Details

analyze1.3s (9.4%)

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)

sample125.0ms (0.9%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
33.0ms	42×	body	1024	nan
15.0ms	27×	body	512	nan
15.0ms	62×	body	128	overflowed
3.0ms	29×	body	128	nan
3.0ms	8×	body	256	nan
2.0ms	10×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune9.0ms (0.1%)

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)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite71.0ms (0.5%)

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:

19.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
18.0ms	(.f64 (.f64 2 PI.f64) n)
13.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

series680.0ms (5.1%)

Counts

3 → 18

Calls

3 calls:

342.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
289.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
49.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify179.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune335.0ms (2.5%)

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

Error

0.0b

Counts

135 → 10

Compiler

Compiled 3068 to 2078 computations (32.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.2b	(/.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	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite122.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

284×	`times-frac_binary64_766`
126×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
111×	`sqrt-prod_binary64_776`
33×	`add-exp-log_binary64_798`
28×	`sqr-pow_binary64_732` `unpow-prod-down_binary64_839`
24×	`associate-/l*_binary64_705`
20×	`pow1_binary64_821`
19×	`add-cbrt-cube_binary64_796`
11×	`div-exp_binary64_811`
9×	`prod-exp_binary64_809` `pow-prod-down_binary64_831`
8×	`div-inv_binary64_757`
6×	`associate-/r_binary64_704` `associate-r*_binary64_700` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799`
3×	`cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `pow-exp_binary64_828`
2×	`associate-l_binary64_701` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `pow-to-exp_binary64_829` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 241

Calls

4 calls:

30.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
11.0ms	(.f64 (.f64 2 PI.f64) n)
10.0ms	(.f64 (.f64 2 PI.f64) n)
7.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series447.0ms (3.3%)

Counts

4 → 15

Calls

4 calls:

280.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
66.0ms	(.f64 (.f64 2 PI.f64) n)
56.0ms	(.f64 (.f64 2 PI.f64) n)
45.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 804 to 671 computations (16.5% saved)

simplify309.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5032	11499

prune912.0ms (6.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	256	10	266

Error

Counts

266 → 10

Compiler

Compiled 8731 to 5653 computations (35.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.2b	(sqrt.f64 (/.f64 1 k))
0.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
27×	`*-un-lft-identity_binary64_760`
26×	`times-frac_binary64_766`
23×	`add-cube-cbrt_binary64_795`
19×	`associate-r_binary64_700`
17×	`pow1_binary64_821`
14×	`add-exp-log_binary64_798`
13×	`associate-l_binary64_701`
12×	`unswap-sqr_binary64_728`
11×	`add-cbrt-cube_binary64_796`
8×	`unpow-prod-down_binary64_839`
6×	`prod-exp_binary64_809` `sqrt-pow1_binary64_778` `pow-prod-down_binary64_831`
5×	`sqr-pow_binary64_732`
4×	`unpow-prod-up_binary64_838` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`rem-sqrt-square_binary64_773` `cancel-sign-sub-inv_binary64_726` `sqrt-div_binary64_777`
2×	`div-inv_binary64_757` `pow1/2_binary64_840` `*-commutative_binary64_691` `pow-sub_binary64_836`
1×	`associate-l/_binary64_703` `pow-exp_binary64_828` `inv-pow_binary64_845` `pow-to-exp_binary64_829` `frac-times_binary64_770` `associate-r/_binary64_702` `sub-neg_binary64_753` `pow-flip_binary64_834`

Counts

4 → 113

Calls

4 calls:

27.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
10.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
5.0ms	(sqrt.f64 (/.f64 1 k))

series312.0ms (2.3%)

Counts

4 → 15

Calls

4 calls:

206.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
46.0ms	(.f64 (.f64 2 PI.f64) n)
35.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
24.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 733 to 622 computations (15.1% saved)

simplify138.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5025	2502

prune265.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	130	8	138

Error

Counts

138 → 8

Compiler

Compiled 2820 to 2090 computations (25.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite103.0ms (0.8%)

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:

29.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
19.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
16.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
12.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

series631.0ms (4.7%)

Counts

4 → 21

Calls

4 calls:

291.0ms	(/.f64 (pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
253.0ms	(pow.f64 (.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 (-.f64 1 k) 2))
48.0ms	(.f64 (.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
39.0ms	(.f64 (.f64 2 PI.f64) (sqrt.f64 n))

Compiler

Compiled 949 to 815 computations (14.1% saved)

simplify173.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5397	3839

prune337.0ms (2.5%)

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

Error

Counts

174 → 8

Compiler

Compiled 3635 to 2306 computations (36.6% saved)

regimes692.0ms (5.2%)

Accuracy

Total 0.4b remaining (99.5%)

Threshold costs 0.4b (99.5%)

Compiler

Compiled 4338 to 3602 computations (17% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	22
1	25	22

end0.0ms (0%)

sample6.1s (45.1%)

Algorithm

1×

intervals

Results

1.1s	1321×	body	1024	nan
1.1s	8000×	body	128	valid
578.0ms	2309×	body	128	overflowed
357.0ms	627×	body	512	nan
112.0ms	971×	body	128	nan
108.0ms	336×	body	256	nan
37.0ms	228×	body	128	invalid

Compiler

Compiled 1104 to 919 computations (16.8% saved)

Details

analyze1.3s (9.4%)

sample125.0ms (0.9%)

simplify98.0ms (0.7%)

prune9.0ms (0.1%)

localize22.0ms (0.2%)

rewrite71.0ms (0.5%)

series680.0ms (5.1%)

simplify179.0ms (1.3%)

prune335.0ms (2.5%)

localize23.0ms (0.2%)

rewrite122.0ms (0.9%)

series447.0ms (3.3%)

simplify309.0ms (2.3%)

prune912.0ms (6.8%)

localize21.0ms (0.2%)

rewrite66.0ms (0.5%)

series312.0ms (2.3%)

simplify138.0ms (1%)

prune265.0ms (2%)

localize23.0ms (0.2%)

rewrite103.0ms (0.8%)

series631.0ms (4.7%)

simplify173.0ms (1.3%)

prune337.0ms (2.5%)

regimes692.0ms (5.2%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.1s (45.1%)

Profiling