Details

sample258.0ms

Algorithm

intervals

Results

188.0ms	153×	body	1280	valid
44.0ms	65×	body	640	valid
7.0ms	17×	body	320	valid
2.0ms	17×	body	80	valid
1.0ms	4×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	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

localize32.0ms

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))

series189.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	124	129
1	276	129
2	622	127
3	1468	126
4	5002	126

prune105.0ms

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

localize34.0ms

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))

rewrite20.0ms

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` `flip3--` `distribute-lft-in` `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))

series280.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
133.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

simplify123.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 4 (120.0ms)

Iter	Nodes	Cost
0	161	150
1	448	149
2	1297	148
3	4053	147
4	5001	146

prune126.0ms

Filtered

26 candidates to 16 candidates (61.5%)

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

localize38.0ms

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)))

rewrite27.0ms

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:

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

series385.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
50.0ms	(* (sin lambda1) (sin lambda2))
97.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify90.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	171	185
1	469	184
2	1192	184
3	3037	184
4	5002	184

prune206.0ms

Filtered

33 candidates to 26 candidates (78.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	33	4	37

Merged error: 0.1b

Counts

37 → 4

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
3.0ms	(* (sin lambda2) (sin phi1))
7.0ms	(* (sin lambda1) (* (cos phi2) (* (sin lambda2) (sin phi1))))
7.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
49.0ms	(* (sin lambda2) (sin phi1))
98.0ms	(* (sin lambda1) (* (cos phi2) (* (sin lambda2) (sin phi1))))
110.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify88.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	169	163
1	443	162
2	1095	162
3	2811	162
4	5001	162

prune161.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	32	3	35

Merged error: 0.1b

Counts

35 → 3

regimes137.0ms

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	37	29
1	37	29

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4651×	body	1280	valid
1.6s	1920×	body	640	valid
255.0ms	563×	body	320	valid
94.0ms	673×	body	80	valid
53.0ms	193×	body	160	valid