Details

analyze2.3s (11.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5820	672
0	6	6
1	6	6

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)

sample89.0ms (0.4%)

Algorithm

1×

intervals

Results

33.0ms	374×	body	128	nan
26.0ms	256×	body	128	valid
3.0ms	31×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5178	39

prune5.0ms (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

27.6b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
9.8b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
16.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

rewrite208.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
29×	`add-sqr-sqrt_binary64_100`
27×	`associate-l_binary64_19`
24×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`times-frac_binary64_84`
18×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
16×	`pow-prod-down_binary64_149`
14×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
12×	`associate-*r/_binary64_20` `cancel-sign-sub-inv_binary64_44`
7×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `frac-times_binary64_88` `sub-neg_binary64_71` `flip3-+_binary64_81`
3×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
2×	`flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
1×	`sqrt-prod_binary64_94` `pow1/2_binary64_158`

Counts

4 → 131

Calls

4 calls:

13.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))

series2.8s (13.9%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U))))))))
439.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U U)))))))
158.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
95.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify95.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5099	4107

prune216.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	9	143
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	136	9	145

Error

20.1b

Counts

145 → 9

Compiler

Compiled 5314 to 2176 computations (59.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(*.f64 n (/.f64 l Om))
8.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
16.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_139`
27×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
23×	`add-sqr-sqrt_binary64_100`
21×	`associate-r_binary64_18`
18×	`*-un-lft-identity_binary64_78`
16×	`add-cube-cbrt_binary64_113` `pow-prod-down_binary64_149`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
10×	`times-frac_binary64_84` `associate-*r/_binary64_20`
6×	`cancel-sign-sub-inv_binary64_44`
5×	`distribute-lft-in_binary64_27` `associate-l_binary64_19` `distribute-rgt-in_binary64_28`
4×	`add-log-exp_binary64_117` `sqrt-pow1_binary64_96`
3×	`*-commutative_binary64_9`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53` `unswap-sqr_binary64_46` `sqrt-div_binary64_95` `sub-neg_binary64_71` `flip3-+_binary64_81`
1×	`sqrt-prod_binary64_94` `distribute-lft-out--_binary64_30` `div-inv_binary64_75` `associate-*l/_binary64_21` `difference-of-squares_binary64_47` `pow1/2_binary64_158`

Counts

4 → 107

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
8.0ms	(*.f64 n (/.f64 l Om))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))

series2.7s (13.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
448.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
100.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
19.0ms	(*.f64 n (/.f64 l Om))

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5059	2829

prune158.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Error

19.3b

Counts

128 → 10

Compiler

Compiled 4320 to 1872 computations (56.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.7b	(.f64 (/.f64 l Om) (-.f64 U U))
5.3b	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
9.4b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
16.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_139`
27×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116`
22×	`*-un-lft-identity_binary64_78`
21×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
20×	`add-cube-cbrt_binary64_113`
18×	`cancel-sign-sub-inv_binary64_44`
17×	`associate-l_binary64_19`
16×	`pow-prod-down_binary64_149`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-*r/_binary64_20`
10×	`times-frac_binary64_84`
9×	`associate-r_binary64_18`
6×	`sub-neg_binary64_71`
4×	`add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53`
3×	`*-commutative_binary64_9`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `sqrt-div_binary64_95` `flip3-+_binary64_81`
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 → 127

Calls

4 calls:

12.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
11.0ms	(.f64 (/.f64 l Om) (-.f64 U U))
10.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))

series2.7s (13.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U))))))))
444.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 n (.f64 (/.f64 l Om) (-.f64 U U)))))))
95.0ms	(.f64 n (.f64 (/.f64 l Om) (-.f64 U* U)))
58.0ms	(.f64 (/.f64 l Om) (-.f64 U U))

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4980	3306
1	4980	3306

prune177.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Error

19.3b

Counts

149 → 10

Compiler

Compiled 4998 to 2101 computations (58% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
7.4b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
8.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
16.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_139`
27×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
20×	`pow-prod-down_binary64_149`
15×	`associate-*r/_binary64_20`
14×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
9×	`distribute-lft-in_binary64_27` `add-cube-cbrt_binary64_113` `distribute-rgt-in_binary64_28` `associate-r_binary64_18`
6×	`cancel-sign-sub-inv_binary64_44`
5×	`associate-l_binary64_19` `sqrt-pow1_binary64_96`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `flip-+_binary64_52` `flip3-+_binary64_81`
2×	`flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53` `sqrt-div_binary64_95` `sub-neg_binary64_71`
1×	`sqrt-prod_binary64_94` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `distribute-lft-out--_binary64_30` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `pow1/2_binary64_158`

Counts

4 → 101

Calls

4 calls:

11.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
10.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))

series3.0s (14.7%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))))
435.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U)))))))
338.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
99.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5368	3449

prune139.0ms (0.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	111	12	123

Error

17.4b

Counts

123 → 12

Compiler

Compiled 3876 to 1544 computations (60.2% saved)

regimes1.0s (5.1%)

Accuracy

Total 10.5b remaining (36.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13970 to 9224 computations (34% saved)

bsearch148.0ms (0.7%)

Steps

Iters	Range	Point
7	3.588852900127953e-86	4.5980083073019985e-84	3.85280491822023e-86
4	-3.53664663862195e-284	-2.326440980852463e-284	-3.389110959089207e-284
8	-1.2265150587743851e-172	-2.2630733224575342e-176	-1.1949065200363964e-175

Iters

Range

Point

3.588852900127953e-86

4.5980083073019985e-84

3.85280491822023e-86

-3.53664663862195e-284

-2.326440980852463e-284

-3.389110959089207e-284

-1.2265150587743851e-172

-2.2630733224575342e-176

-1.1949065200363964e-175

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	118	185
1	118	185

end0.0ms (0%)

sample3.9s (19.2%)

Algorithm

1×

intervals

Results

1.2s	12997×	body	128	nan
738.0ms	8000×	body	128	valid
109.0ms	1217×	body	128	invalid

Compiler

Compiled 1862 to 1209 computations (35.1% saved)

Details

analyze2.3s (11.6%)

sample89.0ms (0.4%)

simplify52.0ms (0.3%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite208.0ms (1%)

series2.8s (13.9%)

simplify95.0ms (0.5%)

prune216.0ms (1.1%)

localize19.0ms (0.1%)

rewrite48.0ms (0.2%)

series2.7s (13.4%)

simplify79.0ms (0.4%)

prune158.0ms (0.8%)

localize16.0ms (0.1%)

rewrite57.0ms (0.3%)

series2.7s (13.4%)

simplify100.0ms (0.5%)

prune177.0ms (0.9%)

localize17.0ms (0.1%)

rewrite48.0ms (0.2%)

series3.0s (14.7%)

simplify68.0ms (0.3%)

prune139.0ms (0.7%)

regimes1.0s (5.1%)

bsearch148.0ms (0.7%)

simplify5.0ms (0%)

end0.0ms (0%)

sample3.9s (19.2%)

Profiling