Details

analyze2.3s (21.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5562	539
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample92.0ms (0.9%)

Algorithm

1×

intervals

Results

20.0ms	189×	body	128	valid
12.0ms	16×	body	1024	invalid
12.0ms	25×	body	1024	valid
10.0ms	29×	body	512	valid
9.0ms	85×	body	128	invalid
4.0ms	10×	body	512	invalid
3.0ms	13×	body	256	valid
1.0ms	4×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify131.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune4.0ms (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: 38.5b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.2b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.3b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite83.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_4454`
102×	`flip--_binary64_4486` `flip3--_binary64_4515`
68×	`frac-times_binary64_4521`
66×	`sqrt-div_binary64_4528`
64×	`frac-add_binary64_4519`
44×	`pow1_binary64_4572`
34×	`associate-*r/_binary64_4453`
17×	`pow-prod-down_binary64_4582`
16×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549`
8×	`prod-exp_binary64_4560` `cbrt-unprod_binary64_4544`
6×	`add-sqr-sqrt_binary64_4533`
5×	`*-un-lft-identity_binary64_4511` `add-cube-cbrt_binary64_4546`
4×	`pow-prod-up_binary64_4581` `add-log-exp_binary64_4550` `pow-sqr_binary64_4484`
3×	`sqrt-prod_binary64_4527`
2×	`pow-plus_binary64_4574`
1×	`flip-+_binary64_4485` `flip3-+_binary64_4514` `pow2_binary64_4592` `associate-l_binary64_4452` `associate-r_binary64_4451` `*-commutative_binary64_4442` `swap-sqr_binary64_4478` `rem-sqrt-square_binary64_4524` `pow1/2_binary64_4591` `sqrt-pow1_binary64_4529`

Counts

4 → 135

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series888.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

704.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
151.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5228	10334

prune303.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 16.7b

Counts

148 → 8

Compiler

Compiled 8804 to 2954 computations (66.4% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 R (-.f64 phi2 phi1))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_4533`
7×	`*-un-lft-identity_binary64_4511`
6×	`cancel-sign-sub-inv_binary64_4477`
5×	`associate-r_binary64_4451` `add-cube-cbrt_binary64_4546`
4×	`distribute-lft-in_binary64_4460` `distribute-rgt-in_binary64_4461`
3×	`pow1_binary64_4572` `add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549` `associate-l_binary64_4452`
2×	`associate-*r/_binary64_4453` `sub-neg_binary64_4504`
1×	`distribute-lft-out--_binary64_4463` `flip--_binary64_4486` `unswap-sqr_binary64_4479` `flip3--_binary64_4515` `add-log-exp_binary64_4550` `prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `difference-of-squares_binary64_4480` `pow-prod-down_binary64_4582` `*-commutative_binary64_4442`

Counts

1 → 30

Calls

1 calls:

7.0ms

(*.f64 R (-.f64 phi2 phi1))

series32.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

32.0ms

(*.f64 R (-.f64 phi2 phi1))

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5688	314

prune43.0ms (0.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	23	10	33
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	23	18	41

Merged error: 16.7b

Counts

41 → 18

Compiler

Compiled 706 to 352 computations (50.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
0.3b	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate-r_binary64_4451`
15×	`add-sqr-sqrt_binary64_4533`
14×	`sqrt-div_binary64_4528`
11×	`*-un-lft-identity_binary64_4511` `sqrt-prod_binary64_4527`
10×	`associate-*r/_binary64_4453`
9×	`pow1_binary64_4572` `add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549`
7×	`flip--_binary64_4486` `flip3--_binary64_4515` `add-cube-cbrt_binary64_4546`
4×	`associate-l_binary64_4452` `prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `pow-prod-down_binary64_4582` `frac-times_binary64_4521`
2×	`distribute-lft-out--_binary64_4463` `unswap-sqr_binary64_4479` `add-log-exp_binary64_4550` `difference-of-squares_binary64_4480` `-commutative_binary64_4442` `associate-l/_binary64_4454`

