Details

analyze4.0s (8.3%)

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

Compiler

Compiled 29 to 24 computations (17.2% saved)

sample172.0ms (0.4%)

Algorithm

1×

intervals

Results

58.0ms	352×	body	128	nan
49.0ms	256×	body	128	valid
4.0ms	26×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

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

29.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
8.3b	(.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)))))))
12.2b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
20.1b	(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))))))))

rewrite430.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

23.1b

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:

22.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
17.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
16.0ms	(.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))))))))

Compiler

Compiled 5195 to 2032 computations (60.9% saved)

series6.4s (13.3%)

Error

17.4b

Counts

4 → 112

Calls

4 calls:

2.8s	(.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))))))))
1.1s	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
499.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

Compiler

Compiled 11564 to 8738 computations (24.4% saved)

simplify234.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4974	7813
1	4974	7813

prune542.0ms (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

13.0b

Counts

245 → 21

Compiler

Compiled 8571 to 3241 computations (62.2% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

6.0b	(.f64 l (.f64 (-.f64 U* U) (/.f64 n Om)))
6.7b	(.f64 (-.f64 U U) (/.f64 n Om))
8.3b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om)))))))
20.1b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om))))))))

rewrite314.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

12.8b

Rules

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

Counts

4 → 103

Calls

4 calls:

26.0ms	(.f64 (-.f64 U U) (/.f64 n Om))
21.0ms	(.f64 l (.f64 (-.f64 U* U) (/.f64 n Om)))
19.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om)))))))
10.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om))))))))

Compiler

Compiled 3954 to 1619 computations (59.1% saved)

series5.7s (11.7%)

Error

13.0b

Counts

4 → 103

Calls

4 calls:

3.0s	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om)))))))
1.5s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 l (.f64 (-.f64 U U) (/.f64 n Om))))))))
595.0ms	(.f64 l (.f64 (-.f64 U* U) (/.f64 n Om)))
297.0ms	(.f64 (-.f64 U U) (/.f64 n Om))

Compiler

Compiled 10668 to 7921 computations (25.7% saved)

simplify202.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4974	6052
1	4974	6052

prune468.0ms (1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	4	16	20
Picked	0	1	1
Done	0	0	0
Total	206	21	227

Error

12.8b

Counts

227 → 21

Compiler

Compiled 7179 to 2851 computations (60.3% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
5.5b	(.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))))))
9.2b	(/.f64 (.f64 l (-.f64 U U)) Om)
20.1b	(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)))))))

rewrite244.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

9.8b

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` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-l_binary64_360`
3×	`associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `div-inv_binary64_416` `associate-/l/_binary64_366` `*-commutative_binary64_350`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `frac-2neg_binary64_430` `clear-num_binary64_418` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364` `unswap-sqr_binary64_387`

Counts

4 → 94

Calls

4 calls:

17.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
16.0ms	(.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))))))
15.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
13.0ms	(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)

series5.9s (12.2%)

Error

12.8b

Counts

4 → 103

Calls

4 calls:

3.2s	(.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))))))
1.6s	(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)))))))
532.0ms	(.f64 n (/.f64 (.f64 l (-.f64 U* U)) Om))
355.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 10668 to 7921 computations (25.7% saved)

simplify177.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4990	6052
1	4990	6052

prune382.0ms (0.8%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	193	4	197
Fresh	2	17	19
Picked	0	1	1
Done	0	1	1
Total	195	23	218

Error

9.8b

Counts

218 → 23

Compiler

Compiled 6979 to 2733 computations (60.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.2b	(/.f64 (.f64 l (-.f64 U U)) Om)
20.1b	(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)))))))
20.1b	(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)))))))
20.1b	(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)))))))

rewrite624.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

9.8b

Rules

43×	`pow1_binary64_480`
24×	`pow-prod-down_binary64_490`
15×	`sqrt-pow1_binary64_437`
14×	`associate-*r/_binary64_361`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `sqrt-div_binary64_436` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458`
3×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `sqrt-prod_binary64_435` `times-frac_binary64_425` `associate-/r*_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 71

Calls

4 calls:

13.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)
10.0ms	(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)))))))
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)))))))
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 6860 to 2967 computations (56.7% saved)

series5.7s (11.8%)

Error

9.8b

Counts

4 → 90

Calls

4 calls:

1.6s	(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)))))))
1.6s	(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)))))))
1.5s	(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)))))))
423.0ms	(/.f64 (.f64 l (-.f64 U U)) Om)

Compiler

Compiled 26016 to 16032 computations (38.4% saved)

simplify158.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4998	5538
1	4998	5538

prune813.0ms (1.7%)

Pruning

23 alts after pruning (20 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	20	20
Picked	0	1	1
Done	0	2	2
Total	161	23	184

Error

9.8b

Counts

184 → 23

Compiler

Compiled 14326 to 6055 computations (57.7% saved)

regimes5.0s (10.3%)

Accuracy

Total 18.0b remaining (61.9%)

Threshold costs 0b (0%)

Compiler

Compiled 36738 to 26794 computations (27.1% saved)

bsearch485.0ms (1%)

Steps

Iters	Range	Point
9	1.3267364841133853e+113	1.2738319763243404e+118	1.444532503604196e+117
8	-3.6023443947436196e+76	-7.752821248195671e+71	-2.293426421173244e+74
9	-2.6797069147090756e+161	-1.6929717431333202e+156	-5.123975402606152e+157

Iters

Range

Point

1.3267364841133853e+113

1.2738319763243404e+118

1.444532503604196e+117

-3.6023443947436196e+76

-7.752821248195671e+71

-2.293426421173244e+74

-2.6797069147090756e+161

-1.6929717431333202e+156

-5.123975402606152e+157

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	236	238
1	236	238

end0.0ms (0%)

sample10.2s (21.2%)

Algorithm

1×

intervals

Results

1.9s	12779×	body	128	nan
1.2s	8000×	body	128	valid
190.0ms	1179×	body	128	invalid

Compiler

Compiled 4763 to 3450 computations (27.6% saved)

Details

analyze4.0s (8.3%)

sample172.0ms (0.4%)

simplify91.0ms (0.2%)

prune10.0ms (0%)

localize33.0ms (0.1%)

rewrite430.0ms (0.9%)

series6.4s (13.3%)

simplify234.0ms (0.5%)

prune542.0ms (1.1%)

localize19.0ms (0%)

rewrite314.0ms (0.6%)

series5.7s (11.7%)

simplify202.0ms (0.4%)

prune468.0ms (1%)

localize35.0ms (0.1%)

rewrite244.0ms (0.5%)

series5.9s (12.2%)

simplify177.0ms (0.4%)

prune382.0ms (0.8%)

localize28.0ms (0.1%)

rewrite624.0ms (1.3%)

series5.7s (11.8%)

simplify158.0ms (0.3%)

prune813.0ms (1.7%)

regimes5.0s (10.3%)

bsearch485.0ms (1%)

simplify6.0ms (0%)

end0.0ms (0%)

sample10.2s (21.2%)

Profiling