Details

sample555.0ms

Algorithm

intervals

Results

298.0ms	136×	body	1280	valid
167.0ms	75×	body	640	valid
53.0ms	23×	body	320	valid
5.0ms	18×	body	80	valid
2.0ms	4×	body	160	valid

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	30	24
2	69	24
3	88	24
done	88	24

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.5b	(sin (- lambda1 lambda2))
6.0b	(cos (- lambda1 lambda2))

rewrite137.0ms

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:

41.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
62.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(sin (- lambda1 lambda2))
12.0ms	(cos (- lambda1 lambda2))

series322.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
167.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
33.0ms	(sin (- lambda1 lambda2))
28.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

72 → 72

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	116	760
1	510	748
done	5000	642

prune539.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0b	(cos (- lambda1 lambda2))

rewrite104.0ms

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` `add-log-exp`
5×	`cos-diff`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `cos-sum` `distribute-lft-in` `*-commutative` `sin-cos-mult` `associate--r+`
1×	`flip3--` `diff-log` `associate-*l/` `flip--` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

17.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
24.0ms	(* (sin lambda1) (cos lambda2))
41.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series442.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
77.0ms	(* (sin lambda1) (cos lambda2))
130.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify3.5s

Counts

76 → 76

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	141	1015
1	665	973
done	5000	871

prune692.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

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:

20.0ms	(* (sin lambda1) (cos lambda2))
24.0ms	(* (sin lambda1) (sin lambda2))
70.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
53.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (cos lambda2))
99.0ms	(* (sin lambda1) (sin lambda2))
159.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
180.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify3.6s

Counts

100 → 100

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	161	1238
1	740	1212
done	5000	952

prune968.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
28.2b	(cbrt (pow (* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) 3))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
5×	`associate-r/` `associate-r*`
4×	`add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `sin-cos-mult`
1×	`cube-div` `cube-mult` `frac-times` `unpow-prod-down` `cbrt-div` `pow1/3` `unpow3` `cube-prod` `associate-*l/` `rem-cbrt-cube` `unswap-sqr` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

14.0ms	(* (sin lambda2) (sin lambda1))
125.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))
91.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
21.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) 3))

series591.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin lambda2) (sin lambda1))
146.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))
202.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
180.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) 3))

simplify3.0s

Counts

96 → 96

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	165	1413
1	754	1247
done	5001	1089

prune855.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	50
1	44	50
done	44	50

end0.0ms

sample21.9s

Algorithm

intervals

Results

15.6s	4619×	body	1280	valid
4.5s	1988×	body	640	valid
658.0ms	570×	body	320	valid
171.0ms	634×	body	80	valid
160.0ms	189×	body	160	valid