Details

sample424.0ms

Algorithm

intervals

Results

274.0ms	120×	body	1280	valid
99.0ms	76×	body	640	valid
23.0ms	30×	body	320	valid
6.0ms	23×	body	80	valid
4.0ms	7×	body	160	valid

simplify339.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))
3.4b	(sin (- lambda1 lambda2))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`cos-diff`
2×	`cos-sum` `associate-+r+` `sub-neg` `sin-sum`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 44

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
19.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
122.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify1.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
4	2001
3	1179
2	486
1	211
0	101

prune924.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.1b	(cos (- lambda1 lambda2))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

85.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms	(cos (- lambda1 lambda2))

series363.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
161.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	2013
3	2013
2	917
1	312
0	128

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`insert-posit16`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `flip-+` `flip--` `sin-mult`

Counts

4 → 65

Calls

4 calls:

88.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
11.0ms	(* (sin lambda1) (sin lambda2))
12.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series511.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
29.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
84.0ms	(* (sin lambda1) (sin lambda2))
205.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.3s

Counts

77 → 77

Iterations

Iter	Nodes
done	2003
3	2003
2	1139
1	367
0	144

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize149.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b	(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1)))
0.4b	(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
1.2b	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

rewrite805.0ms

Algorithm

rewrite-expression-head

Rules

127×	`pow1`
72×	`pow-prod-down`
49×	`add-cbrt-cube` `add-exp-log`
33×	`prod-exp` `cbrt-unprod`
26×	`cos-mult`
24×	`associate-*l/`
15×	`associate-*r/`
9×	`pow-sqr` `pow-prod-up`
8×	`frac-times` `add-log-exp`
7×	`frac-add`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `insert-posit16`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `flip3--` `flip--`
2×	`sqr-cos` `associate-+r+` `cube-unmult` `associate-l` `*-commutative`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `diff-log` `swap-sqr` `sum-cubes` `flip-+`

Counts

4 → 130

Calls

4 calls:

418.0ms	(+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
201.0ms	(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1)))
154.0ms	(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
27.0ms	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

series896.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(+ (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
317.0ms	(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1)))
143.0ms	(* (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
189.0ms	(- (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (cos phi1))

simplify1.2s

Counts

142 → 142

Iterations

Iter	Nodes
done	2003
2	2003
1	725
0	220

prune3.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes860.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	46
1	46
0	32

end0.0ms

sample16.9s

Algorithm

intervals

Results

9.5s	3593×	body	1280	valid
5.4s	2366×	body	640	valid
1.1s	913×	body	320	valid
336.0ms	415×	body	160	valid
271.0ms	713×	body	80	valid