Details

analyze2.1s (8.8%)

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 (0.3%)

Algorithm

1×

intervals

Results

20.0ms	197×	body	128	valid
14.0ms	26×	body	1024	valid
7.0ms	14×	body	1024	invalid
7.0ms	19×	body	512	valid
7.0ms	67×	body	128	invalid
5.0ms	13×	body	512	invalid
3.0ms	14×	body	256	valid
0.0ms	2×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify307.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

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: 41.0b

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))))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(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))))

rewrite85.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_696`
102×	`flip--_binary64_726` `flip3--_binary64_755`
68×	`frac-times_binary64_761`
66×	`sqrt-div_binary64_767`
64×	`frac-add_binary64_759`
44×	`pow1_binary64_809`
34×	`associate-*r/_binary64_695`
17×	`pow-prod-down_binary64_819`
16×	`add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
8×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
6×	`add-sqr-sqrt_binary64_772`
5×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
4×	`pow-sqr_binary64_724` `add-log-exp_binary64_787` `pow-prod-up_binary64_818`
3×	`sqrt-prod_binary64_766`
2×	`pow-plus_binary64_811`
1×	`flip3-+_binary64_754` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `-commutative_binary64_684` `swap-sqr_binary64_718` `associate-l_binary64_694` `associate-r*_binary64_693` `pow2_binary64_829` `sqrt-pow1_binary64_768` `flip-+_binary64_725`

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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.6s (6.9%)

Counts

4 → 12

Calls

4 calls:

1.3s	(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))))
290.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5181	10334

prune318.0ms (1.3%)

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: 24.8b

Counts

148 → 8

Compiler

Compiled 8788 to 2936 computations (66.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(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))))

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*l/_binary64_696`
96×	`flip--_binary64_726` `flip3--_binary64_755`
66×	`sqrt-div_binary64_767`
64×	`frac-times_binary64_761` `frac-add_binary64_759`
32×	`associate-*r/_binary64_695`
8×	`add-sqr-sqrt_binary64_772`
7×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
6×	`pow1_binary64_809`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `log-pow_binary64_837` `add-exp-log_binary64_786`
3×	`exp-prod_binary64_800` `log-prod_binary64_834` `sqrt-prod_binary64_766`
1×	`rem-log-exp_binary64_789` `flip3-+_binary64_754` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768` `flip-+_binary64_725`

Counts

4 → 108

Calls

4 calls:

23.0ms	(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))))
7.0ms	(log.f64 (exp.f64 (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))

series2.2s (9.4%)

Counts

4 → 12

Calls

4 calls:

2.1s	(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))))
85.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify91.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5318	9530

prune257.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	118	10	128

Merged error: 24.3b

Counts

128 → 10

Compiler

Compiled 8174 to 2790 computations (65.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite196.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

328×	`frac-times_binary64_761`
300×	`flip--_binary64_726` `flip3--_binary64_755`
260×	`associate-*l/_binary64_696`
210×	`sqrt-div_binary64_767`
208×	`frac-add_binary64_759`
164×	`associate-*r/_binary64_695`
73×	`flip3-+_binary64_754` `flip-+_binary64_725`
6×	`add-sqr-sqrt_binary64_772`
5×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `*-un-lft-identity_binary64_751`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`sqrt-prod_binary64_766`
1×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768`

Counts

4 → 244

Calls

4 calls:

40.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series4.2s (17.8%)

Counts

4 → 12

Calls

4 calls:

4.2s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
32.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify347.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4997	38851
1	4997	38851

prune1.4s (5.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	253	13	266

Merged error: 24.3b

Counts

266 → 13

Compiler

Compiled 27659 to 12282 computations (55.6% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 lambda1 lambda2) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite193.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

328×	`frac-times_binary64_761`
300×	`flip--_binary64_726` `flip3--_binary64_755`
260×	`associate-*l/_binary64_696`
210×	`sqrt-div_binary64_767`
208×	`frac-add_binary64_759`
164×	`associate-*r/_binary64_695`
73×	`flip3-+_binary64_754` `flip-+_binary64_725`
6×	`add-sqr-sqrt_binary64_772`
5×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `*-un-lft-identity_binary64_751`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
3×	`sqrt-prod_binary64_766`
1×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `sqrt-pow1_binary64_768`

Counts

4 → 244

Calls

4 calls:

43.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 lambda1 lambda2) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series4.6s (19.4%)

Counts

4 → 12

Calls

4 calls:

4.5s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 lambda1 lambda2) (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
31.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
29.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify350.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5004	38851

prune1.3s (5.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	256	13	269

Merged error: 24.3b

Counts

269 → 13

Compiler

Compiled 27099 to 11938 computations (55.9% saved)

regimes640.0ms (2.7%)

Compiler: Compiled 6826 to 4508 computations (34% saved)

bsearch4.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	166
1	61	166

end0.0ms (0%)

sample3.1s (13.2%)

Algorithm

1×

intervals

Results

625.0ms	5999×	body	128	valid
450.0ms	824×	body	1024	valid
270.0ms	734×	body	512	valid
266.0ms	494×	body	1024	invalid
260.0ms	2415×	body	128	invalid
134.0ms	379×	body	512	invalid
105.0ms	440×	body	256	valid
43.0ms	173×	body	256	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 803 to 516 computations (35.7% saved)

Details

analyze2.1s (8.8%)

sample82.0ms (0.3%)

simplify307.0ms (1.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

rewrite85.0ms (0.4%)

series1.6s (6.9%)

simplify96.0ms (0.4%)

prune318.0ms (1.3%)

localize22.0ms (0.1%)

rewrite75.0ms (0.3%)

series2.2s (9.4%)

simplify91.0ms (0.4%)

prune257.0ms (1.1%)

localize29.0ms (0.1%)

rewrite196.0ms (0.8%)

series4.2s (17.8%)

simplify347.0ms (1.5%)

prune1.4s (5.8%)

localize28.0ms (0.1%)

rewrite193.0ms (0.8%)

series4.6s (19.4%)

simplify350.0ms (1.5%)

prune1.3s (5.5%)

regimes640.0ms (2.7%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (13.2%)

Profiling