Details

sample258.0ms

Algorithm

intervals

Results

192.0ms	163×	body	1280	valid
38.0ms	60×	body	640	valid
8.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	12

prune4.0ms

Filtered

1 candidates to 0 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: 16.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.7b	(cos (- lambda1 lambda2))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`cos-diff` `*-commutative`
2×	`cos-sum` `associate-l`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult`

Counts

4 → 11

Calls

4 calls:

5.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0ms	(cos (- lambda1 lambda2))

series175.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	125	172
1	263	172
2	573	172
3	1525	171
4	5001	171

prune72.0ms

Filtered

23 candidates to 12 candidates (52.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	4	24

Merged error: 3.0b

Counts

24 → 4

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
6×	`cos-mult`
4×	`associate-r` `associate-l`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin`

Counts

4 → 18

Calls

4 calls:

7.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
7.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
107.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify63.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	179	276
1	418	276
2	801	276
3	1622	275
4	5002	275

prune148.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Merged error: 2.9b

Counts

34 → 3

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
3×	`sin-mult`
2×	`associate-r` `associate-l` `cos-mult`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (sin phi1) (sin phi2))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
7.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin phi1) (sin phi2))
70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
109.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify397.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	124	219
1	257	219
2	408	219
3	545	219
4	657	219
5	717	219
6	807	219
7	1010	219
8	1306	219
9	1764	219
10	2028	219
11	2253	219
12	2833	219
13	3911	219
14	4303	219
15	4463	219
16	4632	219
17	4664	219
18	4678	219
19	4698	219
20	4698	219

prune96.0ms

Filtered

24 candidates to 14 candidates (58.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Merged error: 2.9b

Counts

27 → 3

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
0.3b	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
1.0b	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-r`
5×	`*-commutative`
1×	`acos-asin` `sin-mult`

Counts

4 → 9

Calls

4 calls:

5.0ms	(* (sin phi1) (sin phi2))
2.0ms	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
6.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
4.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin phi1) (sin phi2))
71.0ms	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
101.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
17.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

simplify19.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	87	188
1	138	188
2	200	188
3	239	188
4	245	188
5	245	188

prune71.0ms

Filtered

21 candidates to 12 candidates (57.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	21	3	24

Merged error: 2.9b

Counts

24 → 3

regimes137.0ms

Accuracy

0% (0.1b remaining)

Error of 3.9b against oracle of 3.8b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	21
1	34	21

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.7s	4788×	body	1280	valid
1.4s	2121×	body	640	valid
304.0ms	673×	body	320	valid
85.0ms	279×	body	160	valid
43.0ms	12×	body	2560	valid
19.0ms	127×	body	80	valid