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

18.0ms	190×	body	80	valid
12.0ms	26×	body	640	valid
11.0ms	17×	body	1280	valid
9.0ms	20×	body	640	invalid
7.0ms	11×	body	160	valid
7.0ms	75×	body	80	invalid
6.0ms	10×	body	1280	invalid
4.0ms	12×	body	320	valid
2.0ms	6×	body	320	invalid
1.0ms	4×	body	160	invalid

simplify103.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

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: 37.8b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.4b	(cos (/ (+ phi1 phi2) 2.0))
2.4b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite57.0ms

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))
23.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series163.0ms

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))
145.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify104.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4972	11939
1	4972	11939

prune494.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	195	9	204
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	196	10	206

Merged error: 18.6b

Counts

206 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.4b	(cos (/ (+ phi1 phi2) 2.0))
2.4b	(cos (/ (+ phi1 phi2) 2.0))
34.8b	(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:

12.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
20.0ms	(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))
139.0ms	(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 (18.0ms)

Iter	Nodes	Cost
0	5172	6821

prune245.0ms

Filtered

77 candidates to 147 candidates (-90.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	146	11	157

Merged error: 18.6b

Counts

157 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
2.4b	(cos (/ (+ phi1 phi2) 2.0))
6.0b	(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `exp-diff`
64×	`associate-*r/`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`unpow-prod-down` `log-prod` `exp-prod` `exp-sum` `sqrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-unpow` `log-pow`
2×	`pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow1/3` `pow-exp` `rem-exp-log` `sqr-pow`

Counts

4 → 193

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
135.0ms	(exp (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5026	11775

prune505.0ms

Filtered

136 candidates to 205 candidates (-50.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	202	14	216

Merged error: 18.6b

Counts

216 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
2.4b	(cos (/ (+ phi1 phi2) 2.0))
6.2b	(pow E (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
34.8b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
66×	`log-div` `pow-sub`
64×	`associate-*r/`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `unpow-prod-down` `pow-unpow`
6×	`unpow-prod-up` `add-exp-log` `log-prod` `sqrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `pow-pow` `pow-exp` `log-pow`
2×	`pow-to-exp` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `sqr-pow`
1×	`rem-sqrt-square` `e-exp-1` `pow1/3`

Counts

4 → 200

Calls

4 calls:

3.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
25.0ms	(pow E (log (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))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
191.0ms	(pow E (log (sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))))
141.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

simplify76.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5660	12608

prune513.0ms

Filtered

140 candidates to 212 candidates (-51.4%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	208	4	212
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	208	18	226

Merged error: 15.3b

Counts

226 → 18

regimes1.6s

Accuracy

48.8% (10.8b remaining)

Error of 28.7b against oracle of 17.9b and baseline of 39.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	69
1	53	69

end0.0ms

sample2.9s

Algorithm

intervals

Results

584.0ms	5864×	body	80	valid
377.0ms	851×	body	640	valid
346.0ms	515×	body	1280	valid
231.0ms	2347×	body	80	invalid
225.0ms	219×	body	320	invalid
211.0ms	305×	body	1280	invalid
206.0ms	463×	body	640	invalid
163.0ms	494×	body	320	valid
62.0ms	276×	body	160	valid
27.0ms	125×	body	160	invalid

Details

analyze2.2s

sample99.0ms

simplify103.0ms

prune16.0ms

localize23.0ms

rewrite57.0ms

series163.0ms

simplify104.0ms

prune494.0ms

localize17.0ms

rewrite53.0ms

series179.0ms

simplify49.0ms

prune245.0ms

localize23.0ms

rewrite71.0ms

series304.0ms

simplify70.0ms

prune505.0ms

localize30.0ms

rewrite74.0ms

series361.0ms

simplify76.0ms

prune513.0ms

regimes1.6s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample2.9s

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