Details

analyze3.4s

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

sample287.0ms

Algorithm

intervals

Results

205.0ms	142×	body	1280	valid
43.0ms	58×	body	640	valid
16.0ms	27×	body	320	valid
4.0ms	21×	body	80	valid
2.0ms	8×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune27.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.7b

Counts

2 → 1

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(cos (- lambda1 lambda2))
3.9b	(sin (- lambda1 lambda2))

rewrite40.0ms

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-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series59.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
11.0ms	(sin (- lambda1 lambda2))

simplify89.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4973	943
1	4973	943

prune191.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 6.9b

Counts

71 → 10

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
4.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series82.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
16.0ms	(* (cos lambda1) (sin lambda2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify82.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5002	1173

prune158.0ms

Filtered

50 candidates to 71 candidates (-42.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Merged error: 0.1b

Counts

81 → 7

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

8.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
8.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (sin lambda1) (sin lambda2))
40.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
36.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify85.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5003	1542

prune223.0ms

Filtered

58 candidates to 99 candidates (-70.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	96	10	106

Merged error: 0.0b

Counts

106 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
4.4b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
5×	`add-log-exp`
3×	`log-prod` `log-pow` `*-commutative`
2×	`cos-mult` `sin-cos-mult` `unswap-sqr`
1×	`frac-times` `exp-prod` `exp-to-pow` `associate-r/` `rem-log-exp` `associate-l/` `sin-mult`

Counts

4 → 76

Calls

4 calls:

8.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (cos lambda1) (sin lambda2))
15.0ms	(* (sin lambda1) (sin lambda2))
38.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
18.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify109.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4903	1182
1	4903	1182

prune110.0ms

Filtered

58 candidates to 88 candidates (-51.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	88	10	98

Merged error: 0.0b

Counts

98 → 10

regimes933.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	77
1	140	77

end0.0ms

sample11.9s

Algorithm

intervals

Results

8.7s	4578×	body	1280	valid
2.1s	1896×	body	640	valid
466.0ms	615×	body	320	valid
153.0ms	683×	body	80	valid
113.0ms	228×	body	160	valid

Details

analyze3.4s

sample287.0ms

simplify31.0ms

prune27.0ms

localize43.0ms

rewrite40.0ms

series59.0ms

simplify89.0ms

prune191.0ms

localize53.0ms

rewrite29.0ms

series82.0ms

simplify82.0ms

prune158.0ms

localize41.0ms

rewrite35.0ms

series96.0ms

simplify85.0ms

prune223.0ms

localize37.0ms

rewrite33.0ms

series86.0ms

simplify109.0ms

prune110.0ms

regimes933.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample11.9s

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