Details

sample266.0ms

Algorithm

intervals

Results

197.0ms	153×	body	1280	valid
41.0ms	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	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: 13.9b

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)))
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))

series287.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
140.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))
28.0ms	(sin (- lambda1 lambda2))

simplify55.0ms

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

prune109.0ms

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))

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 lambda1) (cos lambda2))
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))

series275.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (cos lambda2))
129.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
84.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify143.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	181	155
1	465	155
2	1322	154
3	4252	154
4	5001	154

prune153.0ms

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

localize36.0ms

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)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 24

Calls

4 calls:

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

series426.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (cos lambda2))
135.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
59.0ms	(* (sin lambda1) (sin (- lambda2)))
185.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	298	393
1	1014	383
2	4129	362
3	5001	362

prune236.0ms

Filtered

36 candidates to 27 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	31	5	36
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	37	5	42

Merged error: 0.1b

Counts

42 → 5

localize36.0ms

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)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-*r/`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`sub-neg`
5×	`*-commutative` `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 → 30

Calls

4 calls:

8.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
11.0ms	(* (cos phi2) (* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
4.0ms	(* (sin lambda1) (sin (- lambda2)))
9.0ms	(* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
204.0ms	(* (cos phi2) (* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
54.0ms	(* (sin lambda1) (sin (- lambda2)))
138.0ms	(* (sin phi1) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	231	439
1	717	414
2	2588	394
3	5001	378

prune175.0ms

Filtered

42 candidates to 26 candidates (61.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0.1b

Counts

47 → 4

regimes169.0ms

Accuracy

0% (0.1b 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	46	56
1	46	56

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4697×	body	1280	valid
1.4s	1857×	body	640	valid
278.0ms	566×	body	320	valid
101.0ms	692×	body	80	valid
58.0ms	188×	body	160	valid