Details

analyze620.0ms (4.2%)

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)

sample93.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
20.0ms	38×	body	1024	nan
13.0ms	84×	body	128	overflowed
7.0ms	19×	body	512	nan
2.0ms	34×	body	128	nan
2.0ms	9×	body	256	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

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

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite251.0ms (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×	`difference-of-squares_binary64_729` `pow-prod-down_binary64_831` `pow-exp_binary64_828` `associate-/r*_binary64_704`
5×	`div-exp_binary64_811` `associate-/l*_binary64_705`
3×	`distribute-lft-out--_binary64_712` `pow-pow_binary64_832` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793` `associate-r_binary64_700`
2×	`div-inv_binary64_757` `div-sub_binary64_765` `pow-sub_binary64_836` `pow-to-exp_binary64_829`
1×	`cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707` `associate-l_binary64_701` `*-commutative_binary64_691`

Counts

3 → 115

Calls

3 calls:

15.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
13.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
9.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series526.0ms (3.6%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

242.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
221.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
32.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify128.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune208.0ms (1.4%)

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 3092 to 2098 computations (32.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite706.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
126×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
33×	`add-exp-log_binary64_798`
28×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
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` `cbrt-unprod_binary64_793` `associate-l*_binary64_701`
4×	`add-log-exp_binary64_799`
3×	`pow-exp_binary64_828` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778`
2×	`associate-r_binary64_700` `*-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:

18.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
10.0ms	(.f64 n (.f64 2 PI.f64))
9.0ms	(.f64 n (.f64 2 PI.f64))
7.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 8830 to 5718 computations (35.2% saved)

series334.0ms (2.3%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

213.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
37.0ms	(.f64 n (.f64 2 PI.f64))
34.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))
33.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 1094 to 858 computations (21.6% saved)

simplify196.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5070	11529

prune641.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	258	7	265

Error

Counts

265 → 7

Compiler

Compiled 8741 to 5648 computations (35.4% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite134.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`add-exp-log_binary64_798`
20×	`pow1_binary64_821`
19×	`add-cbrt-cube_binary64_796`
14×	`prod-exp_binary64_809`
9×	`pow-prod-down_binary64_831`
8×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
7×	`cbrt-unprod_binary64_793`
6×	`div-exp_binary64_811` `associate-l_binary64_701`
4×	`add-log-exp_binary64_799` `times-frac_binary64_766` `associate-/l*_binary64_705`
3×	`pow-exp_binary64_828` `sqrt-prod_binary64_776` `sqrt-pow1_binary64_778`
2×	`cbrt-undiv_binary64_794` `associate-r_binary64_700` `*-commutative_binary64_691`
1×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/r*_binary64_704` `pow1/2_binary64_840`

Counts

4 → 75

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))))
5.0ms	(.f64 n (.f64 PI.f64 2))
5.0ms	(.f64 n (.f64 2 PI.f64))
3.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1959 to 1280 computations (34.7% saved)

series306.0ms (2.1%)

Error

Counts

4 → 15

Calls

4 calls:

196.0ms	(/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))))
33.0ms	(.f64 n (.f64 2 PI.f64))
32.0ms	(.f64 n (.f64 PI.f64 2))
22.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1094 to 858 computations (21.6% saved)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4964	1640
1	4964	1640

prune120.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	90	7	97

Error

Counts

97 → 7

Compiler

Compiled 2205 to 1481 computations (32.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite775.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

284×	`times-frac_binary64_766`
129×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
116×	`sqrt-prod_binary64_776`
42×	`add-exp-log_binary64_798`
28×	`add-cbrt-cube_binary64_796` `unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
24×	`associate-/l*_binary64_705`
23×	`pow1_binary64_821`
15×	`prod-exp_binary64_809`
12×	`pow-prod-down_binary64_831` `cbrt-unprod_binary64_793`
11×	`div-exp_binary64_811`
10×	`associate-l_binary64_701`
8×	`associate-r_binary64_700` `div-inv_binary64_757`
6×	`associate-/r*_binary64_704`
4×	`add-log-exp_binary64_799`
3×	`*-commutative_binary64_691` `pow-exp_binary64_828` `cbrt-undiv_binary64_794`
1×	`pow-to-exp_binary64_829` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/l/_binary64_707`

Counts

4 → 256

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (.f64 PI.f64 2) (sqrt.f64 n)))) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
10.0ms	(.f64 (sqrt.f64 n) (.f64 (*.f64 PI.f64 2) (sqrt.f64 n)))
7.0ms	(.f64 (.f64 PI.f64 2) (sqrt.f64 n))
5.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 10824 to 6334 computations (41.5% saved)

series308.0ms (2.1%)

Error

Counts

4 → 15

Calls

4 calls:

189.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (sqrt.f64 n) (.f64 (.f64 PI.f64 2) (sqrt.f64 n)))) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
40.0ms	(.f64 n (.f64 2 PI.f64))
32.0ms	(.f64 (sqrt.f64 n) (.f64 (*.f64 PI.f64 2) (sqrt.f64 n)))
31.0ms	(.f64 (.f64 PI.f64 2) (sqrt.f64 n))

Compiler

Compiled 1178 to 907 computations (23% saved)

simplify219.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5020	11988

prune602.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	271	7	278

Error

Counts

278 → 7

Compiler

Compiled 9328 to 5224 computations (44% saved)

regimes1.4s (9.5%)

Accuracy

Total 0.4b remaining (99.8%)

Threshold costs 0.4b (99.8%)

Compiler

Compiled 16071 to 13159 computations (18.1% 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%)

sample7.0s (47.4%)

Algorithm

1×

intervals

Results

786.0ms	1311×	body	1024	nan
778.0ms	8000×	body	128	valid
421.0ms	2316×	body	128	overflowed
265.0ms	643×	body	512	nan
78.0ms	320×	body	256	nan
73.0ms	994×	body	128	nan
27.0ms	234×	body	128	invalid

Compiler

Compiled 3801 to 3108 computations (18.2% saved)

Details

analyze620.0ms (4.2%)

sample93.0ms (0.6%)

simplify63.0ms (0.4%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite251.0ms (1.7%)

series526.0ms (3.6%)

simplify128.0ms (0.9%)

prune208.0ms (1.4%)

localize11.0ms (0.1%)

rewrite706.0ms (4.8%)

series334.0ms (2.3%)

simplify196.0ms (1.3%)

prune641.0ms (4.3%)

localize29.0ms (0.2%)

rewrite134.0ms (0.9%)

series306.0ms (2.1%)

simplify76.0ms (0.5%)

prune120.0ms (0.8%)

localize16.0ms (0.1%)

rewrite775.0ms (5.2%)

series308.0ms (2.1%)

simplify219.0ms (1.5%)

prune602.0ms (4.1%)

regimes1.4s (9.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample7.0s (47.4%)

Profiling