Details

analyze395.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

sample84.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
20.0ms	33×	body	1280	nan
12.0ms	28×	body	640	nan
11.0ms	84×	body	80	overflowed
4.0ms	15×	body	320	nan
2.0ms	28×	body	80	nan
1.0ms	5×	body	160	nan
0.0ms	5×	body	80	invalid

simplify554.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4909	22
1	4909	22

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.6b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.5b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac_binary64_3447`
42×	`add-sqr-sqrt_binary64_3437` `*-un-lft-identity_binary64_3452`
33×	`add-cube-cbrt_binary64_3423`
26×	`add-exp-log_binary64_3416`
22×	`pow-unpow_binary64_3381`
18×	`sqrt-prod_binary64_3431`
14×	`pow1_binary64_3394`
10×	`add-cbrt-cube_binary64_3424`
9×	`prod-exp_binary64_3399`
8×	`unpow-prod-down_binary64_3383` `sqr-pow_binary64_3484`
6×	`pow-prod-down_binary64_3375` `pow-exp_binary64_3372` `difference-of-squares_binary64_3481` `associate-/r*_binary64_3515`
5×	`associate-/l*_binary64_3516` `div-exp_binary64_3401`
3×	`associate-r_binary64_3511` `cbrt-unprod_binary64_3421` `add-log-exp_binary64_3417` `pow-pow_binary64_3376` `distribute-lft-out--_binary64_3497`
2×	`div-inv_binary64_3453` `pow-sub_binary64_3380` `div-sub_binary64_3446` `pow-to-exp_binary64_3373`
1×	`cbrt-undiv_binary64_3422` `frac-2neg_binary64_3445` `associate-l_binary64_3512` `*-commutative_binary64_3520` `clear-num_binary64_3455` `associate-/l/_binary64_3518`

Counts

3 → 115

Calls

3 calls:

6.0ms	(.f64 (.f64 2 PI.f64) n)
8.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

series645.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms	(.f64 (.f64 2 PI.f64) n)
256.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
168.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	144	2685
1	144	2685
0	4874	2619
1	4874	2619
0	144	2685
1	144	2685
0	4874	2619
1	4874	2619
0	1	3
1	1	3
0	376	2754
1	376	2754
0	4798	2682
1	4798	2682
0	376	2754
1	376	2754
0	4798	2682
1	4798	2682
0	1	3
1	1	3
0	187	1959
1	187	1959
0	4917	1926
1	4917	1926
0	187	1959
1	187	1959
0	4917	1926
1	4917	1926
0	1	3
1	1	3

simplify160.0ms

Counts

124 → 124

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4922	3014
1	4922	3014

prune142.0ms

Filtered

78 candidates to 124 candidates (-59.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	11	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 0.0b

Counts

126 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
0.3b	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.4b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

293×	`times-frac_binary64_3447`
132×	`add-sqr-sqrt_binary64_3437` `*-un-lft-identity_binary64_3452` `add-cube-cbrt_binary64_3423`
111×	`sqrt-prod_binary64_3431`
34×	`add-exp-log_binary64_3416`
29×	`unpow-prod-down_binary64_3383` `sqr-pow_binary64_3484`
24×	`associate-/l*_binary64_3516`
21×	`pow1_binary64_3394`
14×	`add-cbrt-cube_binary64_3424`
13×	`pow-unpow_binary64_3381`
11×	`div-exp_binary64_3401`
9×	`prod-exp_binary64_3399` `pow-prod-down_binary64_3375` `div-inv_binary64_3453`
6×	`pow-exp_binary64_3372` `associate-/r*_binary64_3515`
4×	`add-log-exp_binary64_3417`
3×	`associate-r_binary64_3511` `cbrt-unprod_binary64_3421` `cbrt-undiv_binary64_3422` `pow-pow_binary64_3376` `sqrt-pow1_binary64_3433`
2×	`pow-to-exp_binary64_3373`
1×	`frac-2neg_binary64_3445` `associate-l_binary64_3512` `*-commutative_binary64_3520` `clear-num_binary64_3455` `pow1/2_binary64_3384` `associate-/l/_binary64_3518`

Counts

4 → 252

Calls

4 calls:

6.0ms	(.f64 (.f64 2 PI.f64) n)
8.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
18.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series968.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(.f64 (.f64 2 PI.f64) n)
241.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
261.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
243.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	255	1977
1	255	1977
0	5039	1944
0	255	1977
1	255	1977
0	5039	1944
0	1	3
1	1	3
0	504	2859
1	504	2859
0	4769	2763
1	4769	2763
0	504	2859
1	504	2859
0	4769	2763
1	4769	2763
0	1	3
1	1	3
0	134	2658
1	134	2658
0	5059	2592
0	134	2658
1	134	2658
0	5059	2592
0	1	3
1	1	3
0	187	1959
1	187	1959
0	4917	1926
1	4917	1926
0	187	1959
1	187	1959
0	4917	1926
1	4917	1926
0	1	3
1	1	3

simplify248.0ms

Counts

264 → 264

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	4949	11558
1	4949	11558

prune327.0ms

Filtered

173 candidates to 264 candidates (-52.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	259	5	264
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	264	11	275

