Details

analyze2.1s (11.9%)

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)

sample82.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	192×	body	128	valid
11.0ms	24×	body	1024	valid
9.0ms	26×	body	512	valid
8.0ms	18×	body	1024	invalid
8.0ms	83×	body	128	invalid
3.0ms	13×	body	256	valid
3.0ms	8×	body	512	invalid
1.0ms	5×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify225.0ms (1.3%)

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

40.5b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize16.0ms (0.1%)

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))))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.3b	(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))))

rewrite77.0ms (0.4%)

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))

series918.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

720.0ms	(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))))
165.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify97.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5228	10334

prune298.0ms (1.7%)

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

Error

24.0b

Counts

148 → 8

Compiler

Compiled 8816 to 2945 computations (66.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.3b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite98.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip--_binary64_735` `flip3--_binary64_764`
196×	`frac-times_binary64_770`
138×	`sqrt-div_binary64_777`
136×	`frac-add_binary64_768`
130×	`associate-*l/_binary64_703`
74×	`associate-*r/_binary64_702`
73×	`cos-mult_binary64_914`
12×	`pow1_binary64_821` `add-sqr-sqrt_binary64_782`
9×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
4×	`add-log-exp_binary64_799`
3×	`sqrt-prod_binary64_776` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
1×	`pow2_binary64_841` `unswap-sqr_binary64_728` `rem-sqrt-square_binary64_773` `prod-exp_binary64_809` `flip3-+_binary64_763` `sqr-cos-a_binary64_909` `sqrt-pow1_binary64_778` `pow-sqr_binary64_733` `pow-plus_binary64_823` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 192

Calls

4 calls:

33.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

series784.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

715.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
36.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify186.0ms (1%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5037	17590

prune428.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	204	8	212

Error

23.6b

Counts

212 → 8

Compiler

Compiled 13752 to 4220 computations (69.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.4b	(cbrt.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))))
38.4b	(cbrt.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))))

rewrite111.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_703`
192×	`flip--_binary64_735` `flip3--_binary64_764`
132×	`cbrt-div_binary64_792`
128×	`frac-add_binary64_768` `frac-times_binary64_770`
64×	`associate-*r/_binary64_702`
6×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `cbrt-prod_binary64_791` `add-sqr-sqrt_binary64_782`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
2×	`pow1/3_binary64_842` `flip3-+_binary64_763` `flip-+_binary64_734`

Counts

4 → 168

Calls

4 calls:

23.0ms	(cbrt.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))))
21.0ms	(cbrt.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))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.0s (11.3%)

Counts

4 → 12

Calls

4 calls:

1.0s	(cbrt.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))))
977.0ms	(cbrt.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))))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify156.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4997	18474
1	4997	18474

prune688.0ms (3.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	179	9	188

Error

23.6b

Counts

188 → 9

Compiler

Compiled 19555 to 6664 computations (65.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.5b	(exp.f64 (log.f64 (cbrt.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))))))
38.4b	(cbrt.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))))
38.4b	(cbrt.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))))

rewrite186.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

384×	`associate-*l/_binary64_703`
288×	`flip--_binary64_735` `flip3--_binary64_764`
198×	`cbrt-div_binary64_792`
192×	`frac-add_binary64_768` `frac-times_binary64_770`
96×	`associate-*r/_binary64_702`
66×	`log-div_binary64_847` `exp-diff_binary64_808`
9×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `cbrt-prod_binary64_791` `add-sqr-sqrt_binary64_782`
6×	`exp-sum_binary64_806` `log-prod_binary64_846`
5×	`exp-prod_binary64_812` `pow1_binary64_821`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`pow1/3_binary64_842` `flip3-+_binary64_763` `flip-+_binary64_734`
2×	`log-pow_binary64_849`
1×	`rem-exp-log_binary64_800`

Counts

4 → 246

Calls

4 calls:

35.0ms	(exp.f64 (log.f64 (cbrt.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))))))
21.0ms	(cbrt.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))))
21.0ms	(cbrt.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))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.3s (18.6%)

Counts

4 → 12

Calls

4 calls:

1.3s	(exp.f64 (log.f64 (cbrt.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))))))
1.0s	(cbrt.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))))
1.0s	(cbrt.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))))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify224.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5211	27608

prune1.1s (6.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	258	9	267

Error

23.6b

Counts

267 → 9

Compiler

Compiled 28516 to 9739 computations (65.8% saved)

regimes1.2s (6.6%)

Accuracy

Total 4.2b remaining (14.8%)

Threshold costs 0b (0%)

Compiler

Compiled 13869 to 8470 computations (38.9% saved)

bsearch3.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	105
1	61	105

end0.0ms (0%)

sample3.4s (19.3%)

Algorithm

1×

intervals

Results

631.0ms	6144×	body	128	valid
350.0ms	759×	body	1024	valid
268.0ms	2464×	body	128	invalid
251.0ms	716×	body	512	valid
217.0ms	460×	body	1024	invalid
119.0ms	346×	body	512	invalid
89.0ms	375×	body	256	valid
44.0ms	197×	body	256	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 1527 to 931 computations (39% saved)

Details

analyze2.1s (11.9%)

sample82.0ms (0.5%)

simplify225.0ms (1.3%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite77.0ms (0.4%)

series918.0ms (5.2%)

simplify97.0ms (0.5%)

prune298.0ms (1.7%)

localize17.0ms (0.1%)

rewrite98.0ms (0.6%)

series784.0ms (4.4%)

simplify186.0ms (1%)

prune428.0ms (2.4%)

localize21.0ms (0.1%)

rewrite111.0ms (0.6%)

series2.0s (11.3%)

simplify156.0ms (0.9%)

prune688.0ms (3.9%)

localize26.0ms (0.1%)

rewrite186.0ms (1%)

series3.3s (18.6%)

simplify224.0ms (1.3%)

prune1.1s (6.1%)

regimes1.2s (6.6%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (19.3%)

Profiling