Details

sample270.0ms

Algorithm

intervals

Results

189.0ms	146×	body	1280	valid
53.0ms	67×	body	640	valid
8.0ms	16×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	7×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	79	24
4	88	24
done	88	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
14.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series166.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
85.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify544.0ms

Counts

97 → 97

Iterations

Useful iterations: done (541.0ms)

Iter	Nodes	Cost
0	222	1711
1	450	1374
2	1275	1060
done	5000	1011

prune397.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(cos (- lambda1 lambda2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out` `sin-cos-mult`

Counts

4 → 85

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series201.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin (- lambda2)))
47.0ms	(* (cos phi1) (sin phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify570.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (138.0ms)

Iter	Nodes	Cost
0	226	1336
1	470	1158
2	1532	937
done	5000	937

prune521.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
17.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
14.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos phi1) (sin phi2))
48.0ms	(* (sin lambda1) (sin lambda2))
95.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
118.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify580.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	177	1301
1	448	1274
2	1645	1014
done	5001	1014

prune632.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
2×	`cos-mult`
1×	`frac-times` `associate-*r/` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
27.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
14.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos phi1) (sin phi2))
64.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
96.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
122.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify716.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (137.0ms)

Iter	Nodes	Cost
0	178	1317
1	443	1290
2	1940	1024
done	5001	1024

prune510.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes477.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	29	47
1	40	47
done	40	47

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.4s	4640×	body	1280	valid
1.5s	1986×	body	640	valid
275.0ms	564×	body	320	valid
90.0ms	623×	body	80	valid
57.0ms	187×	body	160	valid