Merged error: 0b

Counts

275 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 2 PI.f64) n)
0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))
0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 1/2 k))))
0.4b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log_binary64_3416`
21×	`pow1_binary64_3394`
14×	`prod-exp_binary64_3399` `add-cbrt-cube_binary64_3424`
9×	`pow-prod-down_binary64_3375`
7×	`add-sqr-sqrt_binary64_3437` `*-un-lft-identity_binary64_3452` `add-cube-cbrt_binary64_3423`
6×	`pow-exp_binary64_3372` `div-exp_binary64_3401`
4×	`cbrt-unprod_binary64_3421` `add-log-exp_binary64_3417` `associate-/l*_binary64_3516` `times-frac_binary64_3447`
3×	`associate-r_binary64_3511` `pow-pow_binary64_3376` `sqrt-prod_binary64_3431` `sqrt-pow1_binary64_3433`
2×	`cbrt-undiv_binary64_3422` `pow-to-exp_binary64_3373`
1×	`unpow-prod-down_binary64_3383` `frac-2neg_binary64_3445` `sqr-pow_binary64_3484` `div-inv_binary64_3453` `associate-l_binary64_3512` `-commutative_binary64_3520` `clear-num_binary64_3455` `pow1/2_binary64_3384` `associate-/r_binary64_3515` `pow-unpow_binary64_3381`

Counts

4 → 74

Calls

4 calls:

6.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))
14.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 1/2 k))))
5.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series900.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(.f64 (.f64 2 PI.f64) n)
167.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))
262.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (.f64 1/2 k))))
244.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	255	1977
1	255	1977
0	5039	1944
0	255	1977
1	255	1977
0	5039	1944
0	1	3
1	1	3
0	390	2859
1	390	2859
0	4839	2763
1	4839	2763
0	390	2859
1	390	2859
0	4839	2763
1	4839	2763
0	1	3
1	1	3
0	131	2658
1	131	2658
0	5127	2592
0	131	2658
1	131	2658
0	5127	2592
0	1	3
1	1	3
0	187	1959
1	187	1959
0	4917	1926
1	4917	1926
0	187	1959
1	187	1959
0	4917	1926
1	4917	1926
0	1	3
1	1	3

simplify113.0ms

Counts

86 → 86

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4945	1429
1	4945	1429

prune76.0ms

Filtered

52 candidates to 86 candidates (-65.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	87	10	97

Merged error: 0b

Counts

97 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))
0.3b	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))))
0.5b	(/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac_binary64_3447`
99×	`add-sqr-sqrt_binary64_3437`
67×	`sqrt-prod_binary64_3431`
56×	`add-exp-log_binary64_3416`
53×	`*-un-lft-identity_binary64_3452` `add-cube-cbrt_binary64_3423`
34×	`associate-r_binary64_3511`
28×	`associate-l_binary64_3512`
21×	`prod-exp_binary64_3399`
18×	`add-cbrt-cube_binary64_3424`
17×	`div-exp_binary64_3401`
15×	`pow1_binary64_3394` `unswap-sqr_binary64_3480`
13×	`sqr-pow_binary64_3484`
9×	`pow-exp_binary64_3372`
7×	`unpow-prod-down_binary64_3383`
6×	`associate-/r*_binary64_3515`
5×	`pow-prod-down_binary64_3375` `cbrt-undiv_binary64_3422`
4×	`cbrt-unprod_binary64_3421` `add-log-exp_binary64_3417` `associate-/l*_binary64_3516`
3×	`div-inv_binary64_3453` `pow-pow_binary64_3376` `pow-to-exp_binary64_3373`
2×	`sqrt-pow1_binary64_3433`
1×	`associate-l/_binary64_3514` `frac-times_binary64_3444` `sqrt-undiv_binary64_3436` `frac-2neg_binary64_3445` `-commutative_binary64_3520` `associate-*r/_binary64_3513` `clear-num_binary64_3455` `pow1/2_binary64_3384` `pow-unpow_binary64_3381`

Counts

4 → 180

Calls

4 calls:

7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))
35.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))))
7.0ms	(/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k))
3.0ms	(sqrt.f64 (*.f64 2 PI.f64))

series676.0ms

Counts

4 → 10

Calls

4 calls:

171.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))
255.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (.f64 (.f64 2 PI.f64) n) (*.f64 1/2 k))))
250.0ms	(/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k))
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	421	1995
1	421	1995
0	5353	1980
0	421	1995
1	421	1995
0	5353	1980
0	1	3
1	1	3
0	216	2877
1	216	2877
0	5121	2799
0	216	2877
1	216	2877
0	5121	2799
0	1	3
1	1	3
0	131	2658
1	131	2658
0	5127	2592
0	131	2658
1	131	2658
0	5127	2592
0	1	3
1	1	3

simplify198.0ms

Counts

190 → 190

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	4928	5603
1	4928	5603

prune164.0ms

Filtered

116 candidates to 190 candidates (-63.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	191	9	200

Merged error: 0b

Counts

200 → 9

regimes70.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	31
1	18	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

704.0ms	8000×	body	80	valid
613.0ms	995×	body	1280	nan
373.0ms	827×	body	640	nan
340.0ms	2514×	body	80	overflowed
124.0ms	416×	body	320	nan
40.0ms	736×	body	80	nan
37.0ms	207×	body	160	nan
24.0ms	238×	body	80	invalid

Details

analyze395.0ms

sample84.0ms

simplify554.0ms

prune4.0ms

localize12.0ms

rewrite32.0ms

series645.0ms

simplify160.0ms

prune142.0ms

localize11.0ms

rewrite54.0ms

series968.0ms

simplify248.0ms

prune327.0ms

localize12.0ms

rewrite34.0ms

series900.0ms

simplify113.0ms

prune76.0ms

localize14.0ms

rewrite64.0ms

series676.0ms

simplify198.0ms

prune164.0ms

regimes70.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample2.5s

Profiling