Details

analyze397.0ms

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

sample82.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
19.0ms	32×	body	1280	nan
10.0ms	71×	body	80	overflowed
9.0ms	20×	body	640	nan
5.0ms	17×	body	320	nan
1.0ms	24×	body	80	nan
0.0ms	6×	body	80	invalid
0.0ms	2×	body	160	nan

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5065	14

prune9.0ms

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: 0.4b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`
18×	`sqrt-prod_binary64`
14×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`prod-exp_binary64`
8×	`sqr-pow_binary64` `unpow-prod-down_binary64`
6×	`pow-prod-down_binary64` `associate-/r*_binary64` `difference-of-squares_binary64` `pow-exp_binary64`
5×	`associate-/l*_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `div-sub_binary64` `pow-sub_binary64` `div-inv_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 115

Calls

3 calls:

5.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

series60.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(.f64 (.f64 2 PI.f64) n)
34.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
23.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

simplify38.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5282	2253

prune174.0ms

Filtered

83 candidates to 124 candidates (-49.4%)

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

284×	`times-frac_binary64`
126×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
111×	`sqrt-prod_binary64`
33×	`add-exp-log_binary64`
28×	`sqr-pow_binary64` `unpow-prod-down_binary64`
24×	`associate-/l*_binary64`
20×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`pow-prod-down_binary64` `prod-exp_binary64`
8×	`div-inv_binary64`
6×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `sqrt-pow1_binary64` `pow-exp_binary64`
2×	`associate-r_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `associate-/l/_binary64` `pow1/2_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 241

Calls

4 calls:

8.0ms	(.f64 n (.f64 2 PI.f64))
5.0ms	(.f64 n (.f64 2 PI.f64))
16.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 n (.f64 2 PI.f64))
7.0ms	(.f64 n (.f64 2 PI.f64))
58.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
7.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

simplify77.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5122	7121

prune336.0ms

Filtered

164 candidates to 253 candidates (-54.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	254	10	264

Merged error: 0b

Counts

264 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

568×	`times-frac_binary64`
280×	`add-sqr-sqrt_binary64`
236×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
229×	`sqrt-prod_binary64`
149×	`associate-r_binary64`
56×	`sqr-pow_binary64`
55×	`add-exp-log_binary64`
52×	`unpow-prod-down_binary64`
24×	`associate-/l*_binary64`
23×	`add-cbrt-cube_binary64`
22×	`div-exp_binary64`
16×	`prod-exp_binary64`
15×	`div-inv_binary64`
14×	`pow1_binary64` `unswap-sqr_binary64`
9×	`associate-l_binary64`
6×	`associate-/r*_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64`
2×	`pow-to-exp_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 410

Calls

4 calls:

6.0ms	(.f64 n (.f64 2 PI.f64))
49.0ms	(.f64 (sqrt.f64 n) (/.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))
15.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
3.0ms	(sqrt.f64 (*.f64 2 PI.f64))

series122.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(.f64 n (.f64 2 PI.f64))
62.0ms	(.f64 (sqrt.f64 n) (/.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))
56.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 PI.f64)) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

simplify107.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5023	10737

prune608.0ms

Filtered

271 candidates to 420 candidates (-55.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	419	1	420
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	422	8	430

Merged error: 0b

Counts

430 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac_binary64`
104×	`add-exp-log_binary64`
90×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
68×	`sqrt-prod_binary64`
59×	`associate-r_binary64`
42×	`div-exp_binary64`
37×	`prod-exp_binary64`
32×	`add-cbrt-cube_binary64`
15×	`div-inv_binary64`
13×	`sqr-pow_binary64` `unpow-prod-down_binary64`
12×	`pow1_binary64` `pow-exp_binary64`
10×	`cbrt-undiv_binary64`
9×	`cbrt-unprod_binary64` `associate-l_binary64` `associate-/l*_binary64`
6×	`associate-/r*_binary64` `unswap-sqr_binary64`
4×	`pow-to-exp_binary64` `pow-prod-down_binary64` `add-log-exp_binary64`
2×	`*-commutative_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 221

Calls

4 calls:

5.0ms	(.f64 n (.f64 2 PI.f64))
30.0ms	(.f64 (sqrt.f64 n) (/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))
13.0ms	(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
2.0ms	(sqrt.f64 PI.f64)

series118.0ms

Counts

4 → 10

Calls

4 calls:

4.0ms	(.f64 n (.f64 2 PI.f64))
65.0ms	(.f64 (sqrt.f64 n) (/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))
49.0ms	(/.f64 (/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.0ms	(sqrt.f64 PI.f64)

simplify81.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5060	5235

prune241.0ms

Filtered

144 candidates to 231 candidates (-60.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	232	7	239

Merged error: 0b

Counts

239 → 7

regimes97.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	21
1	20	21

end0.0ms

sample2.5s

Algorithm

intervals

Results

713.0ms	8000×	body	80	valid
585.0ms	977×	body	1280	nan
373.0ms	816×	body	640	nan
347.0ms	2457×	body	80	overflowed
116.0ms	386×	body	320	nan
43.0ms	712×	body	80	nan
36.0ms	199×	body	160	nan
21.0ms	219×	body	80	invalid

Details

analyze397.0ms

sample82.0ms

simplify42.0ms

prune9.0ms

localize12.0ms

rewrite28.0ms

series60.0ms

simplify38.0ms

prune174.0ms

localize11.0ms

rewrite47.0ms

series76.0ms

simplify77.0ms

prune336.0ms

localize13.0ms

rewrite102.0ms

series122.0ms

simplify107.0ms

prune608.0ms

localize15.0ms

rewrite62.0ms

series118.0ms

simplify81.0ms

prune241.0ms

regimes97.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling