Details

analyze2.4s (11.6%)

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)

sample91.0ms (0.4%)

Algorithm

1×

intervals

Results

34.0ms	382×	body	128	nan
27.0ms	256×	body	128	valid
3.0ms	33×	body	128	invalid

Compiler

Compiled 57 to 53 computations (7% saved)

simplify137.0ms (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

Error

32.8b

Counts

2 → 2

Compiler

Compiled 80 to 63 computations (21.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
6.9b	(/.f64 (*.f64 l l) Om)
9.4b	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
21.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

rewrite61.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_457`
25×	`pow1_binary64_480`
23×	`add-cbrt-cube_binary64_455`
22×	`associate-*r/_binary64_361`
16×	`prod-exp_binary64_468`
13×	`pow-prod-down_binary64_490`
12×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441`
11×	`flip3--_binary64_423` `flip--_binary64_394`
10×	`add-cube-cbrt_binary64_454` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
8×	`distribute-rgt-in_binary64_369` `associate-r_binary64_359` `distribute-lft-in_binary64_368` `frac-sub_binary64_428`
6×	`sqrt-div_binary64_436` `sub-neg_binary64_412`
4×	`associate--l+_binary64_356` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437`
3×	`times-frac_binary64_425` `associate-/r*_binary64_363` `div-exp_binary64_470`
2×	`pow-exp_binary64_487` `-commutative_binary64_350` `associate-l*_binary64_360` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `sqrt-prod_binary64_435` `associate-/l*_binary64_364`

Counts

4 → 107

Calls

4 calls:

15.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
12.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
5.0ms	(/.f64 (*.f64 l l) Om)

series2.6s (12.5%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
431.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (/.f64 (.f64 l l) Om))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
112.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
13.0ms	(/.f64 (*.f64 l l) Om)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5069	4064

prune225.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	11	119
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Error

24.7b

Counts

121 → 11

Compiler

Compiled 5101 to 2498 computations (51% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (pow.f64 (/.f64 l Om) 2))
6.9b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
9.4b	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
21.4b	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))

rewrite70.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-exp-log_binary64_457`
28×	`add-sqr-sqrt_binary64_441`
26×	`associate-r_binary64_359`
25×	`pow1_binary64_480`
22×	`associate-*r/_binary64_361`
20×	`add-cbrt-cube_binary64_455`
19×	`*-un-lft-identity_binary64_419` `prod-exp_binary64_468`
17×	`add-cube-cbrt_binary64_454`
15×	`unpow-prod-down_binary64_498`
13×	`pow-prod-down_binary64_490`
11×	`flip3--_binary64_423` `flip--_binary64_394`
10×	`times-frac_binary64_425` `cbrt-unprod_binary64_452` `cancel-sign-sub-inv_binary64_385`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `frac-sub_binary64_428`
6×	`sqrt-div_binary64_436` `sub-neg_binary64_412`
5×	`unswap-sqr_binary64_387` `associate-l_binary64_360`
4×	`associate--l+_binary64_356` `add-log-exp_binary64_458` `pow-exp_binary64_487` `sqrt-pow1_binary64_437`
3×	`*-commutative_binary64_350`
2×	`sqr-pow_binary64_391` `pow-to-exp_binary64_488` `unpow2_binary64_484` `div-exp_binary64_470`
1×	`difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 125

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
13.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
12.0ms	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
10.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

series2.7s (12.8%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U)))))
441.0ms	(.f64 (.f64 (.f64 2 n) U) (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
119.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
44.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5253	4364

prune229.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	130	7	137
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	133	15	148

Error

22.7b

Counts

148 → 15

Compiler

Compiled 5934 to 2895 computations (51.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (pow.f64 (/.f64 l Om) 2))
6.6b	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
6.9b	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
21.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))))

rewrite66.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_441`
28×	`associate-*r/_binary64_361` `add-exp-log_binary64_457`
26×	`associate-r_binary64_359`
21×	`pow1_binary64_480`
20×	`*-un-lft-identity_binary64_419`
18×	`add-cube-cbrt_binary64_454`
15×	`unpow-prod-down_binary64_498`
14×	`prod-exp_binary64_468`
13×	`add-cbrt-cube_binary64_455`
11×	`flip3--_binary64_423` `flip--_binary64_394`
10×	`pow-prod-down_binary64_490` `times-frac_binary64_425` `cancel-sign-sub-inv_binary64_385`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `frac-sub_binary64_428`
7×	`associate-l_binary64_360`
6×	`sqrt-div_binary64_436` `sub-neg_binary64_412` `unswap-sqr_binary64_387`
5×	`cbrt-unprod_binary64_452` `sqrt-pow1_binary64_437`
4×	`associate--l+_binary64_356` `add-log-exp_binary64_458` `pow-exp_binary64_487`
3×	`*-commutative_binary64_350`
2×	`sqr-pow_binary64_391` `pow-to-exp_binary64_488` `unpow2_binary64_484` `div-exp_binary64_470`
1×	`difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 123

Calls

4 calls:

13.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))
12.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))))
12.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
12.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))

series2.6s (12.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))))
337.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U))))
115.0ms	(.f64 (.f64 n (pow.f64 (/.f64 l Om) 2)) (-.f64 U U*))
42.0ms	(*.f64 n (pow.f64 (/.f64 l Om) 2))

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4986	4020
1	4986	4020

prune242.0ms (1.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	132	18	150

Error

19.6b

Counts

150 → 18

Compiler

Compiled 6048 to 2954 computations (51.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(*.f64 n (/.f64 l Om))
6.6b	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))
6.9b	(.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U))
21.4b	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))))

rewrite90.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*r/_binary64_361`
45×	`frac-times_binary64_429`
44×	`flip3--_binary64_423` `flip--_binary64_394` `frac-sub_binary64_428`
40×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
30×	`associate-*l/_binary64_362` `pow1_binary64_480`
26×	`add-sqr-sqrt_binary64_441`
24×	`sqrt-div_binary64_436`
21×	`associate-r_binary64_359`
20×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
19×	`*-un-lft-identity_binary64_419`
17×	`add-cube-cbrt_binary64_454`
16×	`pow-prod-down_binary64_490`
10×	`times-frac_binary64_425` `cancel-sign-sub-inv_binary64_385`
8×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
7×	`associate-l_binary64_360`
6×	`sub-neg_binary64_412` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
5×	`sqrt-pow1_binary64_437`
4×	`associate--l+_binary64_356` `add-log-exp_binary64_458`
3×	`unswap-sqr_binary64_387` `*-commutative_binary64_350`
1×	`difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `distribute-lft-out--_binary64_371` `sqrt-prod_binary64_435`

Counts

4 → 170

Calls

4 calls:

18.0ms	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))))
16.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))
16.0ms	(.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U))
7.0ms	(*.f64 n (/.f64 l Om))

series2.6s (12.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(sqrt.f64 (.f64 (.f64 2 n) (.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))))
338.0ms	(.f64 U (-.f64 (-.f64 t (.f64 2 (.f64 l (/.f64 l Om)))) (.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U*))))
117.0ms	(.f64 (.f64 (.f64 n (/.f64 l Om)) (/.f64 l Om)) (-.f64 U U))
18.0ms	(*.f64 n (/.f64 l Om))

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5143	8293

prune287.0ms (1.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	5	12	17
Picked	1	0	1
Done	0	0	0
Total	183	17	200

Error

18.4b

Counts

200 → 17

Compiler

Compiled 9006 to 2999 computations (66.7% saved)

regimes1.6s (7.7%)

Accuracy

Total 9.0b remaining (34.3%)

Threshold costs 0b (0%)

Compiler

Compiled 23423 to 15436 computations (34.1% saved)

bsearch6.0ms (0%)

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

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	339	319
1	339	319

end0.0ms (0%)

sample4.5s (21.5%)

Algorithm

1×

intervals

Results

1.2s	12863×	body	128	nan
721.0ms	8000×	body	128	valid
113.0ms	1190×	body	128	invalid

Compiler

Compiled 3068 to 1990 computations (35.1% saved)

Details

analyze2.4s (11.6%)

sample91.0ms (0.4%)

simplify137.0ms (0.7%)

prune5.0ms (0%)

localize18.0ms (0.1%)

rewrite61.0ms (0.3%)

series2.6s (12.5%)

simplify71.0ms (0.3%)

prune225.0ms (1.1%)

localize18.0ms (0.1%)

rewrite70.0ms (0.3%)

series2.7s (12.8%)

simplify74.0ms (0.4%)

prune229.0ms (1.1%)

localize17.0ms (0.1%)

rewrite66.0ms (0.3%)

series2.6s (12.4%)

simplify91.0ms (0.4%)

prune242.0ms (1.2%)

localize18.0ms (0.1%)

rewrite90.0ms (0.4%)

series2.6s (12.4%)

simplify100.0ms (0.5%)

prune287.0ms (1.4%)

regimes1.6s (7.7%)

bsearch6.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample4.5s (21.5%)

Profiling