.0ms

localize33.0ms

rewrite90.0ms

series1.3s

simplify94.0ms

prune112.0ms

regimes112.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

sample1.4s

Profiling