Details

analyze2.3s (7.3%)

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

Symmetry

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample98.0ms (0.3%)

Algorithm

1×

intervals

Results

38.0ms	392×	body	128	nan
23.0ms	256×	body	128	valid
2.0ms	25×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify52.0ms (0.2%)

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

32.1b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.3b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.6b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
12.5b	(.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)))))))
18.1b	(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))))))))

rewrite261.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

30×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
19×	`times-frac_binary64_425`
18×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
16×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`associate-*r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
7×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `flip3-+_binary64_422` `flip-+_binary64_393` `frac-times_binary64_429` `sub-neg_binary64_412`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`sqrt-div_binary64_436` `flip3--_binary64_423` `flip--_binary64_394` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

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))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series4.2s (13%)

Error

19.7b

Counts

4 → 110

Calls

4 calls:

1.9s	(.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)))))))
914.0ms	(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))))))))
825.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
325.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11056 to 8365 computations (24.3% saved)

simplify101.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4980	7581
1	4980	7581

prune328.0ms (1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	219	22	241
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	221	22	243

Error

14.7b

Counts

243 → 22

Compiler

Compiled 8568 to 3266 computations (61.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.0b	(/.f64 (.f64 l (-.f64 U U)) Om)
7.2b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
7.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
18.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

rewrite166.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

11.4b

Rules

31×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
17×	`pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
8×	`associate-r_binary64_359`
6×	`times-frac_binary64_425`
5×	`sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `*-commutative_binary64_350` `div-inv_binary64_416` `associate-/l/_binary64_366`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `unswap-sqr_binary64_387` `frac-2neg_binary64_430` `clear-num_binary64_418` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 94

Calls

4 calls:

10.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
8.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))

Compiler

Compiled 3589 to 1455 computations (59.5% saved)

series3.6s (11.1%)

Error

13.2b

Counts

4 → 101

Calls

4 calls:

2.0s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2))))))
906.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om)) (*.f64 l -2)))))))
327.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
213.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 10160 to 7548 computations (25.7% saved)

simplify90.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4976	5754
1	4976	5754

prune245.0ms (0.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	188	7	195
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	192	25	217

Error

12.0b

Counts

217 → 25

Compiler

Compiled 6944 to 2792 computations (59.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))
7.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
12.1b	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))
18.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))

rewrite184.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

Rules

36×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441` `associate-l_binary64_360`
21×	`*-un-lft-identity_binary64_419`
20×	`pow-prod-down_binary64_490`
15×	`add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `times-frac_binary64_425`
10×	`associate-*r/_binary64_361`
5×	`sqrt-pow1_binary64_437` `associate-r_binary64_359` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `div-inv_binary64_416` `unswap-sqr_binary64_387`

Counts

4 → 105

Calls

4 calls:

12.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
11.0ms	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))

Compiler

Compiled 4245 to 1677 computations (60.5% saved)

series5.0s (15.6%)

Error

11.6b

Counts

4 → 122

Calls

4 calls:

1.9s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2))))))
1.5s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))
907.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (/.f64 (-.f64 U U) Om) (.f64 l n)) (.f64 l -2)))))))
342.0ms	(.f64 (/.f64 (-.f64 U U) Om) (*.f64 l n))

Compiler

Compiled 12222 to 9285 computations (24% saved)

simplify104.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4981	7903
1	4981	7903

prune285.0ms (0.9%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	223	4	227
Fresh	3	21	24
Picked	0	1	1
Done	0	0	0
Total	226	26	252

Error

11.4b

Counts

252 → 26

Compiler

Compiled 8309 to 3060 computations (63.2% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))
7.2b	(.f64 l (.f64 n U*))
7.3b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
18.1b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))))

rewrite152.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

11.2b

Rules

36×	`pow1_binary64_480`
23×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
20×	`pow-prod-down_binary64_490`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`associate-*r/_binary64_361`
9×	`add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454` `-un-lft-identity_binary64_419` `associate-l*_binary64_360`
5×	`sqrt-pow1_binary64_437` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-r_binary64_359`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `unswap-sqr_binary64_387`

Counts

4 → 84

Calls

4 calls:

11.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))
5.0ms	(.f64 l (.f64 n U*))

Compiler

Compiled 3190 to 1391 computations (56.4% saved)

series3.2s (10.1%)

Error

8.5b

Counts

4 → 107

Calls

4 calls:

1.3s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
926.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))
794.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2)))))))
97.0ms	(.f64 l (.f64 n U*))

Compiler

Compiled 8594 to 6703 computations (22% saved)

simplify98.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4982	5809
1	4982	5809

prune204.0ms (0.6%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	10	14	24
Picked	1	0	1
Done	0	1	1
Total	191	26	217

Error

8.3b

Counts

217 → 26

Compiler

Compiled 5405 to 2053 computations (62% saved)

regimes4.6s (14.4%)

Accuracy

Total 18.8b remaining (68.8%)

Threshold costs 0b (0%)

Compiler

Compiled 44026 to 32514 computations (26.1% saved)

bsearch14.0ms (0%)

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

simplify44.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	1211	311
1	1211	311

Removed

()

end0.0ms (0%)

sample6.7s (20.8%)

Algorithm

1×

intervals

Results

1.2s	13195×	body	128	nan
727.0ms	8000×	body	128	valid
104.0ms	1187×	body	128	invalid

Compiler

Compiled 5722 to 4187 computations (26.8% saved)

Details

analyze2.3s (7.3%)

sample98.0ms (0.3%)

simplify52.0ms (0.2%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite261.0ms (0.8%)

series4.2s (13%)

simplify101.0ms (0.3%)

prune328.0ms (1%)

localize17.0ms (0.1%)

rewrite166.0ms (0.5%)

series3.6s (11.1%)

simplify90.0ms (0.3%)

prune245.0ms (0.8%)

localize17.0ms (0.1%)

rewrite184.0ms (0.6%)

series5.0s (15.6%)

simplify104.0ms (0.3%)

prune285.0ms (0.9%)

localize16.0ms (0%)

rewrite152.0ms (0.5%)

series3.2s (10.1%)

simplify98.0ms (0.3%)

prune204.0ms (0.6%)

regimes4.6s (14.4%)

bsearch14.0ms (0%)

simplify44.0ms (0.1%)

end0.0ms (0%)

sample6.7s (20.8%)

Profiling