Details

analyze3.3s (11.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	98.1%	1.9%	7
0%	98.1%	1.9%	8
0%	97.8%	2.2%	9
0%	96.8%	3.2%	10
0%	96.3%	3.7%	11
0%	94.3%	5.7%	12
0.4%	92.1%	7.5%	13
0.6%	90.8%	8.6%	14

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample94.0ms (0.3%)

Algorithm

1×

intervals

Results

39.0ms	382×	body	128	nan
24.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify215.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5178	39

prune10.0ms (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

32.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
6.9b	(/.f64 (*.f64 l l) Om)
9.4b	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
21.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

rewrite107.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_116`
25×	`pow1_binary64_139`
23×	`add-cbrt-cube_binary64_114`
22×	`associate-*r/_binary64_20`
16×	`prod-exp_binary64_127`
13×	`pow-prod-down_binary64_149`
12×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
11×	`flip3--_binary64_82` `flip--_binary64_53`
10×	`cbrt-unprod_binary64_111` `add-cube-cbrt_binary64_113` `cancel-sign-sub-inv_binary64_44`
8×	`distribute-lft-in_binary64_27` `frac-sub_binary64_87` `distribute-rgt-in_binary64_28` `associate-r_binary64_18`
6×	`sqrt-div_binary64_95` `sub-neg_binary64_71`
4×	`add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `associate--l+_binary64_15`
3×	`div-exp_binary64_129` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`-commutative_binary64_9` `associate-l*_binary64_19` `pow-exp_binary64_146` `cbrt-undiv_binary64_112`
1×	`sqrt-prod_binary64_94` `pow-to-exp_binary64_147` `distribute-lft-out--_binary64_30` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `difference-of-squares_binary64_47` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 107

Calls

4 calls:

26.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
25.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
20.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
9.0ms	(/.f64 (*.f64 l l) Om)

series3.8s (13%)

Counts

4 → 12

Calls

4 calls:

3.0s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
655.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
160.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
24.0ms	(/.f64 (*.f64 l l) Om)

simplify84.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5069	4064

prune319.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	11	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Error

24.7b

Counts

121 → 11

Compiler

Compiled 5101 to 2498 computations (51% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (pow.f64 (/.f64 l Om) 2))
6.9b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
9.4b	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
21.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

rewrite98.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64_116`
28×	`add-sqr-sqrt_binary64_100`
26×	`associate-r_binary64_18`
25×	`pow1_binary64_139`
22×	`associate-*r/_binary64_20`
20×	`add-cbrt-cube_binary64_114`
19×	`prod-exp_binary64_127` `*-un-lft-identity_binary64_78`
17×	`add-cube-cbrt_binary64_113`
15×	`unpow-prod-down_binary64_157`
13×	`pow-prod-down_binary64_149`
11×	`flip3--_binary64_82` `flip--_binary64_53`
10×	`cbrt-unprod_binary64_111` `times-frac_binary64_84` `cancel-sign-sub-inv_binary64_44`
8×	`distribute-lft-in_binary64_27` `frac-sub_binary64_87` `distribute-rgt-in_binary64_28`
6×	`sqrt-div_binary64_95` `sub-neg_binary64_71`
5×	`associate-l_binary64_19` `unswap-sqr_binary64_46`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `associate--l+_binary64_15`
3×	`*-commutative_binary64_9`
2×	`pow-to-exp_binary64_147` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50`
1×	`sqrt-prod_binary64_94` `distribute-lft-out--_binary64_30` `div-inv_binary64_75` `difference-of-squares_binary64_47` `pow1/2_binary64_158`

Counts

4 → 125

Calls

4 calls:

21.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
20.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
16.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))
12.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

series3.9s (13.2%)

Counts

4 → 12

Calls

4 calls:

2.9s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
730.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
222.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
71.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

