Details

sample280.0ms

Algorithm

intervals

Results

199.0ms	147×	body	1280	valid
50.0ms	66×	body	640	valid
10.0ms	21×	body	320	valid
3.0ms	9×	body	160	valid
2.0ms	13×	body	80	valid

simplify40.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	70	24
4	72	24
done	72	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

11.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series185.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify4.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (720.0ms)

Iter	Nodes	Cost
0	116	760
1	260	748
2	848	644
3	2510	642
4	4629	642
done	5000	642

prune343.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

17.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin lambda1) (cos lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
44.0ms	(* (sin lambda1) (cos lambda2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	148	1039
1	348	1016
2	1204	882
3	4170	880
done	5001	880

prune437.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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

Counts

4 → 88

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin lambda1) (cos lambda2))
46.0ms	(* (sin lambda1) (sin lambda2))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
99.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify906.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (147.0ms)

Iter	Nodes	Cost
0	157	1238
1	408	1212
2	1452	952
done	5001	952

prune528.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`*-commutative` `add-log-exp`
3×	`associate-*l/` `sin-cos-mult` `sin-mult` `unswap-sqr`
1×	`frac-times` `flip3--` `associate-*r/` `flip--`

Counts

4 → 83

Calls

4 calls:

16.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (sin lambda1) (cos lambda2))
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
45.0ms	(* (sin lambda1) (cos lambda2))
43.0ms	(* (sin lambda1) (sin lambda2))
96.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify931.0ms

Counts

95 → 95

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	159	1209
1	379	1180
2	1289	984
done	5000	984

prune445.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes395.0ms

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	28	53
1	39	53
done	39	53

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.4s	4627×	body	1280	valid
1.7s	1948×	body	640	valid
291.0ms	557×	body	320	valid
95.0ms	652×	body	80	valid
68.0ms	216×	body	160	valid