Details

analyze532.0ms (2.1%)

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)

sample84.0ms (0.3%)

Algorithm

1×

intervals

Results

23.0ms	45×	body	1024	nan
20.0ms	256×	body	128	valid
12.0ms	85×	body	128	overflowed
5.0ms	17×	body	512	nan
3.0ms	18×	body	256	nan
2.0ms	32×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

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)

localize11.0ms (0%)

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)

rewrite194.0ms (0.8%)

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)

series421.0ms (1.7%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

210.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
159.0ms	(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)

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune177.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.0b

Counts

135 → 9

Compiler

Compiled 3062 to 1922 computations (37.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(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)

rewrite209.0ms (0.8%)

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:

9.0ms	(/.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))))
6.0ms	(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)

series292.0ms (1.2%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

135.0ms	(/.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))))
93.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
28.0ms	(.f64 (.f64 2 PI.f64) n)
22.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1100 to 849 computations (22.8% saved)

simplify76.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4999	2500
1	4999	2500

prune166.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Error

Counts

142 → 8

Compiler

Compiled 3248 to 2019 computations (37.8% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite3.5s (14%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1787×	`times-frac_binary64_766`
718×	`add-sqr-sqrt_binary64_782`
714×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
518×	`sqrt-prod_binary64_776`
173×	`associate-/r*_binary64_704`
124×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
94×	`add-exp-log_binary64_798`
58×	`div-exp_binary64_811`
37×	`div-inv_binary64_757`
22×	`add-cbrt-cube_binary64_796`
14×	`prod-exp_binary64_809`
12×	`pow-exp_binary64_828`
9×	`pow1_binary64_821` `cbrt-undiv_binary64_794` `associate-/l*_binary64_705`
7×	`1-exp_binary64_804` `rec-exp_binary64_810`
6×	`associate-l_binary64_701` `associate-r_binary64_700` `associate-/r/_binary64_706`
4×	`add-log-exp_binary64_799` `pow-to-exp_binary64_829`
2×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`inv-pow_binary64_845` `pow-flip_binary64_834`

Counts

4 → 865

Calls

4 calls:

41.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))
15.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 38180 to 22883 computations (40.1% saved)

series337.0ms (1.4%)

Error

Counts

4 → 18

Calls

4 calls:

147.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2)))))
129.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))
22.0ms	(*.f64 n PI.f64)
20.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1504 to 1180 computations (21.5% saved)

simplify421.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

883 → 883

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5480	48568

prune2.8s (11.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	882	1	883
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	883	8	891

Error

Counts

891 → 8

Compiler

Compiled 35023 to 20108 computations (42.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite5.0s (20.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3026×	`times-frac_binary64_766`
1274×	`sqrt-prod_binary64_776`
1195×	`add-sqr-sqrt_binary64_782`
1191×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
196×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
173×	`associate-/r*_binary64_704`
58×	`div-inv_binary64_757`
54×	`add-exp-log_binary64_798`
29×	`div-exp_binary64_811`
22×	`add-cbrt-cube_binary64_796`
12×	`associate-/l*_binary64_705`
9×	`cbrt-undiv_binary64_794` `associate-/r/_binary64_706`
8×	`pow1_binary64_821` `prod-exp_binary64_809`
6×	`pow-exp_binary64_828` `associate-l_binary64_701` `associate-r_binary64_700`
4×	`add-log-exp_binary64_799`
2×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `pow-prod-down_binary64_831` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`

Counts

4 → 1299

Calls

4 calls:

47.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
18.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
4.0ms	(*.f64 n PI.f64)
4.0ms	(*.f64 n PI.f64)

Compiler

Compiled 57121 to 30222 computations (47.1% saved)

series330.0ms (1.3%)

Error

Counts

4 → 18

Calls

4 calls:

147.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
120.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n PI.f64)) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
24.0ms	(*.f64 n PI.f64)
22.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1453 to 1119 computations (23% saved)

simplify756.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1317 → 1317

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4997	79597
1	4997	79597

prune3.9s (15.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1316	1	1317
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	1317	8	1325

Error

Counts

1325 → 8

Compiler

Compiled 53060 to 26700 computations (49.7% saved)

regimes839.0ms (3.4%)

Accuracy

Total 0.4b remaining (99.6%)

Threshold costs 0.4b (99.6%)

Compiler

Compiled 11470 to 9252 computations (19.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	31
1	15	31

end0.0ms (0%)

sample4.6s (18.5%)

Algorithm

1×

intervals

Results

622.0ms	8000×	body	128	valid
612.0ms	1308×	body	1024	nan
334.0ms	2340×	body	128	overflowed
213.0ms	669×	body	512	nan
67.0ms	359×	body	256	nan
55.0ms	935×	body	128	nan
18.0ms	200×	body	128	invalid

Compiler

Compiled 2666 to 2149 computations (19.4% saved)

Details

analyze532.0ms (2.1%)

sample84.0ms (0.3%)

simplify58.0ms (0.2%)

prune4.0ms (0%)

localize11.0ms (0%)

rewrite194.0ms (0.8%)

series421.0ms (1.7%)

simplify90.0ms (0.4%)

prune177.0ms (0.7%)

localize18.0ms (0.1%)

rewrite209.0ms (0.8%)

series292.0ms (1.2%)

simplify76.0ms (0.3%)

prune166.0ms (0.7%)

localize12.0ms (0%)

rewrite3.5s (14%)

series337.0ms (1.4%)

simplify421.0ms (1.7%)

prune2.8s (11.4%)

localize13.0ms (0.1%)

rewrite5.0s (20.2%)

series330.0ms (1.3%)

simplify756.0ms (3%)

prune3.9s (15.6%)

regimes839.0ms (3.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.6s (18.5%)

Profiling