Details

analyze520.0ms (5.2%)

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)

sample74.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
17.0ms	36×	body	1024	nan
13.0ms	60×	body	128	overflowed
6.0ms	18×	body	512	nan
2.0ms	33×	body	128	nan
1.0ms	3×	body	256	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

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

0.3b

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	(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))
0.2b	(.f64 (.f64 2 PI.f64) n)

rewrite202.0ms (2%)

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` `pow-exp_binary64_828` `associate-/r*_binary64_704` `difference-of-squares_binary64_729`
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×	`pow-to-exp_binary64_829` `div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836`
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))
5.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series414.0ms (4.2%)

Error

0.1b

Counts

3 → 18

Calls

3 calls:

188.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
175.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
28.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune177.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	126	7	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	7	135

Error

0.0b

Counts

135 → 7

Compiler

Compiled 3002 to 1883 computations (37.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite219.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

124×	`add-exp-log_binary64_798`
65×	`prod-exp_binary64_809`
36×	`pow-exp_binary64_828`
30×	`div-exp_binary64_811`
18×	`add-sqr-sqrt_binary64_782`
17×	`pow1_binary64_821`
16×	`add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
14×	`times-frac_binary64_766`
13×	`pow-unpow_binary64_837`
12×	`pow-to-exp_binary64_829`
7×	`pow-prod-down_binary64_831`
6×	`associate-r_binary64_700`
5×	`cbrt-unprod_binary64_793` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799` `associate-l_binary64_701`
3×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732` `pow-pow_binary64_832`
2×	`*-commutative_binary64_691` `cbrt-undiv_binary64_794` `div-inv_binary64_757`
1×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r*_binary64_704`

Counts

4 → 118

Calls

4 calls:

10.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 3457 to 2289 computations (33.8% saved)

series307.0ms (3.1%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

147.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
95.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
30.0ms	(.f64 (.f64 2 PI.f64) n)
22.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1100 to 849 computations (22.8% saved)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4999	2500
1	4999	2500

prune166.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	133	7	140

Error

Counts

140 → 7

Compiler

Compiled 3204 to 1997 computations (37.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite393.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

419×	`add-exp-log_binary64_798`
300×	`prod-exp_binary64_809`
111×	`pow-exp_binary64_828`
72×	`div-exp_binary64_811`
37×	`pow-to-exp_binary64_829`
36×	`1-exp_binary64_804` `rec-exp_binary64_810`
25×	`add-cbrt-cube_binary64_796`
17×	`add-sqr-sqrt_binary64_782`
13×	`associate-r_binary64_700`
12×	`pow1_binary64_821` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
9×	`cbrt-unprod_binary64_793` `associate-l_binary64_701`
6×	`times-frac_binary64_766`
4×	`pow-prod-down_binary64_831` `add-log-exp_binary64_799` `cbrt-undiv_binary64_794`
3×	`-commutative_binary64_691` `unswap-sqr_binary64_728` `associate-/l_binary64_705`
2×	`sqr-pow_binary64_732` `div-inv_binary64_757`
1×	`un-div-inv_binary64_758` `associate-r/_binary64_702` `unpow-prod-down_binary64_839` `inv-pow_binary64_845` `pow-flip_binary64_834` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r_binary64_704`

Counts

4 → 197

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))
8.0ms	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
7.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 6082 to 4056 computations (33.3% saved)

series443.0ms (4.4%)

Error

Counts

4 → 18

Calls

4 calls:

227.0ms	(/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
143.0ms	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 1 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))
32.0ms	(.f64 (.f64 2 PI.f64) n)
23.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1428 to 1139 computations (20.2% saved)

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4973	4801
1	4973	4801

prune275.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	215	7	222

Error

Counts

222 → 7

Compiler

Compiled 4928 to 3134 computations (36.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite713.0ms (7.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

245×	`times-frac_binary64_766`
175×	`add-sqr-sqrt_binary64_782`
138×	`associate-r_binary64_700` `sqrt-prod_binary64_776`
118×	`*-un-lft-identity_binary64_760`
112×	`add-cube-cbrt_binary64_795`
75×	`add-exp-log_binary64_798`
74×	`unpow-prod-down_binary64_839`
39×	`prod-exp_binary64_809` `sqr-pow_binary64_732`
27×	`unswap-sqr_binary64_728`
20×	`pow-exp_binary64_828`
17×	`pow1_binary64_821`
16×	`add-cbrt-cube_binary64_796`
15×	`div-exp_binary64_811`
13×	`pow-unpow_binary64_837`
10×	`pow-to-exp_binary64_829` `div-inv_binary64_757`
9×	`associate-l_binary64_701`
7×	`pow-prod-down_binary64_831`
6×	`cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799`
3×	`*-commutative_binary64_691` `pow-pow_binary64_832`
1×	`cbrt-undiv_binary64_794` `associate-*r/_binary64_702`

Counts

4 → 259

Calls

4 calls:

48.0ms	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) k)))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 10002 to 7049 computations (29.5% saved)

series337.0ms (3.4%)

Error

Counts

4 → 15

Calls

4 calls:

178.0ms	(.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (/.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (.f64 2 (*.f64 n PI.f64))) k)))
91.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
27.0ms	(.f64 (.f64 2 PI.f64) n)
24.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1130 to 845 computations (25.2% saved)

simplify144.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4963	8543
1	4963	8543

prune577.0ms (5.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	274	7	281

Error

Counts

281 → 7

Compiler

Compiled 8796 to 5659 computations (35.7% saved)

regimes603.0ms (6%)

Accuracy

Total 0.4b remaining (99.3%)

Threshold costs 0.4b (99.3%)

Compiler

Compiled 7233 to 6001 computations (17% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	32
1	23	32

end0.0ms (0%)

sample4.0s (40.4%)

Algorithm

1×

intervals

Results

625.0ms	8000×	body	128	valid
619.0ms	1323×	body	1024	nan
324.0ms	2378×	body	128	overflowed
201.0ms	642×	body	512	nan
62.0ms	331×	body	256	nan
56.0ms	1011×	body	128	nan
21.0ms	233×	body	128	invalid

Compiler

Compiled 1680 to 1397 computations (16.8% saved)

Details

analyze520.0ms (5.2%)

sample74.0ms (0.7%)

simplify53.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite202.0ms (2%)

series414.0ms (4.2%)

simplify97.0ms (1%)

prune177.0ms (1.8%)

localize19.0ms (0.2%)

rewrite219.0ms (2.2%)

series307.0ms (3.1%)

simplify69.0ms (0.7%)

prune166.0ms (1.7%)

localize17.0ms (0.2%)

rewrite393.0ms (3.9%)

series443.0ms (4.4%)

simplify94.0ms (0.9%)

prune275.0ms (2.8%)

localize17.0ms (0.2%)

rewrite713.0ms (7.2%)

series337.0ms (3.4%)

simplify144.0ms (1.4%)

prune577.0ms (5.8%)

regimes603.0ms (6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.0s (40.4%)

Profiling