Details

analyze386.0ms (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)

sample73.0ms (0.9%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
19.0ms	42×	body	1024	nan
14.0ms	78×	body	128	overflowed
7.0ms	20×	body	512	nan
2.0ms	30×	body	128	nan
1.0ms	4×	body	256	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 33 to 33 computations (0% saved)

simplify139.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4933	22
1	4933	22

prune4.0ms (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

0.3b

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

rewrite39.0ms (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:

12.0ms	(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))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series410.0ms (5.1%)

Counts

3 → 18

Calls

3 calls:

215.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
167.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
28.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 703 to 606 computations (13.8% saved)

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4969	3385
1	4969	3385

prune194.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	122	11	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	11	135

Error

0.0b

Counts

135 → 11

Compiler

Compiled 3096 to 2095 computations (32.3% saved)

localize14.0ms (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 (.f64 2 PI.f64) n)
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.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))))

rewrite39.0ms (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:

10.0ms	(/.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))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(.f64 (.f64 2 PI.f64) n)

series291.0ms (3.6%)

Counts

4 → 15

Calls

4 calls:

138.0ms	(/.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)
30.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 790 to 659 computations (16.6% saved)

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5224	2548

prune176.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Error

Counts

144 → 9

Compiler

Compiled 3255 to 2245 computations (31% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.1b	(sqrt.f64 (/.f64 1 k))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_782`
37×	`sqrt-prod_binary64_776`
27×	`*-un-lft-identity_binary64_760`
26×	`times-frac_binary64_766`
23×	`add-cube-cbrt_binary64_795`
19×	`associate-r_binary64_700`
17×	`pow1_binary64_821`
14×	`add-exp-log_binary64_798`
13×	`associate-l_binary64_701`
12×	`unswap-sqr_binary64_728`
11×	`add-cbrt-cube_binary64_796`
8×	`unpow-prod-down_binary64_839`
6×	`prod-exp_binary64_809` `sqrt-pow1_binary64_778` `pow-prod-down_binary64_831`
5×	`sqr-pow_binary64_732`
4×	`unpow-prod-up_binary64_838` `add-log-exp_binary64_799` `cbrt-unprod_binary64_793`
3×	`rem-sqrt-square_binary64_773` `cancel-sign-sub-inv_binary64_726` `sqrt-div_binary64_777`
2×	`div-inv_binary64_757` `pow1/2_binary64_840` `*-commutative_binary64_691` `pow-sub_binary64_836`
1×	`associate-l/_binary64_703` `pow-exp_binary64_828` `inv-pow_binary64_845` `pow-to-exp_binary64_829` `frac-times_binary64_770` `associate-r/_binary64_702` `sub-neg_binary64_753` `pow-flip_binary64_834`

Counts

4 → 113

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
3.0ms	(sqrt.f64 (/.f64 1 k))

series190.0ms (2.4%)

Counts

4 → 15

Calls

4 calls:

125.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 2 PI.f64) n)) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
28.0ms	(.f64 (.f64 2 PI.f64) n)
22.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
16.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 733 to 622 computations (15.1% saved)

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5025	2502

prune158.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	128	9	137

Error

Counts

137 → 9

Compiler

Compiled 2870 to 2127 computations (25.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))
0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k))))
0.2b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k)))

rewrite118.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

591×	`times-frac_binary64_766`
302×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
215×	`sqrt-prod_binary64_776`
124×	`unpow-prod-up_binary64_838` `unpow-prod-down_binary64_839`
93×	`cancel-sign-sub-inv_binary64_726`
89×	`associate-/r*_binary64_704`
36×	`add-exp-log_binary64_798`
31×	`sqr-pow_binary64_732` `sub-neg_binary64_753`
20×	`div-exp_binary64_811`
16×	`add-cbrt-cube_binary64_796` `pow1_binary64_821`
9×	`associate-/l*_binary64_705`
6×	`associate-/r/_binary64_706` `div-inv_binary64_757` `pow-prod-down_binary64_831`
5×	`pow-sub_binary64_836`
4×	`cbrt-undiv_binary64_794` `add-log-exp_binary64_799` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `rec-exp_binary64_810` `1-exp_binary64_804`
3×	`prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-r_binary64_700` `cbrt-unprod_binary64_793`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`inv-pow_binary64_845` `associate-l_binary64_701` `pow1/2_binary64_840` `*-commutative_binary64_691` `pow-flip_binary64_834`

Counts

4 → 473

Calls

4 calls:

27.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k))))
9.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k)))
5.0ms	(.f64 (.f64 2 PI.f64) n)
4.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

series314.0ms (3.9%)

Counts

4 → 18

Calls

4 calls:

142.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k)))
122.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 (.f64 2 PI.f64) n)) (-.f64 1 k))))
27.0ms	(.f64 (.f64 2 PI.f64) n)
23.0ms	(sqrt.f64 (.f64 (.f64 2 PI.f64) n))

Compiler

Compiled 1050 to 865 computations (17.6% saved)

simplify222.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

491 → 491

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4960	17761
1	4960	17761

prune843.0ms (10.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	489	2	491
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	491	9	500

Error

Counts

500 → 9

Compiler

Compiled 13192 to 8280 computations (37.2% saved)

regimes636.0ms (8%)

Accuracy

Total 0.4b remaining (99.6%)

Threshold costs 0.4b (99.6%)

Compiler

Compiled 5350 to 4450 computations (16.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	30
1	14	30

end0.0ms (0%)

sample3.4s (42.8%)

Algorithm

1×

intervals

Results

623.0ms	8000×	body	128	valid
581.0ms	1273×	body	1024	nan
329.0ms	2322×	body	128	overflowed
197.0ms	653×	body	512	nan
55.0ms	992×	body	128	nan
53.0ms	303×	body	256	nan
30.0ms	281×	body	128	invalid

Compiler

Compiled 1361 to 1133 computations (16.8% saved)

Details

analyze386.0ms (4.8%)

sample73.0ms (0.9%)

simplify139.0ms (1.7%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

rewrite39.0ms (0.5%)

series410.0ms (5.1%)

simplify102.0ms (1.3%)

prune194.0ms (2.4%)

localize14.0ms (0.2%)

rewrite39.0ms (0.5%)

series291.0ms (3.6%)

simplify71.0ms (0.9%)

prune176.0ms (2.2%)

localize11.0ms (0.1%)

rewrite37.0ms (0.5%)

series190.0ms (2.4%)

simplify76.0ms (1%)

prune158.0ms (2%)

localize11.0ms (0.1%)

rewrite118.0ms (1.5%)

series314.0ms (3.9%)

simplify222.0ms (2.8%)

prune843.0ms (10.6%)

regimes636.0ms (8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (42.8%)

Profiling