Details

analyze393.0ms (5.5%)

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)

sample73.0ms (1%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
20.0ms	44×	body	1024	nan
13.0ms	73×	body	128	overflowed
4.0ms	12×	body	512	nan
2.0ms	28×	body	128	nan
2.0ms	9×	body	256	nan
0.0ms	5×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify141.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune5.0ms (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

0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite37.0ms (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:

11.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
10.0ms	(/.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)

series392.0ms (5.5%)

Counts

3 → 18

Calls

3 calls:

203.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
162.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
27.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune195.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.0b

Counts

135 → 10

Compiler

Compiled 3059 to 2067 computations (32.4% saved)

localize13.0ms (0.2%)

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

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

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

series286.0ms (4%)

Counts

4 → 15

Calls

4 calls:

136.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
91.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
31.0ms	(.f64 (.f64 2 PI.f64) n)
27.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 790 to 659 computations (16.6% saved)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5224	2548

prune183.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	131	12	143

Error

Counts

143 → 12

Compiler

Compiled 3321 to 2300 computations (30.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)
0.4b	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_766`
23×	`*-un-lft-identity_binary64_760` `sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
20×	`pow1_binary64_821`
16×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
9×	`pow-prod-down_binary64_831`
6×	`prod-exp_binary64_809` `associate-/r_binary64_704` `associate-r*_binary64_700` `cbrt-unprod_binary64_793`
4×	`add-log-exp_binary64_799` `associate-/l*_binary64_705`
3×	`sqrt-pow1_binary64_778`
2×	`associate-l_binary64_701` `*-commutative_binary64_691`
1×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `sqrt-undiv_binary64_781` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 95

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series147.0ms (2.1%)

Counts

4 → 15

Calls

4 calls:

68.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
29.0ms	(.f64 (.f64 2 PI.f64) n)
25.0ms	(.f64 (.f64 2 PI.f64) n)
24.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 703 to 590 computations (16.1% saved)

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5517	1800

prune143.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	112	10	122

Error

Counts

122 → 10

Compiler

Compiled 2803 to 1819 computations (35.1% saved)

localize13.0ms (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)

rewrite60.0ms (0.8%)

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:

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

series241.0ms (3.4%)

Counts

4 → 15

Calls

4 calls:

154.0ms	(/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
35.0ms	(.f64 (.f64 2 PI.f64) n)
30.0ms	(.f64 (.f64 2 PI.f64) n)
22.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 804 to 671 computations (16.5% saved)

simplify155.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5032	11499

prune515.0ms (7.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

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

Error

Counts

266 → 10

Compiler

Compiled 8533 to 5486 computations (35.7% saved)

regimes389.0ms (5.4%)

Accuracy

Total 0.3b remaining (99.2%)

Threshold costs 0.3b (99.2%)

Compiler

Compiled 4626 to 3894 computations (15.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	35
1	53	35

end0.0ms (0%)

sample3.4s (47.9%)

Algorithm

1×

intervals

Results

645.0ms	8000×	body	128	valid
577.0ms	1221×	body	1024	nan
334.0ms	2383×	body	128	overflowed
198.0ms	624×	body	512	nan
64.0ms	340×	body	256	nan
63.0ms	1033×	body	128	nan
22.0ms	236×	body	128	invalid

Compiler

Compiled 1183 to 997 computations (15.7% saved)

Details

analyze393.0ms (5.5%)

sample73.0ms (1%)

simplify141.0ms (2%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.5%)

series392.0ms (5.5%)

simplify93.0ms (1.3%)

prune195.0ms (2.7%)

localize13.0ms (0.2%)

rewrite37.0ms (0.5%)

series286.0ms (4%)

simplify71.0ms (1%)

prune183.0ms (2.6%)

localize10.0ms (0.1%)

rewrite30.0ms (0.4%)

series147.0ms (2.1%)

simplify85.0ms (1.2%)

prune143.0ms (2%)

localize13.0ms (0.2%)

rewrite60.0ms (0.8%)

series241.0ms (3.4%)

simplify155.0ms (2.2%)

prune515.0ms (7.2%)

regimes389.0ms (5.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (47.9%)

Profiling