Counts

2 → 57

Calls

2 calls:

13.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))
8.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))

series107.0ms (1%)

Counts

2 → 6

Calls

2 calls:

74.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
33.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4982	929
1	4982	929

prune70.0ms (0.7%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	2	14	16
Picked	1	0	1
Done	0	1	1
Total	60	21	81

Merged error: 16.7b

Counts

81 → 21

Compiler

Compiled 1466 to 537 computations (63.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1)))
0.2b	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
0.3b	(.f64 (.f64 (*.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1)))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1))))
0.3b	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1))))

rewrite73.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`sqrt-div_binary64_4528`
46×	`sqrt-prod_binary64_4527`
36×	`associate-*r/_binary64_4453`
35×	`flip--_binary64_4486` `flip3--_binary64_4515`
32×	`frac-times_binary64_4521`
30×	`associate-r_binary64_4451`
29×	`add-sqr-sqrt_binary64_4533`
23×	`*-un-lft-identity_binary64_4511`
22×	`pow1_binary64_4572`
20×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549`
16×	`associate-*l/_binary64_4454`
15×	`add-cube-cbrt_binary64_4546`
10×	`prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `pow-prod-down_binary64_4582`
5×	`associate-l_binary64_4452`
4×	`distribute-lft-out--_binary64_4463` `add-log-exp_binary64_4550` `difference-of-squares_binary64_4480` `sqrt-pow1_binary64_4529`
3×	`*-commutative_binary64_4442`
2×	`unswap-sqr_binary64_4479` `rem-sqrt-square_binary64_4524` `pow1/2_binary64_4591`

Counts

4 → 138

Calls

4 calls:

28.0ms	(.f64 (.f64 (*.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1)))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1))))
15.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1))))
8.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
5.0ms	(sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1)))

series356.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1))))
106.0ms	(sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1)))
61.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
37.0ms	(.f64 (.f64 (*.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1)))) (sqrt.f64 (sqrt.f64 (-.f64 phi2 phi1))))

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4939	3079
1	4939	3079

prune131.0ms (1.2%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	142	8	150
Fresh	5	14	19
Picked	1	0	1
Done	0	1	1
Total	148	23	171

Merged error: 16.7b

Counts

171 → 23

Compiler

Compiled 3520 to 801 computations (77.2% saved)

regimes1.7s (16.6%)

Compiler: Compiled 14137 to 9147 computations (35.3% saved)

bsearch4.0ms (0%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	105
1	55	105

end0.0ms (0%)

sample3.8s (35.9%)

Algorithm

1×

intervals

Results

677.0ms	6030×	body	128	valid
427.0ms	843×	body	1024	valid
255.0ms	2451×	body	128	invalid
243.0ms	721×	body	512	valid
238.0ms	472×	body	1024	invalid
130.0ms	366×	body	512	invalid
95.0ms	402×	body	256	valid
37.0ms	166×	body	256	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 1572 to 1013 computations (35.6% saved)

Details

analyze2.3s (21.8%)

sample92.0ms (0.9%)

simplify131.0ms (1.2%)

prune4.0ms (0%)

localize20.0ms (0.2%)

rewrite83.0ms (0.8%)

series888.0ms (8.5%)

simplify98.0ms (0.9%)

prune303.0ms (2.9%)

localize4.0ms (0%)

rewrite9.0ms (0.1%)

series32.0ms (0.3%)

simplify47.0ms (0.5%)

prune43.0ms (0.4%)

localize6.0ms (0.1%)

rewrite26.0ms (0.2%)

series107.0ms (1%)

simplify43.0ms (0.4%)

prune70.0ms (0.7%)

localize8.0ms (0.1%)

rewrite73.0ms (0.7%)

series356.0ms (3.4%)

simplify106.0ms (1%)

prune131.0ms (1.2%)

regimes1.7s (16.6%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.8s (35.9%)

Profiling