Details

analyze2.9s (12.5%)

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)

sample94.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms	190×	body	128	valid
17.0ms	30×	body	1024	valid
9.0ms	22×	body	512	valid
8.0ms	77×	body	128	invalid
7.0ms	15×	body	512	invalid
6.0ms	11×	body	1024	invalid
3.0ms	13×	body	256	valid
2.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify381.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	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: 37.9b

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))))
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.1b	(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))))

rewrite109.0ms (0.5%)

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:

23.0ms	(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))))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series2.1s (9%)

Counts

4 → 12

Calls

4 calls:

1.6s	(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))))
363.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
36.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify158.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5222	10334

prune396.0ms (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

Merged error: 23.5b

Counts

148 → 8

Compiler

Compiled 8753 to 2920 computations (66.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.1b	(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))))

rewrite174.0ms (0.8%)

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:

36.0ms	(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)))

series1.9s (8.1%)

Counts

4 → 12

Calls

4 calls:

1.7s	(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))))
87.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
39.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify224.0ms (1%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5086	17276

prune510.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	203	9	212

Merged error: 23.5b

Counts

212 → 9

Compiler

Compiled 13536 to 4202 computations (69% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.1b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
35.1b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_782`
6×	`*-un-lft-identity_binary64_760` `sqrt-prod_binary64_776` `add-cube-cbrt_binary64_795` `pow1_binary64_821`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796`
2×	`rem-sqrt-square_binary64_773` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `flip-+_binary64_734` `pow1/2_binary64_840`

Counts

4 → 44

Calls

4 calls:

27.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
11.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
9.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.4s (14.7%)

Counts

4 → 12

Calls

4 calls:

1.7s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
1.7s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
35.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5178	1708

prune168.0ms (0.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	56	9	65

Merged error: 23.5b

Counts

65 → 9

Compiler

Compiled 3475 to 1752 computations (49.6% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
4.1b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0b	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))))
35.1b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite87.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_782`
10×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
8×	`pow1_binary64_821`
6×	`sqrt-prod_binary64_776` `exp-prod_binary64_812` `exp-sum_binary64_806` `log-prod_binary64_846`
5×	`add-exp-log_binary64_798`
4×	`add-log-exp_binary64_799` `sqrt-div_binary64_777` `add-cbrt-cube_binary64_796`
3×	`log-pow_binary64_849` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`log-div_binary64_847` `flip3-+_binary64_763` `sqrt-pow1_binary64_778` `exp-diff_binary64_808` `flip-+_binary64_734` `pow1/2_binary64_840`
1×	`rem-sqrt-square_binary64_773` `unpow2_binary64_825` `pow-exp_binary64_828` `rem-exp-log_binary64_800` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `pow-pow_binary64_832`

Counts

4 → 62

Calls

4 calls:

43.0ms	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))))
20.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
11.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

series4.4s (19%)

Counts

4 → 12

Calls

4 calls:

2.4s	(exp.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))))
1.8s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)) (pow.f64 (-.f64 phi1 phi2) 2)))
105.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
33.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify114.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4911	2074
1	4911	2074

prune148.0ms (0.6%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	69	14	83

Merged error: 15.7b

Counts

83 → 14

Compiler

Compiled 2534 to 1292 computations (49% saved)

regimes1.2s (5.2%)

Compiler: Compiled 8222 to 5821 computations (29.2% saved)

bsearch8.0ms (0%)

Compiler: Compiled 32 to 21 computations (34.4% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	71	166
1	71	166

end0.0ms (0%)

sample4.4s (19.1%)

Algorithm

1×

intervals

Results

843.0ms	6047×	body	128	valid
599.0ms	806×	body	1024	valid
383.0ms	756×	body	512	valid
349.0ms	2487×	body	128	invalid
313.0ms	442×	body	1024	invalid
165.0ms	351×	body	512	invalid
125.0ms	382×	body	256	valid
51.0ms	164×	body	256	invalid
11.0ms	9×	body	2048	valid

Compiler

Compiled 923 to 636 computations (31.1% saved)

Details

analyze2.9s (12.5%)

sample94.0ms (0.4%)

simplify381.0ms (1.7%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite109.0ms (0.5%)

series2.1s (9%)

simplify158.0ms (0.7%)

prune396.0ms (1.7%)

localize24.0ms (0.1%)

rewrite174.0ms (0.8%)

series1.9s (8.1%)

simplify224.0ms (1%)

prune510.0ms (2.2%)

localize45.0ms (0.2%)

rewrite75.0ms (0.3%)

series3.4s (14.7%)

simplify67.0ms (0.3%)

prune168.0ms (0.7%)

localize37.0ms (0.2%)

rewrite87.0ms (0.4%)

series4.4s (19%)

simplify114.0ms (0.5%)

prune148.0ms (0.6%)

regimes1.2s (5.2%)

bsearch8.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample4.4s (19.1%)

Profiling