Details

sample366.0ms

Algorithm

intervals

Results

177.0ms	100×	body	1280	valid
121.0ms	74×	body	640	valid
31.0ms	43×	body	320	valid
6.0ms	13×	body	160	valid
5.0ms	26×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(cos (- lambda1 lambda2))
4.2b	(sin (- lambda1 lambda2))

rewrite75.0ms

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)))))
22.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
146.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (445.0ms)

Iter	Nodes	Cost
0	97	702
1	207	687
2	538	615
3	1521	613
done	5000	613

prune397.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.0b

localize38.0ms

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)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(cos (- lambda1 lambda2))

rewrite66.0ms

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:

24.0ms	(* (sin lambda1) (cos lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
19.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

series298.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin lambda1) (cos lambda2))
29.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
146.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
42.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

61 → 61

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	120	866
1	276	851
2	883	753
3	3989	751
done	5000	750

prune534.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize61.0ms

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

rewrite52.0ms

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

Counts

4 → 61

Calls

4 calls:

19.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))))))
21.0ms	(* (sin (- lambda2)) (sin lambda1))
10.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (cos lambda2))
21.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1))))))
83.0ms	(* (sin (- lambda2)) (sin lambda1))
390.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin (- lambda2)) (sin lambda1)))))

simplify815.0ms

Counts

73 → 73

Iterations

Useful iterations: done (810.0ms)

Iter	Nodes	Cost
0	147	1263
1	342	1234
2	1221	1087
done	5000	1043

prune670.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`log-prod` `log-pow`
3×	`associate-r` `associate-l`
2×	`associate-+l+` `exp-sum` `sum-log` `rem-exp-log`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

121.0ms	(exp (+ (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
18.0ms	(* (sin lambda2) (sin lambda1))
41.0ms	(+ (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))
74.0ms	(log (exp (+ (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))

series1.1s

Counts

4 → 12

Calls

4 calls:

473.0ms	(exp (+ (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))
52.0ms	(* (sin lambda2) (sin lambda1))
283.0ms	(+ (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))
272.0ms	(log (exp (+ (* (cos phi2) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2)))) (cos phi1))))

simplify722.0ms

Counts

73 → 73

Iterations

Useful iterations: done (719.0ms)

Iter	Nodes	Cost
0	124	1366
1	300	1314
2	1175	1152
done	5001	1140

prune607.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes606.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	35	37
2	37	37
done	37	37

end0.0ms

sample11.2s

Algorithm

intervals

Results

6.1s	3469×	body	1280	valid
3.4s	2407×	body	640	valid
683.0ms	965×	body	320	valid
294.0ms	729×	body	80	valid
147.0ms	430×	body	160	valid