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

sample99.0ms

Algorithm

intervals

Results

19.0ms	183×	body	80	valid
17.0ms	18×	body	1280	valid
13.0ms	27×	body	640	valid
8.0ms	76×	body	80	invalid
6.0ms	19×	body	320	valid
6.0ms	9×	body	1280	invalid
6.0ms	12×	body	640	invalid
2.0ms	9×	body	160	valid
2.0ms	5×	body	320	invalid
1.0ms	5×	body	160	invalid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5091	32

prune16.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 35.9b

Counts

2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`associate-r/` `associate-l/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `sqr-cos-a` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
27.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
139.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify102.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4972	11939
1	4972	11939

prune506.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	193	11	204
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	194	12	206

Merged error: 21.1b

Counts

206 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

13.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
138.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5172	6821

prune260.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	147	12	159

Merged error: 21.1b

Counts

159 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6))
0.8b	(pow (cos (/ (+ phi1 phi2) 2.0)) 6)
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `flip--`
80×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`pow1` `unpow-prod-down`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `sqrt-prod`
2×	`sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `pow-exp` `flip-+`

Counts

4 → 118

Calls

4 calls:

2.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6))
2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6)))) (* (- phi1 phi2) (- phi1 phi2))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6))
15.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
135.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 6)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify44.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5024	6178

prune270.0ms

Filtered

75 candidates to 130 candidates (-73.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	130	12	142

Merged error: 21.1b

Counts

142 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (/ (+ phi1 phi2) 2.0))
3.4b	(cos (/ (+ phi1 phi2) 2.0))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))
33.0b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 172

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
136.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))
139.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

simplify87.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	11450
1	4963	11450

prune462.0ms

Filtered

98 candidates to 184 candidates (-87.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	184	12	196

Merged error: 21.1b

Counts

196 → 12

regimes1.3s

Accuracy

62.7% (6.1b remaining)

Error of 28.9b against oracle of 22.7b and baseline of 39.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	69
1	53	69

end0.0ms

sample3.1s

Algorithm

intervals

Results

612.0ms	5837×	body	80	valid
472.0ms	2379×	body	80	invalid
448.0ms	919×	body	640	valid
344.0ms	479×	body	1280	valid
226.0ms	326×	body	1280	invalid
210.0ms	448×	body	640	invalid
179.0ms	518×	body	320	valid
78.0ms	224×	body	320	invalid
63.0ms	247×	body	160	valid
27.0ms	107×	body	160	invalid

Details

analyze2.1s

sample99.0ms

simplify99.0ms

prune16.0ms

localize17.0ms

rewrite62.0ms

series156.0ms

simplify102.0ms

prune506.0ms

localize19.0ms

rewrite53.0ms

series179.0ms

simplify49.0ms

prune260.0ms

localize22.0ms

rewrite38.0ms

series162.0ms

simplify44.0ms

prune270.0ms

localize24.0ms

rewrite69.0ms

series284.0ms

simplify87.0ms

prune462.0ms

regimes1.3s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling