Details

analyze2.2s

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

sample99.0ms

Algorithm

intervals

Results

19.0ms	199×	body	80	valid
13.0ms	29×	body	640	valid
10.0ms	14×	body	1280	invalid
7.0ms	75×	body	80	invalid
6.0ms	8×	body	1280	valid
5.0ms	12×	body	640	invalid
5.0ms	16×	body	320	invalid
5.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	6×	body	160	invalid

simplify130.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	5041	32

prune4.0ms

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: 37.4b

Counts

2 → 1

localize17.0ms

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))))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.6b	(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))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/_binary64`
102×	`flip3--_binary64` `flip--_binary64`
68×	`frac-times_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64`
44×	`pow1_binary64`
34×	`associate-*r/_binary64`
17×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-plus_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

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))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
20.0ms	(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))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(.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))
162.0ms	(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))))

simplify53.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5175	6839

prune150.0ms

Filtered

76 candidates to 147 candidates (-93.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	136	11	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	11	148

Merged error: 25.6b

Counts

148 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/_binary64`
96×	`flip3--_binary64` `flip--_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64` `frac-times_binary64`
32×	`associate-*r/_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(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))
162.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5110	5969

prune133.0ms

Filtered

70 candidates to 128 candidates (-82.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 25.6b

Counts

139 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

1.2b	(log.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/_binary64`
96×	`flip3--_binary64` `flip--_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64` `frac-times_binary64`
32×	`associate-*r/_binary64`
13×	`log-pow_binary64`
12×	`exp-prod_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`log-prod_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `rem-log-exp_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 117

Calls

4 calls:

4.0ms	(log.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
7.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
23.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(log.f64 (exp.f64 (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))
160.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify68.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4987	6033
1	4987	6033

prune136.0ms

Filtered

76 candidates to 129 candidates (-69.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	129	10	139

Merged error: 25.6b

Counts

139 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
34.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

328×	`frac-times_binary64`
300×	`flip3--_binary64` `flip--_binary64`
260×	`associate-*l/_binary64`
210×	`sqrt-div_binary64`
208×	`frac-add_binary64`
164×	`associate-*r/_binary64`
144×	`cbrt-div_binary64`
73×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sqrt-prod_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 244

Calls

4 calls:

5.0ms	(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))
57.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series614.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(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))
599.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 3)))))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify177.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5032	23072

prune614.0ms

Filtered

172 candidates to 256 candidates (-48.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	254	12	266

Merged error: 25.0b

Counts

266 → 12

regimes754.0ms

Accuracy

72.8% (3.9b remaining)

Error of 28.6b against oracle of 24.7b and baseline of 39.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	87
1	66	87

end0.0ms

sample2.8s

Algorithm

intervals

Results

626.0ms	5920×	body	80	valid
400.0ms	835×	body	640	valid
339.0ms	477×	body	1280	valid
232.0ms	2292×	body	80	invalid
208.0ms	440×	body	640	invalid
197.0ms	288×	body	1280	invalid
174.0ms	498×	body	320	valid
69.0ms	212×	body	320	invalid
65.0ms	270×	body	160	valid
26.0ms	99×	body	160	invalid

Details

analyze2.2s

sample99.0ms

simplify130.0ms

prune4.0ms

localize17.0ms

rewrite58.0ms

series209.0ms

simplify53.0ms

prune150.0ms

localize21.0ms

rewrite49.0ms

series193.0ms

simplify50.0ms

prune133.0ms

localize23.0ms

rewrite50.0ms

series182.0ms

simplify68.0ms

prune136.0ms

localize28.0ms

rewrite115.0ms

series614.0ms

simplify177.0ms

prune614.0ms

regimes754.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample2.8s

Profiling