Details

analyze4.7s (9%)

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)

sample185.0ms (0.4%)

Algorithm

1×

intervals

Results

77.0ms	402×	body	128	nan
46.0ms	256×	body	128	valid
6.0ms	37×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify111.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5178	39

prune11.0ms (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

30.4b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.7b	(.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)))))))
10.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.2b	(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))))))))

rewrite110.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
29×	`add-sqr-sqrt_binary64_441`
27×	`associate-l_binary64_360`
24×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
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×	`flip3-+_binary64_422` `sub-neg_binary64_412` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip-+_binary64_393` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `div-inv_binary64_416` `unswap-sqr_binary64_387` `flip3--_binary64_423` `flip--_binary64_394`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435`

Counts

4 → 131

Calls

4 calls:

22.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
18.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
18.0ms	(.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)))))))
14.0ms	(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))))))))

series7.5s (14.5%)

Counts

4 → 113

Calls

4 calls:

3.2s	(.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)))))))
2.4s	(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))))))))
1.3s	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
564.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 8331 to 6807 computations (18.3% saved)

simplify249.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5027	8489

prune652.0ms (1.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	222	22	244
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	224	22	246

Error

17.2b

Counts

246 → 22

Compiler

Compiled 9158 to 3397 computations (62.9% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.5b	(*.f64 n (/.f64 l Om))
6.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
9.7b	(.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))))))
19.2b	(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)))))))

rewrite97.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`times-frac_binary64_425` `associate-*r/_binary64_361`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 107

Calls

4 calls:

21.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
17.0ms	(.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))))))
16.0ms	(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)))))))
14.0ms	(*.f64 n (/.f64 l Om))

series7.0s (13.5%)

Counts

4 → 96

Calls

4 calls:

3.7s	(.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))))))
2.4s	(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)))))))
630.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
199.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 7445 to 6048 computations (18.8% saved)

simplify220.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4976	6592
1	4976	6592

prune555.0ms (1.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	2	19	21
Picked	1	0	1
Done	0	0	0
Total	203	22	225

Error

16.5b

Counts

225 → 22

Compiler

Compiled 7643 to 2970 computations (61.1% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.9b	(.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)))))))
5.9b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
6.3b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
19.2b	(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))))))))

rewrite99.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
20×	`pow-prod-down_binary64_490`
15×	`associate-*r/_binary64_361`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
13×	`add-sqr-sqrt_binary64_441`
11×	`*-un-lft-identity_binary64_419`
9×	`distribute-rgt-in_binary64_369` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `distribute-lft-in_binary64_368`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`associate-l_binary64_360` `sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `*-commutative_binary64_350` `flip-+_binary64_393`
2×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394`
1×	`associate-*l/_binary64_362` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `unswap-sqr_binary64_387` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 101

Calls

4 calls:

23.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
20.0ms	(.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)))))))
17.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
15.0ms	(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))))))))

series9.2s (17.8%)

Counts

4 → 126

Calls

4 calls:

3.5s	(.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)))))))
2.8s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (.f64 n (/.f64 l Om)) (-.f64 U U))))))
2.4s	(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))))))))
597.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))

Compiler

Compiled 9085 to 7436 computations (18.2% saved)

simplify258.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4978	8683
1	4978	8683

prune651.0ms (1.3%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	221	6	227
Fresh	5	16	21
Picked	0	1	1
Done	0	0	0
Total	226	23	249

Error

14.0b

Counts

249 → 23

Compiler

Compiled 8553 to 3063 computations (64.2% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
10.0b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
19.2b	(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))))))))
19.2b	(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))))))))

rewrite138.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`pow1_binary64_480`
32×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
28×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
26×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `associate-l*_binary64_360`
24×	`cancel-sign-sub-inv_binary64_385`
18×	`pow-prod-down_binary64_490` `times-frac_binary64_425`
16×	`associate-*r/_binary64_361`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sub-neg_binary64_412` `sqrt-pow1_binary64_437`
4×	`sqrt-div_binary64_436` `add-log-exp_binary64_458` `frac-times_binary64_429` `flip3--_binary64_423` `flip--_binary64_394` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`flip3-+_binary64_422` `associate-l/_binary64_362` `pow1/2_binary64_499` `div-inv_binary64_416` `associate-r_binary64_359` `-commutative_binary64_350` `flip-+_binary64_393` `sqrt-prod_binary64_435`

Counts

4 → 136

Calls

4 calls:

29.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
28.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
16.0ms	(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))))))))
15.0ms	(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))))))))

series5.9s (11.4%)

Counts

4 → 88

Calls

4 calls:

2.3s	(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))))))))
2.2s	(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))))))))
674.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
658.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 12360 to 8802 computations (28.8% saved)

simplify242.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	5023	6332

prune1.1s (2.2%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	1	20	21
Picked	0	1	1
Done	0	1	1
Total	224	23	247

Error

14.0b

Counts

247 → 23

Compiler

Compiled 13956 to 5688 computations (59.2% saved)

regimes3.9s (7.5%)

Accuracy

Total 15.0b remaining (55.9%)

Threshold costs 0b (0%)

Compiler

Compiled 21298 to 14786 computations (30.6% saved)

bsearch12.0ms (0%)

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

simplify44.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	764	304
1	764	304

end0.0ms (0%)

sample8.6s (16.6%)

Algorithm

1×

intervals

Results

2.2s	12859×	body	128	nan
1.4s	8000×	body	128	valid
209.0ms	1180×	body	128	invalid

Compiler

Compiled 2877 to 1966 computations (31.7% saved)

Details

analyze4.7s (9%)

sample185.0ms (0.4%)

simplify111.0ms (0.2%)

prune11.0ms (0%)

localize37.0ms (0.1%)

rewrite110.0ms (0.2%)

series7.5s (14.5%)

simplify249.0ms (0.5%)

prune652.0ms (1.3%)

localize32.0ms (0.1%)

rewrite97.0ms (0.2%)

series7.0s (13.5%)

simplify220.0ms (0.4%)

prune555.0ms (1.1%)

localize39.0ms (0.1%)

rewrite99.0ms (0.2%)

series9.2s (17.8%)

simplify258.0ms (0.5%)

prune651.0ms (1.3%)

localize49.0ms (0.1%)

rewrite138.0ms (0.3%)

series5.9s (11.4%)

simplify242.0ms (0.5%)

prune1.1s (2.2%)

regimes3.9s (7.5%)

bsearch12.0ms (0%)

simplify44.0ms (0.1%)

end0.0ms (0%)

sample8.6s (16.6%)

Profiling