Details

analyze2.3s (23.9%)

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)

sample86.0ms (0.9%)

Algorithm

1×

intervals

Results

26.0ms	203×	body	128	valid
10.0ms	21×	body	1024	valid
8.0ms	76×	body	128	invalid
7.0ms	15×	body	1024	invalid
6.0ms	19×	body	512	valid
3.0ms	13×	body	256	valid
2.0ms	6×	body	512	invalid
1.0ms	6×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify129.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune3.0ms (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

36.9b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize16.0ms (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))))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.7b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
33.9b	(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))))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_703`
102×	`flip--_binary64_735` `flip3--_binary64_764`
68×	`frac-times_binary64_770`
66×	`sqrt-div_binary64_777`
64×	`frac-add_binary64_768`
44×	`pow1_binary64_821`
34×	`associate-*r/_binary64_702`
17×	`pow-prod-down_binary64_831`
16×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
6×	`add-sqr-sqrt_binary64_782`
5×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
4×	`add-log-exp_binary64_799` `pow-sqr_binary64_733` `pow-prod-up_binary64_830`
3×	`sqrt-prod_binary64_776`
2×	`pow-plus_binary64_823`
1×	`pow2_binary64_841` `rem-sqrt-square_binary64_773` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `flip-+_binary64_734` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701` `pow1/2_binary64_840` `*-commutative_binary64_691`

Counts

4 → 135

Calls

4 calls:

24.0ms	(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))))
17.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series927.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

731.0ms	(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))))
161.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5228	10334

prune307.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	138	10	148

Error

12.7b

Counts

148 → 10

Compiler

Compiled 8917 to 3005 computations (66.3% 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_782`
7×	`*-un-lft-identity_binary64_760`
6×	`cancel-sign-sub-inv_binary64_726`
5×	`add-cube-cbrt_binary64_795` `associate-r_binary64_700`
4×	`distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710`
3×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-l_binary64_701` `pow1_binary64_821`
2×	`associate-*r/_binary64_702` `sub-neg_binary64_753`
1×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `add-log-exp_binary64_799` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

1 → 30

Calls

1 calls:

7.0ms

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

series34.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

34.0ms

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

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5688	314

prune47.0ms (0.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	24	9	33
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	26	17	43

Error

12.7b

Counts

43 → 17

Compiler

Compiled 721 to 351 computations (51.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 R phi2) (.f64 R (neg.f64 phi1)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_799`
1×	`distribute-rgt-neg-out_binary64_720` `*-un-lft-identity_binary64_760` `distribute-lft-out_binary64_711` `flip3-+_binary64_763` `add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `unsub-neg_binary64_754` `flip-+_binary64_734` `add-cbrt-cube_binary64_796` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1_binary64_821` `add-sqr-sqrt_binary64_782`

Counts

1 → 13

Calls

1 calls:

4.0ms

(+.f64 (*.f64 R phi2) (*.f64 R (neg.f64 phi1)))

series36.0ms (0.4%)

Counts

1 → 3

Calls

1 calls:

36.0ms

(+.f64 (*.f64 R phi2) (*.f64 R (neg.f64 phi1)))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5235	170

prune29.0ms (0.3%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	15	18	33

Error

12.7b

Counts

33 → 18

Compiler

Compiled 589 to 331 computations (43.8% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 phi2 phi1))
0.0b	(sqrt.f64 (-.f64 phi2 phi1))
0.2b	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
0.3b	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_782`
21×	`sqrt-prod_binary64_776`
19×	`*-un-lft-identity_binary64_760`
18×	`sqrt-div_binary64_777`
16×	`associate-r_binary64_700`
13×	`pow1_binary64_821`
11×	`add-exp-log_binary64_798` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796`
10×	`associate-*r/_binary64_702`
9×	`flip--_binary64_735` `flip3--_binary64_764`
4×	`prod-exp_binary64_809` `add-log-exp_binary64_799` `difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `associate-l_binary64_701` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831`
2×	`unswap-sqr_binary64_728` `rem-sqrt-square_binary64_773` `associate-l/_binary64_703` `sqrt-pow1_binary64_778` `pow1/2_binary64_840` `-commutative_binary64_691`

Counts

4 → 91

Calls

4 calls:

16.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))
8.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
3.0ms	(sqrt.f64 (-.f64 phi2 phi1))
3.0ms	(sqrt.f64 (-.f64 phi2 phi1))

series172.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(*.f64 R (sqrt.f64 (-.f64 phi2 phi1)))
34.0ms	(sqrt.f64 (-.f64 phi2 phi1))
34.0ms	(.f64 (.f64 R (sqrt.f64 (-.f64 phi2 phi1))) (sqrt.f64 (-.f64 phi2 phi1)))
33.0ms	(sqrt.f64 (-.f64 phi2 phi1))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5272	1453

prune74.0ms (0.8%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	4	11	15
Picked	1	0	1
Done	0	2	2
Total	101	20	121

Error

12.7b

Counts

121 → 20

Compiler

Compiled 1683 to 392 computations (76.7% saved)

regimes1.3s (14%)

Accuracy

Total 3.3b remaining (17.3%)

Threshold costs 0b (0%)

Compiler

Compiled 11999 to 7575 computations (36.9% saved)

bsearch4.0ms (0%)

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

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	91
1	58	91

Compiler

Compiled 240 to 132 computations (45% saved)

end0.0ms (0%)

sample3.5s (37.6%)

Algorithm

1×

intervals

Results

667.0ms	6046×	body	128	valid
395.0ms	833×	body	1024	valid
261.0ms	2465×	body	128	invalid
245.0ms	709×	body	512	valid
216.0ms	474×	body	1024	invalid
121.0ms	360×	body	512	invalid
97.0ms	401×	body	256	valid
36.0ms	162×	body	256	invalid
12.0ms	11×	body	2048	valid

Compiler

Compiled 1347 to 846 computations (37.2% saved)

Details

analyze2.3s (23.9%)

sample86.0ms (0.9%)

simplify129.0ms (1.4%)

prune3.0ms (0%)

localize16.0ms (0.2%)

rewrite81.0ms (0.9%)

series927.0ms (9.8%)

simplify100.0ms (1.1%)

prune307.0ms (3.3%)

localize4.0ms (0%)

rewrite9.0ms (0.1%)

series34.0ms (0.4%)

simplify49.0ms (0.5%)

prune47.0ms (0.5%)

localize6.0ms (0.1%)

rewrite5.0ms (0.1%)

series36.0ms (0.4%)

simplify74.0ms (0.8%)

prune29.0ms (0.3%)

localize6.0ms (0.1%)

rewrite37.0ms (0.4%)

series172.0ms (1.8%)

simplify50.0ms (0.5%)

prune74.0ms (0.8%)

regimes1.3s (14%)

bsearch4.0ms (0%)

simplify15.0ms (0.2%)

end0.0ms (0%)

sample3.5s (37.6%)

Profiling