Details

sample257.0ms

Algorithm

intervals

Results

188.0ms	151×	body	1280	valid
39.0ms	62×	body	640	valid
8.0ms	17×	body	320	valid
3.0ms	23×	body	80	valid
1.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15
done	94	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(sin (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))

rewrite73.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

11.0ms	(* (sin phi1) (cos phi2))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(sin (- lambda1 lambda2))
13.0ms	(cos (- lambda1 lambda2))

series183.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
96.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
19.0ms	(cos (- lambda1 lambda2))

simplify40.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776
done	5001	776

prune391.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (cos lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite74.0ms

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×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 86

Calls

4 calls:

11.0ms	(* (sin phi1) (cos phi2))
14.0ms	(* (cos lambda1) (sin (- lambda2)))
33.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series220.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
59.0ms	(* (cos lambda1) (sin (- lambda2)))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	429	817
1	1608	656
2	5001	655
done	5001	655

prune514.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

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`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 96

Calls

4 calls:

15.0ms	(* (cos lambda1) (sin (- lambda2)))
11.0ms	(* (sin lambda1) (sin lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos lambda1) (sin (- lambda2)))
45.0ms	(* (sin lambda1) (sin lambda2))
118.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
107.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify55.0ms

Counts

108 → 108

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	432	855
1	1954	672
2	5001	672
done	5001	672

prune585.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (* (cos lambda1) (sin (- lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

0.0ms	(log1p (* (cos lambda1) (sin (- lambda2))))
12.0ms	(* (sin lambda1) (sin lambda2))
42.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
43.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(log1p (* (cos lambda1) (sin (- lambda2))))
46.0ms	(* (sin lambda1) (sin lambda2))
123.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
106.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify49.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	394	804
1	1667	627
2	5001	625
done	5001	625

prune469.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes516.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	32
1	40	32
done	40	32

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4615×	body	1280	valid
1.4s	2033×	body	640	valid
235.0ms	514×	body	320	valid
82.0ms	643×	body	80	valid
60.0ms	195×	body	160	valid