Details

analyze2.1s (1.4%)

Algorithm

1×

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)

sample79.0ms (0.1%)

Algorithm

1×

intervals

Results

19.0ms	185×	body	128	valid
11.0ms	25×	body	1024	valid
10.0ms	30×	body	512	valid
8.0ms	79×	body	128	invalid
5.0ms	14×	body	512	invalid
3.0ms	15×	body	256	valid
3.0ms	7×	body	1024	invalid
2.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify227.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

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

Merged error: 38.1b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize15.0ms (0%)

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))))
5.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.7b	(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))))

rewrite79.0ms (0.1%)

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:

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))))
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))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series913.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

708.0ms	(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))))
160.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5228	10334

prune289.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Merged error: 24.3b

Counts

148 → 8

Compiler

Compiled 8769 to 2931 computations (66.6% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.6b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite66.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_703`
96×	`flip--_binary64_735` `flip3--_binary64_764`
66×	`sqrt-div_binary64_777`
64×	`frac-add_binary64_768` `frac-times_binary64_770`
32×	`associate-*r/_binary64_702`
8×	`add-sqr-sqrt_binary64_782`
7×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
6×	`pow1_binary64_821`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `log-pow_binary64_849`
3×	`sqrt-prod_binary64_776` `exp-prod_binary64_812` `log-prod_binary64_846`
1×	`rem-sqrt-square_binary64_773` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `flip-+_binary64_734` `rem-log-exp_binary64_801` `pow1/2_binary64_840`

Counts

4 → 108

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(log.f64 (exp.f64 (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))

series1.3s (0.8%)

Counts

4 → 12

Calls

4 calls:

1.2s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
48.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5363	9530

prune249.0ms (0.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	118	10	128

Merged error: 22.8b

Counts

128 → 10

Compiler

Compiled 8108 to 2752 computations (66.1% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

28.3b	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
28.3b	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
28.3b	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
34.7b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (cbrt.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))))

rewrite5.5s (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

29930×	`associate-*l/_binary64_703`
20428×	`frac-times_binary64_770`
16050×	`flip--_binary64_735` `flip3--_binary64_764`
15576×	`cbrt-div_binary64_792`
5990×	`associate-*r/_binary64_702`
5826×	`sqrt-div_binary64_777`
5824×	`frac-add_binary64_768`
6×	`add-sqr-sqrt_binary64_782`
5×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `pow1_binary64_821`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`pow1/3_binary64_842` `sqrt-prod_binary64_776` `cbrt-prod_binary64_791`
1×	`rem-sqrt-square_binary64_773` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `flip-+_binary64_734` `pow1/2_binary64_840`

Counts

4 → 5890

Calls

4 calls:

549.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (cbrt.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))))
16.0ms	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
13.0ms	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
13.0ms	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

series1.9s (1.3%)

Counts

4 → 12

Calls

4 calls:

740.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (cbrt.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))))
399.0ms	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
399.0ms	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))
396.0ms	(cbrt.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))

simplify11.9s (7.9%)

Algorithm

1×	egg-herbie

Counts

5902 → 5902

Iterations

Useful iterations: 0 (310.0ms)

Iter	Nodes	Cost
0	22399	1728874

Details

analyze2.1s (1.4%)

sample79.0ms (0.1%)

simplify227.0ms (0.2%)

prune3.0ms (0%)

localize15.0ms (0%)

rewrite79.0ms (0.1%)

series913.0ms (0.6%)

simplify99.0ms (0.1%)

prune289.0ms (0.2%)

localize19.0ms (0%)

rewrite66.0ms (0%)

series1.3s (0.8%)

simplify91.0ms (0.1%)

prune249.0ms (0.2%)

localize21.0ms (0%)

rewrite5.5s (3.6%)

series1.9s (1.3%)

simplify11.9s (7.9%)

prune2.1min (83.5%)

Profiling