Details

analyze395.0ms (3.5%)

Algorithm

1×

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)

sample78.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	44×	body	1024	nan
19.0ms	256×	body	128	valid
11.0ms	80×	body	128	overflowed
6.0ms	20×	body	512	nan
2.0ms	36×	body	128	nan
2.0ms	10×	body	256	nan
0.0ms	4×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify141.0ms (1.2%)

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

0.7b

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)
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.6b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite212.0ms (1.9%)

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:

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)

series440.0ms (3.9%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

208.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
180.0ms	(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)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune186.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	125	8	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Error

0.0b

Counts

135 → 8

Compiler

Compiled 3055 to 2071 computations (32.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 n (.f64 2 PI.f64))
0.2b	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

rewrite248.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

128×	`add-exp-log_binary64_798`
67×	`prod-exp_binary64_809`
39×	`pow-exp_binary64_828`
30×	`div-exp_binary64_811`
26×	`pow-unpow_binary64_837`
23×	`times-frac_binary64_766`
21×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760` `pow1_binary64_821`
14×	`add-cbrt-cube_binary64_796`
13×	`pow-to-exp_binary64_829`
9×	`pow-prod-down_binary64_831`
6×	`pow-pow_binary64_832`
5×	`associate-/l*_binary64_705`
4×	`unpow-prod-down_binary64_839` `add-log-exp_binary64_799` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793`
3×	`div-inv_binary64_757` `associate-l_binary64_701`
2×	`cbrt-undiv_binary64_794`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r_binary64_704` `associate-r_binary64_700` `-commutative_binary64_691`

Counts

4 → 129

Calls

4 calls:

9.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
9.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
7.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
5.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 3815 to 2688 computations (29.5% saved)

series440.0ms (3.9%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

144.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
133.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
107.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
29.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 1551 to 1225 computations (21% saved)

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5024	3021

prune202.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	150	8	158

Error

Counts

158 → 8

Compiler

Compiled 3773 to 2621 computations (30.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 n (.f64 2 PI.f64))
0.2b	(pow.f64 (.f64 n (.f64 2 PI.f64)) k)
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) k) (/.f64 1 2))))
0.4b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))

rewrite253.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

157×	`add-exp-log_binary64_798`
83×	`prod-exp_binary64_809`
70×	`pow-exp_binary64_828`
40×	`div-exp_binary64_811`
21×	`pow1_binary64_821`
20×	`pow-to-exp_binary64_829`
16×	`pow-unpow_binary64_837`
15×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
14×	`times-frac_binary64_766` `add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
6×	`pow-pow_binary64_832`
5×	`associate-/l*_binary64_705`
4×	`unpow-prod-down_binary64_839` `add-log-exp_binary64_799` `sqr-pow_binary64_732` `cbrt-unprod_binary64_793`
3×	`associate-l_binary64_701`
2×	`div-inv_binary64_757` `cbrt-undiv_binary64_794`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r_binary64_704` `associate-r_binary64_700` `-commutative_binary64_691`

Counts

4 → 129

Calls

4 calls:

11.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) k) (/.f64 1 2))))
7.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) k)
5.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 4037 to 2915 computations (27.8% saved)

series416.0ms (3.7%)

Error

Counts

4 → 21

Calls

4 calls:

136.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) k)
126.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (pow.f64 (.f64 n (*.f64 2 PI.f64)) k) (/.f64 1 2))))
97.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
31.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 1577 to 1252 computations (20.6% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5871	2993

prune222.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	151	7	158

Error

Counts

158 → 7

Compiler

Compiled 3764 to 2646 computations (29.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 n (.f64 2 PI.f64))
0.2b	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
0.3b	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))))
0.4b	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

rewrite656.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

293×	`times-frac_binary64_766`
132×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
111×	`sqrt-prod_binary64_776`
34×	`add-exp-log_binary64_798`
29×	`unpow-prod-down_binary64_839` `sqr-pow_binary64_732`
24×	`associate-/r*_binary64_704`
21×	`pow1_binary64_821`
14×	`add-cbrt-cube_binary64_796`
13×	`pow-unpow_binary64_837`
11×	`div-exp_binary64_811`
9×	`pow-prod-down_binary64_831` `prod-exp_binary64_809` `div-inv_binary64_757`
6×	`pow-exp_binary64_828` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`sqrt-pow1_binary64_778` `cbrt-undiv_binary64_794` `pow-pow_binary64_832` `cbrt-unprod_binary64_793` `associate-l_binary64_701`
2×	`pow-to-exp_binary64_829`
1×	`pow1/2_binary64_840` `frac-2neg_binary64_771` `clear-num_binary64_759` `associate-/r/_binary64_706` `associate-r_binary64_700` `*-commutative_binary64_691`

Counts

4 → 252

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))))
7.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
5.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 9647 to 6442 computations (33.2% saved)

series360.0ms (3.2%)

Error

Counts

4 → 21

Calls

4 calls:

145.0ms	(pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))
140.0ms	(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (pow.f64 (.f64 n (.f64 2 PI.f64)) (/.f64 k 2))))
27.0ms	(.f64 n (.f64 2 PI.f64))
25.0ms	(sqrt.f64 (.f64 n (.f64 2 PI.f64)))

Compiler

Compiled 1619 to 1294 computations (20.1% saved)

simplify147.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5025	11927

prune543.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	273	7	280

Error

Counts

280 → 7

Compiler

Compiled 9477 to 5655 computations (40.3% saved)

regimes997.0ms (8.8%)

Accuracy

Total 0.4b remaining (99.6%)

Threshold costs 0.4b (99.6%)

Compiler

Compiled 13243 to 10979 computations (17.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	35
1	20	35

end0.0ms (0%)

sample5.1s (45.1%)

Algorithm

1×

intervals

Results

648.0ms	1334×	body	1024	nan
624.0ms	8000×	body	128	valid
323.0ms	2357×	body	128	overflowed
234.0ms	711×	body	512	nan
67.0ms	372×	body	256	nan
54.0ms	958×	body	128	nan
23.0ms	263×	body	128	invalid

Compiler

Compiled 3024 to 2508 computations (17.1% saved)

Details

analyze395.0ms (3.5%)

sample78.0ms (0.7%)

simplify141.0ms (1.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite212.0ms (1.9%)

series440.0ms (3.9%)

simplify94.0ms (0.8%)

prune186.0ms (1.6%)

localize16.0ms (0.1%)

rewrite248.0ms (2.2%)

series440.0ms (3.9%)

simplify76.0ms (0.7%)

prune202.0ms (1.8%)

localize16.0ms (0.1%)

rewrite253.0ms (2.2%)

series416.0ms (3.7%)

simplify59.0ms (0.5%)

prune222.0ms (2%)

localize13.0ms (0.1%)

rewrite656.0ms (5.8%)

series360.0ms (3.2%)

simplify147.0ms (1.3%)

prune543.0ms (4.8%)

regimes997.0ms (8.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.1s (45.1%)

Profiling