Details

analyze515.0ms (4.1%)

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)

sample65.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
10.0ms	22×	body	1024	nan
9.0ms	69×	body	128	overflowed
7.0ms	24×	body	512	nan
2.0ms	13×	body	256	nan
2.0ms	36×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify52.0ms (0.4%)

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

Error

0.3b

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

rewrite210.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64_766`
42×	`add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
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×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
6×	`pow-prod-down_binary64_831` `difference-of-squares_binary64_729` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700` `distribute-lft-out--_binary64_712` `pow-pow_binary64_832`
2×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836` `pow-to-exp_binary64_829`
1×	`associate-l_binary64_701` `*-commutative_binary64_691` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

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))
6.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series426.0ms (3.4%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

202.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
172.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
29.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune181.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.0b

Counts

135 → 9

Compiler

Compiled 3078 to 1940 computations (37% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
0.2b	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.2b	(*.f64 n PI.f64)
0.2b	(*.f64 n PI.f64)

rewrite493.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
132×	`add-sqr-sqrt_binary64_782`
128×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
28×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
27×	`add-exp-log_binary64_798`
24×	`associate-/l*_binary64_705`
14×	`pow1_binary64_821`
13×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
8×	`div-inv_binary64_757`
6×	`associate-l_binary64_701` `associate-r_binary64_700` `associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831` `prod-exp_binary64_809`
4×	`add-log-exp_binary64_799`
3×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778`
2×	`cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`
1×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `pow1/2_binary64_840`

Counts

4 → 241

Calls

4 calls:

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

Compiler

Compiled 8806 to 4891 computations (44.5% saved)

series235.0ms (1.9%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

153.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
24.0ms	(sqrt.f64 (.f64 2 (.f64 n PI.f64)))
23.0ms	(*.f64 n PI.f64)
22.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1094 to 837 computations (23.5% saved)

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5004	11439

prune486.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	258	7	265

Error

Counts

265 → 7

Compiler

Compiled 8772 to 5412 computations (38.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.1s (8.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

568×	`times-frac_binary64_766`
284×	`add-sqr-sqrt_binary64_782`
238×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
228×	`sqrt-prod_binary64_776`
152×	`associate-r_binary64_700`
57×	`add-exp-log_binary64_798`
56×	`sqr-pow_binary64_732`
52×	`unpow-prod-down_binary64_839`
25×	`add-cbrt-cube_binary64_796`
24×	`associate-/l*_binary64_705`
22×	`div-exp_binary64_811`
17×	`prod-exp_binary64_809`
15×	`unswap-sqr_binary64_728` `div-inv_binary64_757`
13×	`pow1_binary64_821`
12×	`associate-l_binary64_701`
7×	`cbrt-unprod_binary64_793`
6×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `associate-/r*_binary64_704`
5×	`pow-prod-down_binary64_831`
4×	`add-log-exp_binary64_799`
3×	`*-commutative_binary64_691`
2×	`pow-to-exp_binary64_829`
1×	`associate-*r/_binary64_702` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 417

Calls

4 calls:

55.0ms	(.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k)))
14.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
5.0ms	(.f64 n (.f64 PI.f64 2))
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 16129 to 8681 computations (46.2% saved)

series367.0ms (2.9%)

Error

Counts

4 → 18

Calls

4 calls:

166.0ms	(.f64 (sqrt.f64 2) (/.f64 (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k)))
130.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
32.0ms	(.f64 n (.f64 PI.f64 2))
23.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1461 to 1133 computations (22.5% saved)

simplify220.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4984	17585
1	4984	17585

prune803.0ms (6.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	435	7	442

Error

Counts

442 → 7

Compiler

Compiled 15585 to 8241 computations (47.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 n (.f64 PI.f64 2))
0.2b	(/.f64 (/.f64 (sqrt.f64 PI.f64) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 n))
1.0b	(sqrt.f64 PI.f64)

rewrite774.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

414×	`times-frac_binary64_766`
223×	`sqrt-prod_binary64_776`
208×	`add-sqr-sqrt_binary64_782`
199×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
42×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
34×	`associate-/l*_binary64_705`
30×	`add-exp-log_binary64_798`
16×	`add-cbrt-cube_binary64_796`
14×	`pow1_binary64_821`
11×	`div-exp_binary64_811`
9×	`associate-l_binary64_701`
8×	`div-inv_binary64_757`
7×	`prod-exp_binary64_809` `associate-r_binary64_700`
6×	`pow-prod-down_binary64_831` `associate-/r*_binary64_704`
4×	`add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728`
3×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `pow-exp_binary64_828` `cbrt-undiv_binary64_794`
2×	`*-commutative_binary64_691`
1×	`rem-sqrt-square_binary64_773` `sqrt-unprod_binary64_780` `pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 324

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (sqrt.f64 PI.f64) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 n))
5.0ms	(.f64 n (.f64 PI.f64 2))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 12193 to 6856 computations (43.8% saved)

series296.0ms (2.3%)

Error

Counts

4 → 12

Calls

4 calls:

236.0ms	(/.f64 (/.f64 (sqrt.f64 PI.f64) (pow.f64 (.f64 n (.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
26.0ms	(.f64 n (.f64 PI.f64 2))
23.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 n))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 877 to 695 computations (20.8% saved)

simplify166.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5236	13469

prune685.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	336	7	343

Error

Counts

343 → 7

Compiler

Compiled 11622 to 6448 computations (44.5% saved)

regimes759.0ms (6%)

Accuracy

Total 0.5b remaining (99.8%)

Threshold costs 0.5b (99.8%)

Compiler

Compiled 10286 to 8286 computations (19.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	32
1	18	32

end0.0ms (0%)

sample4.5s (35.7%)

Algorithm

1×

intervals

Results

599.0ms	8000×	body	128	valid
568.0ms	1282×	body	1024	nan
310.0ms	2269×	body	128	overflowed
200.0ms	652×	body	512	nan
63.0ms	1031×	body	128	nan
57.0ms	289×	body	256	nan
20.0ms	233×	body	128	invalid

Compiler

Compiled 2597 to 2094 computations (19.4% saved)

Details

analyze515.0ms (4.1%)

sample65.0ms (0.5%)

simplify52.0ms (0.4%)

prune5.0ms (0%)

localize14.0ms (0.1%)

rewrite210.0ms (1.7%)

series426.0ms (3.4%)

simplify94.0ms (0.7%)

prune181.0ms (1.4%)

localize12.0ms (0.1%)

rewrite493.0ms (3.9%)

series235.0ms (1.9%)

simplify141.0ms (1.1%)

prune486.0ms (3.8%)

localize13.0ms (0.1%)

rewrite1.1s (8.7%)

series367.0ms (2.9%)

simplify220.0ms (1.7%)

prune803.0ms (6.4%)

localize19.0ms (0.1%)

rewrite774.0ms (6.1%)

series296.0ms (2.3%)

simplify166.0ms (1.3%)

prune685.0ms (5.4%)

regimes759.0ms (6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.5s (35.7%)

Profiling