Details

sample797.0ms

Algorithm

intervals

Results

572.0ms	153×	body	1280	valid
168.0ms	61×	body	640	valid
23.0ms	18×	body	320	valid
8.0ms	19×	body	80	valid
5.0ms	5×	body	160	valid

simplify65.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (sin phi1) (cos phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin phi1) (cos phi2))
122.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	2001
3	2001
2	783
1	272
0	118

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 72

Calls

4 calls:

21.0ms	(* (cos lambda1) (sin lambda2))
17.0ms	(* (sin lambda1) (cos lambda2))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series308.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos lambda1) (sin lambda2))
56.0ms	(* (sin lambda1) (cos lambda2))
143.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	2002
3	2002
2	1046
1	364
0	152

prune2.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
5×	`sin-cos-mult`
4×	`*-commutative` `insert-posit16` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

11.0ms	(* (sin lambda1) (cos lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
11.0ms	(* (sin lambda1) (sin lambda2))
55.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin lambda1) (cos lambda2))
156.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
79.0ms	(* (sin lambda1) (sin lambda2))
169.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.3s

Counts

104 → 104

Iterations

Iter	Nodes
done	2001
3	2001
2	1531
1	412
0	159

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
4×	`*-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`associate-*l/` `sin-mult`
2×	`unswap-sqr`
1×	`frac-times` `associate-*r/`

Counts

4 → 89

Calls

4 calls:

22.0ms	(* (sin lambda1) (cos lambda2))
86.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
53.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(* (sin lambda1) (sin lambda2))

series497.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin lambda1) (cos lambda2))
183.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
158.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
84.0ms	(* (sin lambda1) (sin lambda2))

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	2004
3	2004
2	1553
1	407
0	160

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes716.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample24.3s

Algorithm

intervals

Results

17.3s	4667×	body	1280	valid
5.1s	1913×	body	640	valid
783.0ms	511×	body	320	valid
591.0ms	689×	body	80	valid
199.0ms	220×	body	160	valid