Details

analyze2.3s

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

sample186.0ms

Algorithm

intervals

Results

21.0ms	192×	body	80	valid
12.0ms	26×	body	640	valid
9.0ms	13×	body	1280	valid
6.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5091	32

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 39.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
12.3b	(cos (/ (+ phi1 phi2) 2.0))
12.3b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite61.0ms

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:

5.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
8.0ms	(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))))

series157.0ms

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))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify101.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4972	11939
1	4972	11939

prune486.0ms

Filtered

138 candidates to 204 candidates (-47.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	195	9	204
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	195	10	205

Merged error: 18.8b

Counts

205 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
12.3b	(cos (/ (+ phi1 phi2) 2.0))
12.3b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
6.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
130.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4989	6302
1	4989	6302

prune249.0ms

Filtered

72 candidates to 120 candidates (-66.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	119	11	130

Merged error: 18.8b

Counts

130 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

12.3b	(cos (/ (+ phi1 phi2) 2.0))
12.3b	(cos (/ (+ phi1 phi2) 2.0))
36.1b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
36.1b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

396×	`flip3--` `flip--`
392×	`frac-times`
276×	`sqrt-div`
272×	`frac-add`
196×	`associate-r/` `associate-l/`
144×	`cos-mult`
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 → 316

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
7.0ms	(cos (/ (+ phi1 phi2) 2.0))
22.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
23.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
128.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
133.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify182.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5006	23728

prune1.3s

Filtered

220 candidates to 328 candidates (-49.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	328	0	328
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	328	11	339

Merged error: 18.8b

Counts

339 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

12.3b	(cos (/ (+ phi1 phi2) 2.0))
12.3b	(cos (/ (+ phi1 phi2) 2.0))
37.2b	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))
37.2b	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-*l/`
132×	`cbrt-div`
128×	`frac-times` `frac-add`
64×	`associate-*r/`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 168

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))
17.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
179.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))
182.0ms	(cbrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6))) (* (- phi1 phi2) (- phi1 phi2))))

simplify68.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4963	11646
1	4963	11646

prune486.0ms

Filtered

100 candidates to 180 candidates (-80.0%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	179	12	191

Merged error: 18.8b

Counts

191 → 12

regimes1.0s

Accuracy

29.8% (11.4b remaining)

Error of 34.6b against oracle of 23.2b and baseline of 39.4b

bsearch311.0ms

Steps

Iters	Range		Point
9	7.389217136175392e+134	2.444376509548231e+143	2.3905762670983812e+143
10	2.9626710579953475e-177	1.2654380503080994e-166	2.9967616150076527e-177
8	4.577339148167174e-228	5.463904063155284e-225	4.5117636662343897e-225
5	-7.413864690737324e+93	-1.856195023068244e+93	-6.762865944055262e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	93
1	80	93

end0.0ms

sample5.3s

Algorithm

intervals

Results

551.0ms	5835×	body	80	valid
377.0ms	842×	body	640	valid
355.0ms	526×	body	1280	valid
177.0ms	546×	body	320	valid
56.0ms	251×	body	160	valid

Details

analyze2.3s

sample186.0ms

simplify104.0ms

prune12.0ms

localize23.0ms

rewrite61.0ms

series157.0ms

simplify101.0ms

prune486.0ms

localize34.0ms

rewrite44.0ms

series146.0ms

simplify58.0ms

prune249.0ms

localize27.0ms

rewrite94.0ms

series271.0ms

simplify182.0ms

prune1.3s

localize35.0ms

rewrite61.0ms

series370.0ms

simplify68.0ms

prune486.0ms

regimes1.0s

bsearch311.0ms

simplify2.0ms

end0.0ms

sample5.3s

Profiling