Details

analyze570.0ms (3.3%)

Algorithm

1×

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

Compiler

Compiled 17 to 16 computations (5.9% saved)

sample68.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
13.0ms	30×	body	1024	nan
10.0ms	77×	body	128	overflowed
7.0ms	24×	body	512	nan
2.0ms	14×	body	256	nan
2.0ms	37×	body	128	nan
1.0ms	9×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify142.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune4.0ms (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

Error

0.6b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_766`
42×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
33×	`add-cube-cbrt_binary64_795`
26×	`add-exp-log_binary64_798`
22×	`pow-unpow_binary64_837`
18×	`sqrt-prod_binary64_776`
14×	`pow1_binary64_821`
10×	`add-cbrt-cube_binary64_796`
9×	`prod-exp_binary64_809`
8×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
6×	`associate-/r*_binary64_704` `pow-exp_binary64_828` `difference-of-squares_binary64_729` `pow-prod-down_binary64_831`
5×	`associate-/l*_binary64_705` `div-exp_binary64_811`
3×	`add-log-exp_binary64_799` `distribute-lft-out--_binary64_712` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-pow_binary64_832`
2×	`div-inv_binary64_757` `pow-to-exp_binary64_829` `div-sub_binary64_765` `pow-sub_binary64_836`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `associate-l_binary64_701` `clear-num_binary64_759` `*-commutative_binary64_691`

Counts

3 → 115

Calls

3 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series270.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

163.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
88.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
19.0ms	(.f64 (.f64 2 PI.f64) n)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune193.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	11	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	12	126

Error

0.0b

Counts

126 → 12

Compiler

Compiled 3214 to 2205 computations (31.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64_798`
67×	`prod-exp_binary64_809`
36×	`pow-exp_binary64_828`
30×	`div-exp_binary64_811`
20×	`pow1_binary64_821`
19×	`add-cbrt-cube_binary64_796`
15×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
14×	`times-frac_binary64_766`
13×	`pow-unpow_binary64_837`
12×	`pow-to-exp_binary64_829`
9×	`pow-prod-down_binary64_831`
7×	`cbrt-unprod_binary64_793`
6×	`associate-r_binary64_700`
5×	`associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839` `pow-pow_binary64_832`
2×	`cbrt-undiv_binary64_794` `div-inv_binary64_757` `associate-l_binary64_701` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `associate-/r*_binary64_704` `clear-num_binary64_759`

Counts

4 → 118

Calls

4 calls:

9.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

series384.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

231.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
115.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
20.0ms	(.f64 (.f64 2 PI.f64) n)
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5259	2652

prune177.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	131	11	142

Error

0.0b

Counts

142 → 11

Compiler

Compiled 3358 to 2336 computations (30.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
0.4b	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
0.6b	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

rewrite112.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

565×	`times-frac_binary64_766`
283×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
265×	`add-cube-cbrt_binary64_795`
181×	`unpow-prod-down_binary64_839`
150×	`sqrt-prod_binary64_776`
93×	`sqr-pow_binary64_732`
54×	`associate-/r*_binary64_704`
53×	`add-exp-log_binary64_798`
44×	`pow-unpow_binary64_837`
31×	`div-exp_binary64_811`
16×	`pow-exp_binary64_828`
12×	`difference-of-squares_binary64_729`
11×	`add-cbrt-cube_binary64_796` `associate-/l*_binary64_705` `pow-to-exp_binary64_829`
10×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836`
8×	`associate-/r/_binary64_706` `pow1_binary64_821`
6×	`distribute-lft-out--_binary64_712`
5×	`prod-exp_binary64_809`
4×	`cbrt-undiv_binary64_794` `add-log-exp_binary64_799`
3×	`pow-pow_binary64_832`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`associate-/l/_binary64_707` `pow-prod-down_binary64_831`

Counts

4 → 461

Calls

4 calls:

21.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
8.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))
6.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
6.0ms	(/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))

series390.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
92.0ms	(/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
53.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
21.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

simplify195.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

473 → 473

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5149	21867

prune1.3s (7.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	472	1	473
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	474	10	484

