Details

sample106.0ms

Algorithm

intervals

Results

25.0ms	39×	body	1280	valid
24.0ms	258×	body	80	valid
16.0ms	37×	body	640	valid
10.0ms	32×	body	320	valid
2.0ms	11×	body	160	valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5002	32

prune19.0ms

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: 37.6b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.8b	(cos (/ (+ phi1 phi2) 2.0))
5.8b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(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))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series187.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (- 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))
143.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify48.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5122	6821

prune286.0ms

Filtered

78 candidates to 147 candidates (-88.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	136	11	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Merged error: 25.9b

Counts

149 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.8b	(cos (/ (+ phi1 phi2) 2.0))
5.8b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

146×	`associate-*l/`
97×	`flip3--` `flip--`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`add-log-exp`
3×	`associate-r` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

7.0ms	(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (cos (/ (+ phi1 phi2) 2.0))) (* (- phi1 phi2) (- phi1 phi2))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (- lambda1 lambda2) (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))))

simplify64.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5021	6367

prune244.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	126	12	138

Merged error: 25.9b

Counts

138 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

5.8b	(cos (/ (+ phi1 phi2) 2.0))
5.8b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
33.6b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

192×	`flip3--` `flip--`
160×	`associate-r/` `associate-l/`
132×	`sqrt-div`
128×	`frac-times` `frac-add`
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))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
17.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
142.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify93.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	12042
1	4971	12042

prune497.0ms

Filtered

98 candidates to 184 candidates (-87.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	184	12	196

Merged error: 25.9b

Counts

196 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

5.8b	(cos (/ (+ phi1 phi2) 2.0))
33.6b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
33.6b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
33.6b	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

288×	`flip3--` `flip--`
240×	`associate-r/` `associate-l/`
198×	`sqrt-div`
192×	`frac-times` `frac-add`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 244

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
17.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
142.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify126.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	17897
1	4971	17897

prune1.0s

Filtered

129 candidates to 256 candidates (-98.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	256	12	268

Merged error: 25.9b

Counts

268 → 12

regimes757.0ms

Accuracy

36.7% (9.4b remaining)

Error of 34.0b against oracle of 24.7b and baseline of 39.5b

bsearch87.0ms

Steps

Iters	Range		Point
10	-2.396888041990356e+158	-1.8735641909983224e+141	-1.915885584649851e+141

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms

sample2.9s

Algorithm

intervals

Results

811.0ms	8384×	body	80	valid
588.0ms	1295×	body	640	valid
531.0ms	783×	body	1280	valid
226.0ms	698×	body	320	valid
89.0ms	361×	body	160	valid

Details

sample106.0ms

simplify80.0ms

prune19.0ms

localize16.0ms

rewrite53.0ms

series187.0ms

simplify48.0ms

prune286.0ms

localize18.0ms

rewrite46.0ms

series177.0ms

simplify64.0ms

prune244.0ms

localize24.0ms

rewrite70.0ms

series292.0ms

simplify93.0ms

prune497.0ms

localize27.0ms

rewrite94.0ms

series429.0ms

simplify126.0ms

prune1.0s

regimes757.0ms

bsearch87.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling