Details

sample282.0ms

Algorithm

intervals

Results

205.0ms	165×	body	1280	valid
41.0ms	54×	body	640	valid
8.0ms	15×	body	320	valid
2.0ms	7×	body	160	valid
2.0ms	15×	body	80	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	38
1	98	38
2	182	38
3	309	38
4	609	38
5	2160	38
6	5002	38

prune6.0ms

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: 23.4b

Counts

2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`div-sub` `sin-diff`

Counts

4 → 4

Calls

4 calls:

4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))

series149.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sin (/ (- lambda1 lambda2) 2.0))
38.0ms	(sin (/ (- lambda1 lambda2) 2.0))
35.0ms	(sin (/ (- lambda1 lambda2) 2.0))
40.0ms	(sin (/ (- lambda1 lambda2) 2.0))

simplify190.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	88
1	71	84
2	158	84
3	344	84
4	1212	84
5	4926	84
6	5003	84

prune136.0ms

Filtered

16 candidates to 12 candidates (75.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Merged error: 22.7b

Counts

17 → 6

localize56.0ms

Local error

Found 4 expressions with local error:

2.2b	(sin (/ (- phi1 phi2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`div-sub` `sin-diff`

Counts

4 → 4

Calls

4 calls:

4.0ms	(sin (/ (- phi1 phi2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))

series146.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(sin (/ (- phi1 phi2) 2.0))
35.0ms	(sin (/ (- lambda1 lambda2) 2.0))
39.0ms	(sin (/ (- lambda1 lambda2) 2.0))
36.0ms	(sin (/ (- lambda1 lambda2) 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	78	88
1	134	84
2	296	84
3	634	84
4	2058	84
5	5002	84

prune172.0ms

Filtered

16 candidates to 12 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	17	5	22

Merged error: 22.2b

Counts

22 → 5

localize58.0ms

Local error

Found 4 expressions with local error:

2.2b	(sin (/ (- phi1 phi2) 2.0))
2.2b	(sin (/ (- phi1 phi2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`div-sub` `sin-diff`

Counts

4 → 4

Calls

4 calls:

4.0ms	(sin (/ (- phi1 phi2) 2.0))
4.0ms	(sin (/ (- phi1 phi2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))

series142.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sin (/ (- phi1 phi2) 2.0))
35.0ms	(sin (/ (- phi1 phi2) 2.0))
38.0ms	(sin (/ (- lambda1 lambda2) 2.0))
35.0ms	(sin (/ (- lambda1 lambda2) 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	78	88
1	134	84
2	296	84
3	634	84
4	2058	84
5	5002	84

prune200.0ms

Filtered

16 candidates to 12 candidates (75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	13	8	21

Merged error: 21.8b

Counts

21 → 8

localize69.0ms

Local error

Found 4 expressions with local error:

0.6b	(- 1.0 (+ (pow (sin (/ (- phi1 phi2) 2.0)) 2.0) (* (* (* (cos phi1) (cos phi2)) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0))))) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0)))))))
2.2b	(sin (/ (- phi1 phi2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))
2.8b	(sin (/ (- lambda1 lambda2) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate--r+`
4×	`associate-+r+`
3×	`sub-neg` `div-sub` `sin-diff`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`+-commutative` `flip3--` `flip--`

Counts

4 → 13

Calls

4 calls:

7.0ms	(- 1.0 (+ (pow (sin (/ (- phi1 phi2) 2.0)) 2.0) (* (* (* (cos phi1) (cos phi2)) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0))))) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0)))))))
4.0ms	(sin (/ (- phi1 phi2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))
4.0ms	(sin (/ (- lambda1 lambda2) 2.0))

series807.0ms

Counts

4 → 12

Calls

4 calls:

698.0ms	(- 1.0 (+ (pow (sin (/ (- phi1 phi2) 2.0)) 2.0) (* (* (* (cos phi1) (cos phi2)) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0))))) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0)))))))
37.0ms	(sin (/ (- phi1 phi2) 2.0))
35.0ms	(sin (/ (- lambda1 lambda2) 2.0))
38.0ms	(sin (/ (- lambda1 lambda2) 2.0))

simplify124.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	293	574
1	905	563
2	4044	562
3	5001	562

prune235.0ms

Filtered

25 candidates to 18 candidates (72.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	18	7	25
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	22	11	33

Merged error: 14.1b

Counts

33 → 11

regimes1.1s

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	70
1	57	70

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4811×	body	1280	valid
1.5s	1919×	body	640	valid
288.0ms	524×	body	320	valid
88.0ms	573×	body	80	valid
60.0ms	173×	body	160	valid