Error

Counts

484 → 10

Compiler

Compiled 17247 to 11846 computations (31.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2))))
0.3b	(.f64 (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2)))))
0.3b	(*.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2)))
0.6b	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

rewrite431.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1828×	`times-frac_binary64_766`
955×	`unpow-prod-down_binary64_839`
894×	`add-sqr-sqrt_binary64_782`
877×	`*-un-lft-identity_binary64_760`
868×	`add-cube-cbrt_binary64_795`
726×	`sqrt-prod_binary64_776`
482×	`add-exp-log_binary64_798`
470×	`associate-r_binary64_700`
256×	`prod-exp_binary64_809`
231×	`sqr-pow_binary64_732` `div-exp_binary64_811`
162×	`pow-exp_binary64_828` `pow-to-exp_binary64_829`
65×	`associate-/r*_binary64_704`
32×	`add-cbrt-cube_binary64_796`
29×	`div-sub_binary64_765` `pow-sub_binary64_836`
22×	`pow-unpow_binary64_837`
18×	`div-inv_binary64_757`
17×	`associate-/r/_binary64_706`
12×	`unswap-sqr_binary64_728`
10×	`cbrt-unprod_binary64_793`
9×	`cbrt-undiv_binary64_794`
8×	`associate-l_binary64_701`
7×	`associate-/l*_binary64_705` `pow1_binary64_821`
6×	`associate-*l/_binary64_703` `difference-of-squares_binary64_729` `frac-times_binary64_770`
4×	`add-log-exp_binary64_799` `associate-*r/_binary64_702`
3×	`distribute-lft-out--_binary64_712`
2×	`pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `clear-num_binary64_759` `pow-pow_binary64_832`

Counts

4 → 1254

Calls

4 calls:

102.0ms	(.f64 (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2)))))
24.0ms	(/.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2))))
9.0ms	(*.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2)))
9.0ms	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

series934.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

493.0ms	(.f64 (.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2)))))
245.0ms	(/.f64 (pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2))))
180.0ms	(*.f64 (pow.f64 2 (/.f64 (-.f64 1 k) 2)) (pow.f64 (sqrt.f64 n) (/.f64 (-.f64 1 k) 2)))
15.0ms	(pow.f64 PI.f64 (/.f64 (-.f64 1 k) 2))

simplify575.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1266 → 1266

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5309	69601

prune7.4s (43.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1266	0	1266
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	1266	10	1276

Error

Counts

1276 → 10

Compiler

Compiled 67333 to 43819 computations (34.9% saved)

regimes462.0ms (2.7%)

Accuracy

Total 0.5b remaining (99.1%)

Threshold costs 0.5b (99.1%)

Compiler

Compiled 5990 to 5015 computations (16.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	40
1	26	40

end0.0ms (0%)

sample3.4s (19.6%)

Algorithm

1×

intervals

Results

618.0ms	8000×	body	128	valid
602.0ms	1324×	body	1024	nan
313.0ms	2315×	body	128	overflowed
223.0ms	685×	body	512	nan
64.0ms	365×	body	256	nan
54.0ms	916×	body	128	nan
24.0ms	234×	body	128	invalid

Compiler

Compiled 1295 to 1086 computations (16.1% saved)

Details

analyze570.0ms (3.3%)

sample68.0ms (0.4%)

simplify142.0ms (0.8%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite31.0ms (0.2%)

series270.0ms (1.6%)

simplify82.0ms (0.5%)

prune193.0ms (1.1%)

localize14.0ms (0.1%)

rewrite40.0ms (0.2%)

series384.0ms (2.2%)

simplify58.0ms (0.3%)

prune177.0ms (1%)

localize12.0ms (0.1%)

rewrite112.0ms (0.6%)

series390.0ms (2.3%)

simplify195.0ms (1.1%)

prune1.3s (7.4%)

localize16.0ms (0.1%)

rewrite431.0ms (2.5%)

series934.0ms (5.4%)

simplify575.0ms (3.3%)

prune7.4s (43.1%)

regimes462.0ms (2.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (19.6%)

Profiling