Details

analyze2.1s

Algorithm

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

sample108.0ms

Algorithm

intervals

Results

20.0ms	22×	body	1280	valid
18.0ms	182×	body	80	valid
14.0ms	30×	body	640	valid
7.0ms	15×	body	640	invalid
7.0ms	69×	body	80	invalid
5.0ms	14×	body	320	valid
4.0ms	6×	body	1280	invalid
2.0ms	8×	body	160	valid
1.0ms	4×	body	320	invalid
1.0ms	3×	body	160	invalid

simplify314.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	5213	49

prune7.0ms

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: 38.2b

Counts

2 → 1

localize24.0ms

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))))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.4b	(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))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/_binary64_636`
102×	`flip3--_binary64_573` `flip--_binary64_600`
68×	`frac-times_binary64_566`
66×	`sqrt-div_binary64_554`
64×	`frac-add_binary64_564`
44×	`pow1_binary64_520`
34×	`associate-*r/_binary64_635`
17×	`pow-prod-down_binary64_501`
16×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
8×	`cbrt-unprod_binary64_543` `prod-exp_binary64_525`
6×	`add-sqr-sqrt_binary64_559`
5×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
4×	`pow-prod-up_binary64_500` `pow-sqr_binary64_607` `add-log-exp_binary64_539`
3×	`sqrt-prod_binary64_553`
2×	`pow-plus_binary64_515`
1×	`rem-sqrt-square_binary64_562` `associate-l_binary64_634` `sqrt-pow1_binary64_555` `flip3-+_binary64_572` `pow2_binary64_511` `flip-+_binary64_599` `swap-sqr_binary64_601` `pow1/2_binary64_510` `associate-r_binary64_633` `*-commutative_binary64_642`

Counts

4 → 135

Calls

4 calls:

14.0ms	(.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))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(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))))

series836.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
652.0ms	(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))))

simplify125.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5048	10709

prune338.0ms

Filtered

76 candidates to 147 candidates (-93.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	7	148

Merged error: 23.6b

Counts

148 → 7

localize26.0ms

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)))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.4b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--_binary64_573` `flip--_binary64_600`
196×	`frac-times_binary64_566`
138×	`sqrt-div_binary64_554`
136×	`frac-add_binary64_564`
98×	`associate-l/_binary64_636` `associate-r/_binary64_635`
73×	`cos-mult_binary64_444`
12×	`pow1_binary64_520` `add-sqr-sqrt_binary64_559`
9×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
6×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
4×	`add-log-exp_binary64_539`
3×	`associate-l_binary64_634` `swap-sqr_binary64_601` `sqrt-prod_binary64_553` `associate-r_binary64_633`
1×	`pow-plus_binary64_515` `rem-sqrt-square_binary64_562` `sqr-cos-a_binary64_439` `sqrt-pow1_binary64_555` `unswap-sqr_binary64_602` `flip3-+_binary64_572` `pow2_binary64_511` `flip-+_binary64_599` `pow-prod-up_binary64_500` `cbrt-unprod_binary64_543` `pow1/2_binary64_510` `pow-sqr_binary64_607` `*-commutative_binary64_642` `pow-prod-down_binary64_501` `prod-exp_binary64_525`

Counts

4 → 192

Calls

4 calls:

4.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (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))
29.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
645.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

simplify185.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5100	18312

prune764.0ms

Filtered

134 candidates to 204 candidates (-52.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	201	10	211

Merged error: 23.5b

Counts

211 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.4b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--_binary64_573` `flip--_binary64_600`
80×	`associate-*l/_binary64_636`
66×	`sqrt-div_binary64_554`
64×	`frac-times_binary64_566` `frac-add_binary64_564`
32×	`associate-*r/_binary64_635`
8×	`add-sqr-sqrt_binary64_559`
7×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
6×	`pow1_binary64_520`
4×	`add-cbrt-cube_binary64_546` `log-pow_binary64_495` `add-exp-log_binary64_538` `add-log-exp_binary64_539`
3×	`exp-prod_binary64_528` `log-prod_binary64_492` `sqrt-prod_binary64_553`
1×	`rem-sqrt-square_binary64_562` `sqrt-pow1_binary64_555` `flip3-+_binary64_572` `flip-+_binary64_599` `pow1/2_binary64_510` `rem-log-exp_binary64_537`

Counts

4 → 108

Calls

4 calls:

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))
25.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
648.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify117.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4949	9595
1	4949	9595

prune314.0ms

Filtered

69 candidates to 120 candidates (-73.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	120	10	130

Merged error: 23.5b

Counts

130 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.4b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--_binary64_573` `flip--_binary64_600`
80×	`associate-*l/_binary64_636`
66×	`sqrt-div_binary64_554`
64×	`frac-times_binary64_566` `frac-add_binary64_564`
32×	`associate-*r/_binary64_635`
9×	`add-sqr-sqrt_binary64_559`
8×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545`
6×	`pow1_binary64_520`
5×	`add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
4×	`add-log-exp_binary64_539`
3×	`unpow-prod-down_binary64_509` `sqrt-prod_binary64_553` `pow-unpow_binary64_507` `cube-prod_binary64_547`
1×	`rem-sqrt-square_binary64_562` `pow-to-exp_binary64_499` `sqr-pow_binary64_606` `rem-cube-cbrt_binary64_550` `sqrt-pow1_binary64_555` `pow-exp_binary64_498` `flip3-+_binary64_572` `flip-+_binary64_599` `pow-pow_binary64_502` `pow1/2_binary64_510` `unpow3_binary64_518` `cube-mult_binary64_549`

Counts

4 → 116

Calls

4 calls:

2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
21.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
646.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify121.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4987	9195
1	4987	9195

prune257.0ms

Filtered

70 candidates to 128 candidates (-82.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	6	7
Picked	0	1	1
Done	1	1	2
Total	129	9	138

Merged error: 23.5b

Counts

138 → 9

regimes1.2s

Accuracy

69.9% (4.3b remaining)

Error of 28.8b against oracle of 24.5b and baseline of 38.9b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	109
1	65	109

end0.0ms

sample2.8s

Algorithm

intervals

Results

594.0ms	5954×	body	80	valid
378.0ms	831×	body	640	valid
323.0ms	476×	body	1280	valid
230.0ms	2327×	body	80	invalid
204.0ms	450×	body	640	invalid
183.0ms	270×	body	1280	invalid
172.0ms	503×	body	320	valid
77.0ms	233×	body	320	invalid
55.0ms	236×	body	160	valid
22.0ms	100×	body	160	invalid

Details

analyze2.1s

sample108.0ms

simplify314.0ms

prune7.0ms

localize24.0ms

rewrite63.0ms

series836.0ms

simplify125.0ms

prune338.0ms

localize26.0ms

rewrite65.0ms

series713.0ms

simplify185.0ms

prune764.0ms

localize31.0ms

rewrite51.0ms

series698.0ms

simplify117.0ms

prune314.0ms

localize31.0ms

rewrite43.0ms

series735.0ms

simplify121.0ms

prune257.0ms

regimes1.2s

bsearch2.0ms

simplify3.0ms

end0.0ms

sample2.8s

Profiling