Details

sample365.0ms

Algorithm

intervals

Results

231.0ms	109×	body	1280	valid
78.0ms	71×	body	640	valid
24.0ms	39×	body	320	valid
6.0ms	15×	body	160	valid
4.0ms	22×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(cos (- lambda1 lambda2))
4.0b	(sin (- lambda1 lambda2))

rewrite95.0ms

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:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
22.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
48.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

series250.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
166.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify5.0s

Counts

52 → 52

Iterations

Useful iterations: 3 (327.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	458	615
3	970	613
4	2017	613
5	4604	613
done	5000	613

prune793.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(cos (- lambda1 lambda2))

rewrite98.0ms

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×	`distribute-rgt-in` `cos-sum` `associate-+r+` `distribute-lft-in` `flip3-+` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

69.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
15.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(cos (- lambda1 lambda2))

series434.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
32.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
145.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
27.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

64 → 64

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	127	1191
1	323	1173
2	1089	1031
3	3961	997
done	5001	997

prune499.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

rewrite120.0ms

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

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (sin lambda1) (sin (- lambda2)))
80.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
18.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin lambda1) (sin (- lambda2)))
185.0ms	(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
21.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
286.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

simplify1.3s

Counts

76 → 76

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	154	1588
1	384	1556
2	1336	1365
done	5001	1322

prune638.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))))
0.3b	(exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
0.5b	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
0.6b	(log (exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1`
4×	`add-exp-log` `log-prod` `log-pow` `add-cbrt-cube`
2×	`associate-+l+` `exp-sum` `sum-log` `rem-exp-log`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `rem-log-exp` `flip-+`

Counts

4 → 49

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))))
65.0ms	(exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
33.0ms	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
37.0ms	(log (exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

23.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (log (exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))))
440.0ms	(exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
283.0ms	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
323.0ms	(log (exp (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))))

simplify1.7s

Counts

61 → 61

Iterations

Useful iterations: 3 (593.0ms)

Iter	Nodes	Cost
0	113	1673
1	245	1603
2	644	1386
3	2583	1363
done	5002	1363

prune392.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes611.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	37
1	35	37
done	35	37

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.3s	3545×	body	1280	valid
3.6s	2386×	body	640	valid
1.7s	1003×	body	320	valid
193.0ms	362×	body	160	valid
181.0ms	704×	body	80	valid