Details

analyze2.4s (12.3%)

Algorithm

1×

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)

sample105.0ms (0.5%)

Algorithm

1×

intervals

Results

45.0ms	477×	body	128	nan
23.0ms	256×	body	128	valid
4.0ms	50×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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

Merged error: 29.6b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.9b	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
9.3b	(.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)))))))
10.3b	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))
18.3b	(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))))))))

rewrite58.0ms (0.3%)

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:

16.0ms	(.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)))))))
8.0ms	(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))))))))

series1.6s (8.1%)

Counts

4 → 66

Calls

4 calls:

699.0ms	(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))))))))
398.0ms	(.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)))))))
297.0ms	(.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))))
165.0ms	(.f64 (/.f64 l Om) (.f64 n (-.f64 U* U)))

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4996	8190
1	4996	8190

prune345.0ms (1.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	181	16	197
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	183	16	199

Merged error: 15.8b

Counts

199 → 16

Compiler

Compiled 8809 to 3339 computations (62.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(.f64 n (.f64 l (-.f64 U* U)))
5.8b	(/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om)
9.3b	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))
18.3b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om))))))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`pow1_binary64_480`
27×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
17×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
15×	`pow-prod-down_binary64_490`
12×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `add-sqr-sqrt_binary64_441` `associate-r/_binary64_361` `cancel-sign-sub-inv_binary64_385`
4×	`sub-neg_binary64_412` `add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360` `sqrt-pow1_binary64_437`
3×	`times-frac_binary64_425` `associate-/r*_binary64_363` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `flip3--_binary64_423` `*-commutative_binary64_350` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`

Counts

4 → 101

Calls

4 calls:

11.0ms	(/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om)
9.0ms	(.f64 n (.f64 l (-.f64 U* U)))
9.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) 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 (-.f64 U U))) Om))))))

series1.3s (6.9%)

Counts

4 → 63

Calls

4 calls:

686.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om))))))
389.0ms	(.f64 (.f64 (.f64 2 n) U) (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))
162.0ms	(/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om)
79.0ms	(.f64 n (.f64 l (-.f64 U* U)))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5738	6442

prune241.0ms (1.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	162	18	180

Merged error: 15.3b

Counts

180 → 18

Compiler

Compiled 7335 to 2949 computations (59.8% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

18.3b	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
19.3b	(cbrt.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))))))))
19.3b	(cbrt.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))))))))
19.3b	(cbrt.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))))))))

rewrite65.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`associate-*r/_binary64_361`
60×	`cbrt-div_binary64_451`
30×	`flip3-+_binary64_422` `flip-+_binary64_393`
28×	`frac-times_binary64_429`
26×	`sqrt-div_binary64_436`
24×	`pow1_binary64_480`
15×	`sqrt-pow1_binary64_437`
14×	`associate-*l/_binary64_362`
12×	`pow1/3_binary64_501`
9×	`pow-prod-up_binary64_489`
6×	`pow-plus_binary64_482`
5×	`pow-prod-down_binary64_490`
4×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`cbrt-prod_binary64_450` `pow-sqr_binary64_392`
2×	`pow2_binary64_500`
1×	`pow1/2_binary64_499` `sqrt-prod_binary64_435` `pow3_binary64_502`

Counts

4 → 83

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
7.0ms	(cbrt.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))))))))
7.0ms	(cbrt.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))))))))
7.0ms	(cbrt.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))))))))

series3.8s (19.7%)

Counts

4 → 72

Calls

4 calls:

1.1s	(sqrt.f64 (.f64 (.f64 (cbrt.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)))))))) (cbrt.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))))))))) (cbrt.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))))))))))
903.0ms	(cbrt.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))))))))
890.0ms	(cbrt.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))))))))
878.0ms	(cbrt.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))))))))

simplify174.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4970	19064
1	4970	19064

prune768.0ms (4%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	3	13	16
Picked	0	1	1
Done	0	1	1
Total	153	20	173

Merged error: 15.3b

Counts

173 → 20

Compiler

Compiled 19263 to 7800 computations (59.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.7b	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))
5.8b	(/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om)
7.0b	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om))))))
18.3b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

11.0ms	(/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om)
9.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om))))))
8.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))))
6.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))

series1.6s (8.1%)

Counts

4 → 69

Calls

4 calls:

692.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))))
391.0ms	(.f64 (.f64 2 n) (.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om))))))
291.0ms	(.f64 U (+.f64 t (.f64 (/.f64 l Om) (+.f64 (.f64 l -2) (/.f64 (.f64 n (.f64 l (-.f64 U U))) Om)))))
181.0ms	(/.f64 (.f64 n (.f64 l (-.f64 U* U))) Om)

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5001	7726

prune234.0ms (1.2%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	6	11	17
Picked	1	0	1
Done	0	2	2
Total	160	20	180

Merged error: 12.7b

Counts

180 → 20

Compiler

Compiled 6793 to 2386 computations (64.9% saved)

regimes1.6s (8.3%)

Compiler: Compiled 23474 to 14530 computations (38.1% saved)

bsearch7.0ms (0%)

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

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	1210	267
1	1210	267

end0.0ms (0%)

sample4.4s (22.9%)

Algorithm

1×

intervals

Results

1.1s	12897×	body	128	nan
734.0ms	8000×	body	128	valid
110.0ms	1219×	body	128	invalid

Compiler

Compiled 3125 to 1922 computations (38.5% saved)

Details

analyze2.4s (12.3%)

sample105.0ms (0.5%)

simplify139.0ms (0.7%)

prune5.0ms (0%)

localize17.0ms (0.1%)

rewrite58.0ms (0.3%)

series1.6s (8.1%)

simplify84.0ms (0.4%)

prune345.0ms (1.8%)

localize18.0ms (0.1%)

rewrite50.0ms (0.3%)

series1.3s (6.9%)

simplify75.0ms (0.4%)

prune241.0ms (1.3%)

localize26.0ms (0.1%)

rewrite65.0ms (0.3%)

series3.8s (19.7%)

simplify174.0ms (0.9%)

prune768.0ms (4%)

localize19.0ms (0.1%)

rewrite44.0ms (0.2%)

series1.6s (8.1%)

simplify96.0ms (0.5%)

prune234.0ms (1.2%)

regimes1.6s (8.3%)

bsearch7.0ms (0%)

simplify56.0ms (0.3%)

end0.0ms (0%)

sample4.4s (22.9%)

Profiling