simplify112.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5253	4364

prune322.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	133	15	148

Error

22.7b

Counts

148 → 15

Compiler

Compiled 5934 to 2895 computations (51.2% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (pow.f64 (/.f64 l Om) 2))
6.6b	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
6.9b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
21.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_100`
28×	`add-exp-log_binary64_116` `associate-*r/_binary64_20`
26×	`associate-r_binary64_18`
21×	`pow1_binary64_139`
20×	`*-un-lft-identity_binary64_78`
18×	`add-cube-cbrt_binary64_113`
15×	`unpow-prod-down_binary64_157`
14×	`prod-exp_binary64_127`
13×	`add-cbrt-cube_binary64_114`
11×	`flip3--_binary64_82` `flip--_binary64_53`
10×	`times-frac_binary64_84` `pow-prod-down_binary64_149` `cancel-sign-sub-inv_binary64_44`
8×	`distribute-lft-in_binary64_27` `frac-sub_binary64_87` `distribute-rgt-in_binary64_28`
7×	`associate-l_binary64_19`
6×	`unswap-sqr_binary64_46` `sqrt-div_binary64_95` `sub-neg_binary64_71`
5×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `associate--l+_binary64_15`
3×	`*-commutative_binary64_9`
2×	`pow-to-exp_binary64_147` `div-exp_binary64_129` `unpow2_binary64_143` `sqr-pow_binary64_50`
1×	`sqrt-prod_binary64_94` `distribute-lft-out--_binary64_30` `div-inv_binary64_75` `difference-of-squares_binary64_47` `pow1/2_binary64_158`

Counts

4 → 123

Calls

4 calls:

24.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
22.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
18.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))))
10.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

series3.3s (11.2%)

Counts

4 → 12

Calls

4 calls:

2.7s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))))
406.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
157.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
44.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

simplify90.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4986	4020
1	4986	4020

prune300.0ms (1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	132	18	150

Error

19.6b

Counts

150 → 18

Compiler

Compiled 6048 to 2954 computations (51.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (/.f64 l Om))
6.6b	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))
6.9b	(.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U))
21.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))))

rewrite88.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*r/_binary64_20`
45×	`frac-times_binary64_88`
44×	`frac-sub_binary64_87` `flip3--_binary64_82` `flip--_binary64_53`
40×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
30×	`associate-*l/_binary64_21` `pow1_binary64_139`
26×	`add-sqr-sqrt_binary64_100`
24×	`sqrt-div_binary64_95`
21×	`associate-r_binary64_18`
20×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
19×	`*-un-lft-identity_binary64_78`
17×	`add-cube-cbrt_binary64_113`
16×	`pow-prod-down_binary64_149`
10×	`times-frac_binary64_84` `cancel-sign-sub-inv_binary64_44`
8×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
7×	`associate-l_binary64_19`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `sub-neg_binary64_71`
5×	`sqrt-pow1_binary64_96`
4×	`add-log-exp_binary64_117` `associate--l+_binary64_15`
3×	`*-commutative_binary64_9` `unswap-sqr_binary64_46`
1×	`sqrt-prod_binary64_94` `distribute-lft-out--_binary64_30` `div-inv_binary64_75` `difference-of-squares_binary64_47` `pow1/2_binary64_158`

Counts

4 → 170

Calls

4 calls:

20.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))))
16.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))
15.0ms	(.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U))
7.0ms	(*.f64 n (/.f64 l Om))

series3.6s (12.2%)

Counts

4 → 12

Calls

4 calls:

3.0s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))))
461.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))
147.0ms	(.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U))
34.0ms	(*.f64 n (/.f64 l Om))

simplify124.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5143	8293

prune367.0ms (1.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	183	17	200

Error

18.4b

Counts

200 → 17

Compiler

Compiled 9006 to 2999 computations (66.7% saved)

regimes2.3s (7.8%)

Accuracy

Total 9.0b remaining (34.3%)

Threshold costs 0b (0%)

Compiler

Compiled 23423 to 15436 computations (34.1% saved)

bsearch10.0ms (0%)

Compiler: Compiled 28 to 23 computations (17.9% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	339	319
1	339	319

end0.0ms (0%)

sample6.7s (22.6%)

Algorithm

1×

intervals

Results

1.7s	12863×	body	128	nan
1.1s	8000×	body	128	valid
161.0ms	1190×	body	128	invalid

Compiler

Compiled 3068 to 1990 computations (35.1% saved)

Details

analyze3.3s (11.3%)

sample94.0ms (0.3%)

simplify215.0ms (0.7%)

prune10.0ms (0%)

localize42.0ms (0.1%)

rewrite107.0ms (0.4%)

series3.8s (13%)

simplify84.0ms (0.3%)

prune319.0ms (1.1%)

localize31.0ms (0.1%)

rewrite98.0ms (0.3%)

series3.9s (13.2%)

simplify112.0ms (0.4%)

prune322.0ms (1.1%)

localize22.0ms (0.1%)

rewrite88.0ms (0.3%)

series3.3s (11.2%)

simplify90.0ms (0.3%)

prune300.0ms (1%)

localize19.0ms (0.1%)

rewrite88.0ms (0.3%)

series3.6s (12.2%)

simplify124.0ms (0.4%)

prune367.0ms (1.2%)

regimes2.3s (7.8%)

bsearch10.0ms (0%)

simplify16.0ms (0.1%)

end0.0ms (0%)

sample6.7s (22.6%)

Profiling