Details

analyze528.0ms (4.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4942	44
1	4942	44
0	2	2
1	2	2

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 (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
20.0ms	40×	body	1024	nan
12.0ms	79×	body	128	overflowed
7.0ms	20×	body	512	nan
3.0ms	14×	body	256	nan
2.0ms	27×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms (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)

localize14.0ms (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)
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite32.0ms (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:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
6.0ms	(/.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)

series267.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

171.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
78.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify90.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4989	3537
1	4989	3537

prune191.0ms (1.8%)

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

Merged error: 0.0b

Counts

126 → 12

Compiler

Compiled 3273 to 2241 computations (31.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-exp-log_binary64_798` `add-sqr-sqrt_binary64_782`
62×	`times-frac_binary64_766`
57×	`*-un-lft-identity_binary64_760`
44×	`add-cube-cbrt_binary64_795`
38×	`prod-exp_binary64_809`
25×	`sqrt-prod_binary64_776`
23×	`associate-l_binary64_701`
22×	`pow-unpow_binary64_837`
17×	`pow1_binary64_821`
16×	`add-cbrt-cube_binary64_796`
15×	`pow-exp_binary64_828`
12×	`div-exp_binary64_811`
10×	`unswap-sqr_binary64_728`
8×	`associate-r_binary64_700`
7×	`sqr-pow_binary64_732`
6×	`associate-/r*_binary64_704` `difference-of-squares_binary64_729` `rec-exp_binary64_810` `pow-prod-down_binary64_831` `1-exp_binary64_804`
5×	`pow-to-exp_binary64_829` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799`
3×	`div-inv_binary64_757` `associate-/l*_binary64_705` `distribute-lft-out--_binary64_712` `div-sub_binary64_765` `pow-pow_binary64_832` `pow-sub_binary64_836` `pow-flip_binary64_834`
2×	`cbrt-undiv_binary64_794` `*-commutative_binary64_691` `unpow-prod-down_binary64_839`
1×	`frac-2neg_binary64_771` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `inv-pow_binary64_845` `frac-times_binary64_770` `associate-r/_binary64_702` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 172

Calls

4 calls:

13.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(/.f64 1 (sqrt.f64 k))

series267.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
82.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
24.0ms	(/.f64 1 (sqrt.f64 k))
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4948	3852
1	4948	3852

prune238.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	181	3	184
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	186	10	196

Merged error: 0.0b

Counts

196 → 10

Compiler

Compiled 4300 to 2976 computations (30.8% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_798`
33×	`add-sqr-sqrt_binary64_782`
30×	`prod-exp_binary64_809`
26×	`*-un-lft-identity_binary64_760`
22×	`pow-unpow_binary64_837`
18×	`times-frac_binary64_766`
17×	`add-cube-cbrt_binary64_795` `pow-exp_binary64_828`
14×	`pow1_binary64_821`
10×	`add-cbrt-cube_binary64_796`
9×	`pow-to-exp_binary64_829`
8×	`associate-r_binary64_700` `associate-l_binary64_701` `sqr-pow_binary64_732`
7×	`unpow-prod-down_binary64_839`
6×	`unswap-sqr_binary64_728` `difference-of-squares_binary64_729` `pow-prod-down_binary64_831`
4×	`cbrt-unprod_binary64_793`
3×	`add-log-exp_binary64_799` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832`
2×	`div-sub_binary64_765` `*-commutative_binary64_691` `pow-sub_binary64_836`
1×	`div-inv_binary64_757` `associate-*r/_binary64_702`

Counts

3 → 100

Calls

3 calls:

10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series226.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

122.0ms	(.f64 (pow.f64 k -1/2) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
85.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
19.0ms	(.f64 (.f64 2 PI.f64) n)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4968	2580
1	4968	2580

prune152.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	111	8	119

Merged error: 0b

Counts

119 → 8

Compiler

Compiled 2616 to 1978 computations (24.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 1 (sqrt.f64 k)) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k)))
0.6b	(pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 1 (sqrt.f64 k)) 2))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`times-frac_binary64_766`
78×	`add-sqr-sqrt_binary64_782`
74×	`*-un-lft-identity_binary64_760`
57×	`unpow-prod-down_binary64_839`
56×	`add-cube-cbrt_binary64_795`
43×	`sqrt-prod_binary64_776`
37×	`add-exp-log_binary64_798`
36×	`pow-unpow_binary64_837`
19×	`pow-exp_binary64_828`
17×	`sqr-pow_binary64_732`
15×	`pow1_binary64_821`
12×	`prod-exp_binary64_809` `difference-of-squares_binary64_729`
11×	`add-cbrt-cube_binary64_796`
10×	`associate-/l*_binary64_705`
9×	`unpow-prod-up_binary64_838`
7×	`div-exp_binary64_811`
6×	`associate-/r*_binary64_704` `distribute-lft-out--_binary64_712` `pow-prod-down_binary64_831`
5×	`pow-to-exp_binary64_829`
4×	`add-log-exp_binary64_799` `pow-pow_binary64_832`
3×	`associate-r_binary64_700` `cbrt-unprod_binary64_793`
2×	`distribute-lft-out_binary64_711` `div-inv_binary64_757` `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

4 → 188

Calls

4 calls:

11.0ms	(pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 1 (sqrt.f64 k)) 2))
10.0ms	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 1 (sqrt.f64 k)) 2)) (sqrt.f64 k))
9.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k)))
5.0ms	(.f64 (.f64 2 PI.f64) n)

series3.7s (33.9%)

Counts

4 → 12

Calls

4 calls:

2.7s	(/.f64 (pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 1 (sqrt.f64 k)) 2)) (sqrt.f64 k))
823.0ms	(pow.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 1 (sqrt.f64 k)) 2))
154.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (+.f64 1 (sqrt.f64 k)))
18.0ms	(.f64 (.f64 2 PI.f64) n)

simplify199.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4994	18833
1	4994	18833

prune806.0ms (7.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	200	8	208

Merged error: 0b

Counts

208 → 8

Compiler

Compiled 12781 to 8450 computations (33.9% saved)

regimes358.0ms (3.3%)

Compiler: Compiled 4398 to 3730 computations (15.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	23
1	27	23

end0.0ms (0%)

sample3.3s (30.6%)

Algorithm

1×

intervals

Results

630.0ms	1393×	body	1024	nan
611.0ms	8000×	body	128	valid
339.0ms	2379×	body	128	overflowed
215.0ms	679×	body	512	nan
68.0ms	359×	body	256	nan
57.0ms	965×	body	128	nan
22.0ms	245×	body	128	invalid

Compiler

Compiled 1120 to 952 computations (15% saved)

Details

analyze528.0ms (4.9%)

sample76.0ms (0.7%)

simplify52.0ms (0.5%)

prune5.0ms (0%)

localize14.0ms (0.1%)

rewrite32.0ms (0.3%)

series267.0ms (2.5%)

simplify90.0ms (0.8%)

prune191.0ms (1.8%)

localize14.0ms (0.1%)

rewrite47.0ms (0.4%)

series267.0ms (2.5%)

simplify102.0ms (0.9%)

prune238.0ms (2.2%)

localize19.0ms (0.2%)

rewrite33.0ms (0.3%)

series226.0ms (2.1%)

simplify70.0ms (0.6%)

prune152.0ms (1.4%)

localize14.0ms (0.1%)

rewrite56.0ms (0.5%)

series3.7s (33.9%)

simplify199.0ms (1.8%)

prune806.0ms (7.4%)

regimes358.0ms (3.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (30.6%)

Profiling