Details

sample442.0ms

Algorithm

intervals

Results

221.0ms	112×	body	1280	valid
138.0ms	74×	body	640	valid
32.0ms	41×	body	320	valid
8.0ms	16×	body	160	valid
3.0ms	13×	body	80	valid

simplify16.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	21	20
done	21	20

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize120.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0b	(sin (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
20.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
199.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
41.0ms	(sin (- lambda1 lambda2))
46.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

52 → 52

Iterations

Useful iterations: 3 (526.0ms)

Iter	Nodes	Cost
0	97	702
1	207	687
2	532	615
3	1518	613
done	5000	613

prune677.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

25.0ms	(* (sin lambda1) (cos lambda2))
1.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
31.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

series363.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sin lambda1) (cos lambda2))
31.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
210.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
34.0ms	(cos (- lambda1 lambda2))

simplify4.3s

Counts

61 → 61

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	127	880
1	296	864
2	927	764
3	4048	751
done	5001	750

prune786.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))
0.2b	(* (sin lambda2) (sin lambda1))
0.6b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 58

Calls

4 calls:

21.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))
24.0ms	(* (sin lambda2) (sin lambda1))
38.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (sin lambda1) (cos lambda2))
36.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1))))))
81.0ms	(* (sin lambda2) (sin lambda1))
410.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))))

simplify1.1s

Counts

70 → 70

Iterations

Useful iterations: 2 (306.0ms)

Iter	Nodes	Cost
0	146	1185
1	343	1160
2	1312	1005
done	5001	1005

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize148.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) 3))
0.3b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) 3)
0.7b	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`pow-unpow`
4×	`unpow-prod-down` `cube-prod`
3×	`cube-div` `pow-pow` `associate-*r/` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `associate--l+` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `cos-mult` `sum-cubes` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out`

Counts

4 → 75

Calls

4 calls:

40.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) 3))
6.0ms	(pow (cos phi1) 3)
42.0ms	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) 3)
94.0ms	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))

series3.6s

Counts

4 → 12

Calls

4 calls:

2.7s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) 3))
68.0ms	(pow (cos phi1) 3)
420.0ms	(pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) 3)
448.0ms	(- (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))

simplify3.8s

Counts

87 → 87

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	211	1843
1	728	1658
2	3923	1500
done	5000	1500

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes1.3s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify20.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	37	112
1	52	112
2	55	112
3	57	112
done	57	112

end0.0ms

sample13.7s

Algorithm

intervals

Results

8.4s	3558×	body	1280	valid
3.1s	2329×	body	640	valid
1.2s	980×	body	320	valid
192.0ms	441×	body	160	valid
134.0ms	692×	body	80	valid