Details

analyze3.0s (7.4%)

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)

sample142.0ms (0.4%)

Algorithm

1×

intervals

Results

53.0ms	403×	body	128	nan
32.0ms	256×	body	128	valid
5.0ms	40×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify68.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5178	39

prune6.0ms (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

30.9b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
11.0b	(.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)))))))
11.8b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
17.7b	(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))))))))

rewrite301.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

22.1b

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×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `*-commutative_binary64_350`
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:

27.0ms	(.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))))))))
10.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.0ms	(.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)))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series5.4s (13.6%)

Error

19.1b

Counts

4 → 112

Calls

4 calls:

2.3s	(.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)))))))
1.7s	(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))))))))
902.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
299.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 12661 to 9569 computations (24.4% saved)

simplify139.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5047	8711

prune433.0ms (1.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	223	20	243
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	224	21	245

Error

15.5b

Counts

245 → 21

Compiler

Compiled 9117 to 3360 computations (63.1% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

4.7b	(*.f64 n (/.f64 l Om))
10.7b	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
11.0b	(.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))))))
17.7b	(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)))))))

rewrite236.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

14.5b

Rules

30×	`pow1_binary64_480`
27×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
23×	`add-sqr-sqrt_binary64_441`
21×	`associate-r_binary64_359`
18×	`*-un-lft-identity_binary64_419`
16×	`add-cube-cbrt_binary64_454` `pow-prod-down_binary64_490`
13×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
10×	`associate-*r/_binary64_361` `times-frac_binary64_425`
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` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `sub-neg_binary64_412` `unswap-sqr_binary64_387`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `associate-*l/_binary64_362` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `div-inv_binary64_416`

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))))))
10.0ms	(*.f64 n (/.f64 l Om))
8.0ms	(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)))))))

Compiler

Compiled 4070 to 1665 computations (59.1% saved)

series4.8s (11.8%)

Error

15.2b

Counts

4 → 95

Calls

4 calls:

2.4s	(.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))))))
1.8s	(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)))))))
330.0ms	(.f64 (.f64 n (/.f64 l Om)) (-.f64 U* U))
125.0ms	(*.f64 n (/.f64 l Om))

Compiler

Compiled 11221 to 8416 computations (25% saved)

simplify92.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4983	6812
1	4983	6812

prune351.0ms (0.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	203	20	223

Error

14.5b

Counts

223 → 20

Compiler

Compiled 7623 to 2913 computations (61.8% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

3.4b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))
7.0b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
11.8b	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
17.7b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))

rewrite217.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

11.3b

Rules

36×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
20×	`pow-prod-down_binary64_490`
17×	`associate-r_binary64_359`
15×	`add-sqr-sqrt_binary64_441` `associate-*r/_binary64_361` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
13×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
9×	`times-frac_binary64_425`
5×	`sqrt-pow1_binary64_437` `associate-l_binary64_360` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `*-commutative_binary64_350`
2×	`sqrt-div_binary64_436` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `flip3--_binary64_423` `frac-times_binary64_429` `flip--_binary64_394` `associate-*l/_binary64_362`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `div-inv_binary64_416` `unswap-sqr_binary64_387`

Counts

4 → 103

Calls

4 calls:

16.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
16.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))
7.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))

Compiler

Compiled 4161 to 1660 computations (60.1% saved)

series6.5s (16.2%)

Error

14.2b

Counts

4 → 125

Calls

4 calls:

2.4s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2))))))
1.8s	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))
1.6s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om)) (*.f64 l -2)))))))
342.0ms	(.f64 (.f64 n (-.f64 U* U)) (/.f64 l Om))

Compiler

Compiled 13907 to 10549 computations (24.1% saved)

simplify105.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5045	8900

prune404.0ms (1%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	219	9	228
Fresh	6	13	19
Picked	0	1	1
Done	0	0	0
Total	225	23	248

Error

11.3b

Counts

248 → 23

Compiler

Compiled 8731 to 3141 computations (64% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.5b	(.f64 l (.f64 n U*))
6.3b	(/.f64 (.f64 l (.f64 n U*)) Om)
7.0b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
17.7b	(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)))))))

rewrite200.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

11.3b

Rules

34×	`pow1_binary64_480`
30×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
19×	`pow-prod-down_binary64_490`
14×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`associate-*r/_binary64_361`
7×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
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`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `associate-r_binary64_359` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l*_binary64_364`

Counts

4 → 85

Calls

4 calls:

9.0ms	(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)))))))
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
9.0ms	(.f64 l (.f64 n U*))
7.0ms	(/.f64 (.f64 l (.f64 n U*)) Om)

Compiler

Compiled 3007 to 1324 computations (56% saved)

series3.1s (7.7%)

Error

9.8b

Counts

4 → 87

Calls

4 calls:

1.5s	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (/.f64 (.f64 l (.f64 n U)) Om) (.f64 l -2))))))
1.1s	(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)))))))
201.0ms	(/.f64 (.f64 l (.f64 n U*)) Om)
98.0ms	(.f64 l (.f64 n U*))

Compiler

Compiled 7816 to 5955 computations (23.8% saved)

simplify114.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4979	4859
1	4979	4859

prune243.0ms (0.6%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	164	8	172
Fresh	6	15	21
Picked	0	1	1
Done	1	0	1
Total	171	24	195

Error

9.8b

Counts

195 → 24

Compiler

Compiled 4902 to 2002 computations (59.2% saved)

regimes5.6s (14%)

Accuracy

Total 18.4b remaining (68.8%)

Threshold costs 0b (0%)

Compiler

Compiled 49018 to 35810 computations (26.9% saved)

bsearch18.0ms (0%)

Compiler: Compiled 27 to 22 computations (18.5% saved)

simplify40.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	1043	214
1	1043	214

end0.0ms (0%)

sample8.6s (21.5%)

Algorithm

1×

intervals

Results

1.4s	12816×	body	128	nan
919.0ms	8000×	body	128	valid
130.0ms	1204×	body	128	invalid

Compiler

Compiled 6283 to 4573 computations (27.2% saved)

Details

analyze3.0s (7.4%)

sample142.0ms (0.4%)

simplify68.0ms (0.2%)

prune6.0ms (0%)

localize21.0ms (0.1%)

rewrite301.0ms (0.8%)

series5.4s (13.6%)

simplify139.0ms (0.3%)

prune433.0ms (1.1%)

localize17.0ms (0%)

rewrite236.0ms (0.6%)

series4.8s (11.8%)

simplify92.0ms (0.2%)

prune351.0ms (0.9%)

localize19.0ms (0%)

rewrite217.0ms (0.5%)

series6.5s (16.2%)

simplify105.0ms (0.3%)

prune404.0ms (1%)

localize22.0ms (0.1%)

rewrite200.0ms (0.5%)

series3.1s (7.7%)

simplify114.0ms (0.3%)

prune243.0ms (0.6%)

regimes5.6s (14%)

bsearch18.0ms (0%)

simplify40.0ms (0.1%)

end0.0ms (0%)

sample8.6s (21.5%)

Profiling