Details

analyze2.6s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample288.0ms

Algorithm

intervals

Results

205.0ms	143×	body	1280	valid
51.0ms	63×	body	640	valid
9.0ms	17×	body	320	valid
5.0ms	14×	body	160	valid
3.0ms	19×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune20.0ms

Filtered

1 candidates to 1 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: 14.1b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
3.9b	(cos (- lambda1 lambda2))
3.9b	(sin (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
5×	`cos-diff`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`cos-sum` `sin-sum` `associate-*r/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

6.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
6.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series47.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4875	663
1	4875	663

prune169.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	60	14	74

Merged error: 7.2b

Counts

74 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
0.2b	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
3.9b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`cos-diff` `associate-r`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`*-commutative`
2×	`associate-*l/` `sin-cos-mult` `unswap-sqr`
1×	`sub-neg` `cos-sum` `flip3--` `associate-*r/` `flip--`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
6.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(cos (- lambda1 lambda2))

series69.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
23.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
30.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(cos (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4969	976
1	4969	976

prune159.0ms

Filtered

63 candidates to 85 candidates (-34.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Merged error: 0.1b

Counts

99 → 9

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-l`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`*-commutative` `add-log-exp`
2×	`associate-*l/`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

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

series98.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (cos lambda1) (* (cos lambda2) (* (cos phi2) (sin phi1))))
25.0ms	(* (sin lambda1) (* (sin lambda2) (* (cos phi2) (sin phi1))))
29.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
15.0ms	(* (sin lambda2) (* (cos phi2) (sin phi1)))

simplify39.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5251	1077

prune162.0ms

Filtered

62 candidates to 92 candidates (-48.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	91	10	101

Merged error: 0.0b

Counts

101 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
9×	`associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`flip3-+` `associate-*l/` `frac-add` `cos-mult` `flip-+`
1×	`flip3--` `flip--`

Counts

4 → 87

Calls

4 calls:

10.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
8.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))

series115.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
32.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))
28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))

simplify51.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4994	1431
1	4994	1431

prune111.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 0.0b

Counts

109 → 10

regimes582.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	135	38
1	135	38

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.9s	4649×	body	1280	valid
1.6s	1936×	body	640	valid
301.0ms	562×	body	320	valid
102.0ms	634×	body	80	valid
74.0ms	219×	body	160	valid

Details

analyze2.6s

sample288.0ms

simplify13.0ms

prune20.0ms

localize26.0ms

rewrite21.0ms

series47.0ms

simplify70.0ms

prune169.0ms

localize35.0ms

rewrite24.0ms

series69.0ms

simplify42.0ms

prune159.0ms

localize36.0ms

rewrite33.0ms

series98.0ms

simplify39.0ms

prune162.0ms

localize39.0ms

rewrite33.0ms

series115.0ms

simplify51.0ms

prune111.0ms

regimes582.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.3s

Profiling