Details

sample198.0ms

Algorithm

intervals

Results

117.0ms	120×	body	1280	valid
39.0ms	71×	body	640	valid
12.0ms	32×	body	320	valid
6.0ms	18×	body	80	valid
4.0ms	15×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	21	20
done	21	20

prune5.0ms

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: 0.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.5b	(sin (- lambda1 lambda2))
4.6b	(cos (- lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series49.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
26.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
6.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

52 → 52

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	447	615
3	1015	613
4	2290	613
done	5000	613

prune136.0ms

Filtered

41 candidates to 52 candidates (-26.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	43	9	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	9	53

Merged error: 0.2b

Counts

53 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.6b	(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

series49.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
10.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

61 → 61

Iterations

Useful iterations: 3 (267.0ms)

Iter	Nodes	Cost
0	126	866
1	266	850
2	650	822
3	1477	750
4	3211	750
done	5000	750

prune116.0ms

Filtered

46 candidates to 61 candidates (-32.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Merged error: 0.1b

Counts

70 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

9.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
53.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.4s

Counts

74 → 74

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	154	1487
1	374	1414
2	1194	1270
3	4751	1270
done	5000	1270

prune131.0ms

Filtered

59 candidates to 74 candidates (-25.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 0.1b

Counts

82 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

4.5b	(sin (- lambda1 lambda2))
4.6b	(cos (- lambda1 lambda2))
4.6b	(cos (- lambda1 lambda2))
4.6b	(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff`
2×	`sin-sum`
1×	`sin-diff`

Counts

4 → 40

Calls

4 calls:

4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series18.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	48	410
1	84	402
2	149	370
3	291	364
4	763	364
5	2182	364
done	5001	364

prune66.0ms

Filtered

40 candidates to 52 candidates (-30.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	52	8	60

Merged error: 0.1b

Counts

60 → 8

regimes500.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	34
1	30	34
done	30	34

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.5s	3685×	body	1280	valid
1.3s	2281×	body	640	valid
370.0ms	952×	body	320	valid
103.0ms	413×	body	160	valid
89.0ms	669×	body	80	valid

Details

sample198.0ms

simplify7.0ms

prune5.0ms

localize19.0ms

rewrite15.0ms

series49.0ms

simplify1.6s

prune136.0ms

localize30.0ms

rewrite16.0ms

series49.0ms

simplify1.8s

prune116.0ms

localize30.0ms

rewrite22.0ms

series113.0ms

simplify2.4s

prune131.0ms

localize25.0ms

rewrite19.0ms

series18.0ms

simplify1.8s

prune66.0ms

regimes500.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample5.8s

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