Details

sample248.0ms

Algorithm

intervals

Results

170.0ms	145×	body	1280	valid
43.0ms	58×	body	640	valid
15.0ms	21×	body	320	valid
3.0ms	26×	body	80	valid
2.0ms	6×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	71	24
4	74	24
done	74	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- lambda1 lambda2))

rewrite24.0ms

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

Counts

4 → 59

Calls

4 calls:

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

series175.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (411.0ms)

Iter	Nodes	Cost
0	128	709
1	291	697
2	1010	601
3	4078	599
done	5000	599

prune312.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite25.0ms

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

Counts

4 → 68

Calls

4 calls:

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos lambda1) (sin (- lambda2)))
47.0ms	(* (cos phi1) (sin phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

80 → 80

Iterations

Useful iterations: 3 (504.0ms)

Iter	Nodes	Cost
0	150	804
1	345	790
2	1233	678
3	4997	676
done	5000	676

prune448.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-neg` `distribute-rgt-neg-out` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/`

Counts

4 → 88

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos lambda1) (sin (- lambda2)))
42.0ms	(* (cos phi1) (sin phi2))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
180.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify671.0ms

Counts

100 → 100

Iterations

Useful iterations: done (668.0ms)

Iter	Nodes	Cost
0	203	1467
1	515	1419
2	2084	1213
done	5000	1211

prune550.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin lambda1) (* (sin lambda1) (* (sin lambda2) (sin lambda2))))) (* (sin phi1) (cos phi2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow1`
26×	`associate-*r/`
25×	`add-exp-log` `add-cbrt-cube`
22×	`pow-prod-down`
16×	`cos-mult`
15×	`add-sqr-sqrt`
13×	`prod-exp` `cbrt-unprod`
12×	`associate-*l/` `sin-mult`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`frac-times` `associate-l`
8×	`associate-r` `sin-cos-mult`
6×	`frac-sub`
5×	`pow-sqr` `pow-prod-up`
4×	`swap-sqr` `*-commutative` `sub-div` `add-log-exp`
3×	`pow-plus`
2×	`pow2` `flip3--` `flip--` `unswap-sqr`
1×	`sin-neg` `distribute-rgt-neg-out` `sqr-sin`

Counts

4 → 117

Calls

4 calls:

4.0ms	(* (sin lambda2) (sin lambda2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
83.0ms	(* (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin lambda1) (* (sin lambda1) (* (sin lambda2) (sin lambda2))))) (* (sin phi1) (cos phi2)))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (sin lambda2) (sin lambda2))
52.0ms	(* (sin lambda1) (sin (- lambda2)))
207.0ms	(* (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin lambda1) (* (sin lambda1) (* (sin lambda2) (sin lambda2))))) (* (sin phi1) (cos phi2)))
57.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))

simplify977.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (202.0ms)

Iter	Nodes	Cost
0	229	2448
1	599	2034
2	2551	1707
done	5001	1707

prune700.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes374.0ms

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	32	64
1	44	64
done	44	64

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.1s	4553×	body	1280	valid
1.4s	1976×	body	640	valid
256.0ms	583×	body	320	valid
94.0ms	674×	body	80	valid
61.0ms	214×	body	160	valid