Details

sample270.0ms

Algorithm

intervals

Results

199.0ms	153×	body	1280	valid
44.0ms	65×	body	640	valid
8.0ms	17×	body	320	valid
2.0ms	17×	body	80	valid
1.0ms	4×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

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: 12.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(cos (- lambda1 lambda2))
3.8b	(sin (- lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 14

Calls

4 calls:

4.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
5.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(cos (- lambda1 lambda2))
3.0ms	(sin (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	124	129
1	270	129
2	581	129
3	1323	129
4	5001	129

prune108.0ms

Filtered

26 candidates to 16 candidates (61.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	5	27

Merged error: 6.7b

Counts

27 → 5

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-commutative`
3×	`cos-diff` `associate-*l/`
2×	`cos-sum` `associate-l` `sin-cos-mult`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 14

Calls

4 calls:

3.0ms	(* (sin phi1) (cos phi2))
8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
5.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
129.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify119.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	176	155
1	460	155
2	1263	154
3	3854	154
4	5001	154

prune133.0ms

Filtered

26 candidates to 17 candidates (65.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	22	4	26
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	27	4	31

Merged error: 0.2b

Counts

31 → 4

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-commutative`
4×	`associate-r` `associate-l` `associate-*l/` `sin-cos-mult`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult`
1×	`flip3-+` `flip-+`

Counts

4 → 21

Calls

4 calls:

7.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
3.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
7.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
44.0ms	(* (sin lambda1) (sin lambda2))
97.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
115.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify82.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	189	190
1	487	190
2	1135	189
3	2912	189
4	5001	189

prune215.0ms

Filtered

33 candidates to 27 candidates (81.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	34	3	37

Merged error: 0.1b

Counts

37 → 3

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (* (sin phi1) (cos phi2)) (sin lambda2)) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`associate-l`
9×	`*-commutative`
6×	`associate-*l/`
4×	`sin-cos-mult`
2×	`associate-r` `cos-mult`
1×	`frac-times` `flip3-+` `associate-*r/` `flip-+`

Counts

4 → 21

Calls

4 calls:

8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
8.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda2)) (sin lambda1))
5.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda2))
7.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
101.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda2)) (sin lambda1))
70.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda2))
115.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify82.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	176	179
1	444	179
2	1042	178
3	2700	178
4	5001	178

prune202.0ms

Filtered

33 candidates to 27 candidates (81.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	34	2	36

Merged error: 0.1b

Counts

36 → 2

regimes106.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	30
1	40	30

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.1s	4651×	body	1280	valid
1.4s	1920×	body	640	valid
476.0ms	563×	body	320	valid
94.0ms	673×	body	80	valid
62.0ms	193×	body	160	valid