Details

analyze392.0ms (4.1%)

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)

sample76.0ms (0.8%)

Algorithm

1×

intervals

Results

23.0ms	52×	body	1024	nan
20.0ms	256×	body	128	valid
10.0ms	74×	body	128	overflowed
5.0ms	18×	body	512	nan
2.0ms	38×	body	128	nan
2.0ms	10×	body	256	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify141.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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

Merged error: 0.5b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (0.1%)

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))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite34.0ms (0.3%)

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:

11.0ms	(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)

series450.0ms (4.7%)

Counts

3 → 18

Calls

3 calls:

220.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
206.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
23.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 707 to 610 computations (13.7% saved)

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5050	3480

prune196.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	10	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Merged error: 0.0b

Counts

135 → 10

Compiler

Compiled 3154 to 2155 computations (31.7% saved)

localize13.0ms (0.1%)

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))
0.3b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

293×	`times-frac_binary64_766`
132×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
111×	`sqrt-prod_binary64_776`
34×	`add-exp-log_binary64_798`
29×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
24×	`associate-/l*_binary64_705`
21×	`pow1_binary64_821`
14×	`add-cbrt-cube_binary64_796`
13×	`pow-unpow_binary64_837`
11×	`div-exp_binary64_811`
9×	`prod-exp_binary64_809` `div-inv_binary64_757` `pow-prod-down_binary64_831`
6×	`associate-/r*_binary64_704` `pow-exp_binary64_828`
4×	`add-log-exp_binary64_799`
3×	`cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `associate-r_binary64_700` `cbrt-unprod_binary64_793` `pow-pow_binary64_832`
2×	`pow-to-exp_binary64_829`
1×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `associate-l_binary64_701` `pow1/2_binary64_840` `clear-num_binary64_759` `*-commutative_binary64_691`

Counts

4 → 252

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
6.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series370.0ms (3.8%)

Counts

4 → 21

Calls

4 calls:

163.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))
148.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
29.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
29.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1016 to 848 computations (16.5% saved)

simplify170.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4971	11997
1	4971	11997

prune587.0ms (6.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	273	10	283

Merged error: 0.0b

Counts

283 → 10

Compiler

Compiled 9195 to 5957 computations (35.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 n (/.f64 (-.f64 1 k) 2))
0.3b	(/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
0.3b	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
0.7b	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

rewrite112.0ms (1.2%)

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:

19.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
9.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))
7.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
6.0ms	(/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))

series766.0ms (7.9%)

Counts

4 → 27

Calls

4 calls:

345.0ms	(/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))))
213.0ms	(/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
149.0ms	(pow.f64 n (/.f64 (-.f64 1 k) 2))
58.0ms	(pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2))

Compiler

Compiled 1377 to 1205 computations (12.5% saved)

simplify225.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4973	21863
1	4973	21863

prune1.4s (14%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	487	1	488
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	490	8	498

Merged error: 0b

Counts

498 → 8

Compiler

Compiled 17296 to 11837 computations (31.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

15.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
12.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
9.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
7.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

series605.0ms (6.3%)

Counts

4 → 21

Calls

4 calls:

391.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
169.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
26.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
19.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

Compiler

Compiled 961 to 827 computations (13.9% saved)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4993	3942
1	4993	3942

prune199.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	166	8	174

Merged error: 0b

Counts

174 → 8

Compiler

Compiled 3725 to 2393 computations (35.8% saved)

regimes412.0ms (4.3%)

Compiler: Compiled 5077 to 4261 computations (16.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	40
1	26	40

end0.0ms (0%)

sample3.3s (33.9%)

Algorithm

1×

intervals

Results

647.0ms	8000×	body	128	valid
635.0ms	1352×	body	1024	nan
330.0ms	2336×	body	128	overflowed
216.0ms	665×	body	512	nan
68.0ms	362×	body	256	nan
56.0ms	980×	body	128	nan
24.0ms	248×	body	128	invalid

Compiler

Compiled 1096 to 923 computations (15.8% saved)

Details

analyze392.0ms (4.1%)

sample76.0ms (0.8%)

simplify141.0ms (1.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite34.0ms (0.3%)

series450.0ms (4.7%)

simplify57.0ms (0.6%)

prune196.0ms (2%)

localize13.0ms (0.1%)

rewrite66.0ms (0.7%)

series370.0ms (3.8%)

simplify170.0ms (1.8%)

prune587.0ms (6.1%)

localize13.0ms (0.1%)

rewrite112.0ms (1.2%)

series766.0ms (7.9%)

simplify225.0ms (2.3%)

prune1.4s (14%)

localize13.0ms (0.1%)

rewrite57.0ms (0.6%)

series605.0ms (6.3%)

simplify67.0ms (0.7%)

prune199.0ms (2.1%)

regimes412.0ms (4.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (33.9%)

Profiling