Details

analyze393.0ms (4.8%)

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)

sample81.0ms (1%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
20.0ms	42×	body	1024	nan
10.0ms	71×	body	128	overflowed
10.0ms	20×	body	512	nan
2.0ms	37×	body	128	nan
2.0ms	11×	body	256	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify219.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4908	22
1	4908	22

prune8.0ms (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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 44 to 41 computations (6.8% saved)

localize13.0ms (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 (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64_757`
42×	`*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
33×	`add-cube-cbrt_binary64_783`
26×	`add-exp-log_binary64_786`
22×	`pow-unpow_binary64_825`
18×	`sqrt-prod_binary64_766`
14×	`pow1_binary64_809`
10×	`add-cbrt-cube_binary64_784`
9×	`prod-exp_binary64_797`
8×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827`
6×	`pow-exp_binary64_816` `associate-/r*_binary64_697` `pow-prod-down_binary64_819` `difference-of-squares_binary64_720`
5×	`associate-/l*_binary64_698` `div-exp_binary64_799`
3×	`distribute-lft-out--_binary64_705` `add-log-exp_binary64_787` `pow-pow_binary64_820` `associate-r_binary64_693` `cbrt-unprod_binary64_781`
2×	`pow-to-exp_binary64_817` `div-sub_binary64_756` `div-inv_binary64_748` `pow-sub_binary64_824`
1×	`associate-/l/_binary64_700` `-commutative_binary64_684` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `associate-l*_binary64_694` `clear-num_binary64_750`

Counts

3 → 115

Calls

3 calls:

12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
8.0ms	(/.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)

series514.0ms (6.2%)

Counts

3 → 9

Calls

3 calls:

314.0ms	(/.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))
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5241	3540

prune221.0ms (2.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

Compiler

Compiled 3243 to 2215 computations (31.7% 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 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-exp-log_binary64_786`
67×	`prod-exp_binary64_797`
36×	`pow-exp_binary64_816`
30×	`div-exp_binary64_799`
20×	`pow1_binary64_809`
19×	`add-cbrt-cube_binary64_784`
15×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
14×	`times-frac_binary64_757`
13×	`pow-unpow_binary64_825`
12×	`pow-to-exp_binary64_817`
9×	`pow-prod-down_binary64_819`
7×	`cbrt-unprod_binary64_781`
6×	`associate-r_binary64_693`
5×	`associate-/l*_binary64_698`
4×	`add-log-exp_binary64_787`
3×	`sqr-pow_binary64_723` `unpow-prod-down_binary64_827` `pow-pow_binary64_820`
2×	`-commutative_binary64_684` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `associate-l*_binary64_694`
1×	`associate-/r*_binary64_697` `frac-2neg_binary64_762` `clear-num_binary64_750`

Counts

4 → 118

Calls

4 calls:

11.0ms	(/.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))))
8.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series717.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

435.0ms	(/.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))))
206.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
38.0ms	(.f64 (.f64 2 PI.f64) n)
38.0ms	(.f64 (.f64 2 PI.f64) n)

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5437	2652

prune203.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	129	11	140

Merged error: 0b

Counts

140 → 11

Compiler

Compiled 3418 to 2373 computations (30.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_757`
23×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `sqrt-prod_binary64_766` `add-sqr-sqrt_binary64_772`
20×	`pow1_binary64_809`
16×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
9×	`pow-prod-down_binary64_819`
6×	`prod-exp_binary64_797` `associate-/r_binary64_697` `associate-r*_binary64_693` `cbrt-unprod_binary64_781`
4×	`add-log-exp_binary64_787` `associate-/l*_binary64_698`
3×	`sqrt-pow1_binary64_768`
2×	`-commutative_binary64_684` `associate-l*_binary64_694`
1×	`pow1/2_binary64_828` `sqrt-undiv_binary64_771` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `div-exp_binary64_799`

Counts

4 → 95

Calls

4 calls:

8.0ms	(/.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)
5.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series278.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (sqrt.f64 k))
47.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
39.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (.f64 2 PI.f64) n)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4957	1953
1	4957	1953

prune157.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	111	7	118

Merged error: 0b

Counts

118 → 7

Compiler

Compiled 2846 to 1841 computations (35.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`sqrt-prod_binary64_766`
42×	`times-frac_binary64_757`
37×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
21×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
19×	`pow1_binary64_809`
9×	`prod-exp_binary64_797` `pow-prod-down_binary64_819` `associate-r_binary64_693` `cbrt-unprod_binary64_781`
7×	`associate-/l*_binary64_698`
6×	`associate-/r*_binary64_697`
4×	`add-log-exp_binary64_787`
3×	`-commutative_binary64_684` `associate-l*_binary64_694`
1×	`sqrt-undiv_binary64_771` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `div-exp_binary64_799`

Counts

4 → 122

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (sqrt.f64 k))
8.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)
6.0ms	(.f64 (.f64 2 PI.f64) n)

series324.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n))) (sqrt.f64 k))
38.0ms	(.f64 (.f64 2 PI.f64) n)
37.0ms	(.f64 (.f64 2 PI.f64) n)
36.0ms	(.f64 (.f64 2 PI.f64) n)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5483	2757

prune260.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	134	7	141

Merged error: 0b

Counts

141 → 7

Compiler

Compiled 4640 to 3116 computations (32.8% saved)

regimes491.0ms (6%)

Compiler: Compiled 5762 to 4770 computations (17.2% 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%)

sample3.9s (47.3%)

Algorithm

1×

intervals

Results

756.0ms	8000×	body	128	valid
639.0ms	1344×	body	1024	nan
333.0ms	2381×	body	128	overflowed
209.0ms	648×	body	512	nan
62.0ms	308×	body	256	nan
59.0ms	961×	body	128	nan
22.0ms	230×	body	128	invalid

Compiler

Compiled 1465 to 1214 computations (17.1% saved)

Details

analyze393.0ms (4.8%)

sample81.0ms (1%)

simplify219.0ms (2.7%)

prune8.0ms (0.1%)

localize13.0ms (0.2%)

rewrite37.0ms (0.4%)

series514.0ms (6.2%)

simplify64.0ms (0.8%)

prune221.0ms (2.7%)

localize19.0ms (0.2%)

rewrite44.0ms (0.5%)

series717.0ms (8.7%)

simplify58.0ms (0.7%)

prune203.0ms (2.5%)

localize12.0ms (0.1%)

rewrite33.0ms (0.4%)

series278.0ms (3.4%)

simplify72.0ms (0.9%)

prune157.0ms (1.9%)

localize14.0ms (0.2%)

rewrite44.0ms (0.5%)

series324.0ms (3.9%)

simplify60.0ms (0.7%)

prune260.0ms (3.2%)

regimes491.0ms (6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.9s (47.3%)

Profiling