Details

sample196.0ms

Algorithm

intervals

Results

119.0ms	120×	body	1280	valid
39.0ms	71×	body	640	valid
12.0ms	32×	body	320	valid
4.0ms	15×	body	160	valid
2.0ms	18×	body	80	valid

simplify6.0ms

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))

rewrite16.0ms

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
31.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

52 → 52

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	97	702
1	208	687
2	465	615
3	1004	613
4	1949	613
5	4233	613
done	5000	613

prune142.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

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

localize32.0ms

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
26.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify957.0ms

Counts

61 → 61

Iterations

Useful iterations: 3 (190.0ms)

Iter	Nodes	Cost
0	126	866
1	277	850
2	681	752
3	1496	750
4	2715	750
done	5000	750

prune120.0ms

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

localize28.0ms

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)))))

rewrite23.0ms

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:

10.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
6.0ms	(* (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)))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
58.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	154	1487
1	381	1414
2	1221	1270
3	4887	1270
done	5000	1270

prune134.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

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

localize23.0ms

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))

rewrite22.0ms

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))
7.0ms	(cos (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series17.0ms

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))

simplify1.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	48	410
1	84	402
2	154	370
3	285	364
4	517	364
5	1052	364
6	3397	364
done	5000	364

prune73.0ms

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

regimes733.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

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

3.4s	3685×	body	1280	valid
1.3s	2281×	body	640	valid
371.0ms	952×	body	320	valid
120.0ms	413×	body	160	valid
85.0ms	669×	body	80	valid

Details

sample196.0ms

simplify6.0ms

prune5.0ms

localize19.0ms

rewrite16.0ms

series51.0ms

simplify1.5s

prune142.0ms

localize32.0ms

rewrite16.0ms

series51.0ms

simplify957.0ms

prune120.0ms

localize28.0ms

rewrite23.0ms

series118.0ms

simplify1.5s

prune134.0ms

localize23.0ms

rewrite22.0ms

series17.0ms

simplify1.3s

prune73.0ms

regimes733.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.8s

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