Details

sample261.0ms

Algorithm

intervals

Results

194.0ms	153×	body	1280	valid
40.0ms	59×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	21×	body	80	valid
2.0ms	5×	body	160	valid

simplify9.0ms

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: 13.9b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.9b	(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))

series195.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify60.0ms

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

prune113.0ms

Filtered

26 candidates to 16 candidates (61.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	19	7	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	7	27

Merged error: 7.1b

Counts

27 → 7

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite21.0ms

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 lambda1) (cos lambda2))
8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(cos (- lambda1 lambda2))

series279.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin lambda1) (cos lambda2))
131.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify139.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	185	152
1	493	152
2	1436	150
3	4672	149
4	5001	149

prune144.0ms

Filtered

26 candidates to 17 candidates (65.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	20	6	26
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	27	6	33

Merged error: 0.1b

Counts

33 → 6

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-commutative`
8×	`prod-diff`
6×	`distribute-rgt-in` `distribute-lft-in` `sin-cos-mult`
5×	`sin-mult`
4×	`frac-times` `associate-*r/` `cos-mult`
3×	`associate-*l/`
2×	`sub-neg` `flip3--` `associate-l` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 32

Calls

4 calls:

3.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (cos lambda2))
126.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
179.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	358	587
1	1151	554
2	4695	531
3	5001	530

prune233.0ms

Filtered

44 candidates to 29 candidates (65.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	39	5	44
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	45	5	50

Merged error: 0.1b

Counts

50 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

30×	`distribute-rgt-in` `distribute-lft-in`
29×	`*-commutative`
24×	`prod-diff`
12×	`associate-*r/`
6×	`sub-neg`
5×	`sin-mult`
4×	`cos-mult`
2×	`flip3--` `associate-r` `associate-*l/` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 54

Calls

4 calls:

8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms	(* (cos phi2) (* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
4.0ms	(* (sin lambda1) (sin (- lambda2)))
14.0ms	(* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series509.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
193.0ms	(* (cos phi2) (* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
131.0ms	(* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	323	1004
1	873	929
2	3061	884
3	5001	652

prune202.0ms

Filtered

66 candidates to 29 candidates (43.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0.1b

Counts

71 → 4

regimes163.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	56
1	46	56

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.3s	4697×	body	1280	valid
1.4s	1857×	body	640	valid
269.0ms	566×	body	320	valid
101.0ms	692×	body	80	valid
62.0ms	188×	body	160	valid