Details

sample382.0ms

Algorithm

intervals

Results

224.0ms	108×	body	1280	valid
84.0ms	76×	body	640	valid
35.0ms	30×	body	320	valid
7.0ms	34×	body	80	valid
3.0ms	8×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	584
1	20	584
2	21	584
done	21	584

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.4b	(sin (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))

rewrite42.0ms

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`
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 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms	(sin (- lambda1 lambda2))
9.0ms	(cos (- lambda1 lambda2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
152.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms	(sin (- lambda1 lambda2))
25.0ms	(cos (- lambda1 lambda2))

simplify3.7s

Counts

52 → 52

Iterations

Useful iterations: 3 (458.0ms)

Iter	Nodes	Cost
0	97	18618
1	207	17405
2	476	17405
3	1176	17365
4	2583	17365
done	5002	17365

prune553.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(cos (- lambda1 lambda2))

rewrite34.0ms

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

Counts

4 → 48

Calls

4 calls:

16.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms	(cos (- lambda1 lambda2))

series262.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos lambda1) (sin lambda2))
20.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
148.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

60 → 60

Iterations

Useful iterations: 3 (876.0ms)

Iter	Nodes	Cost
0	118	23780
1	269	22365
2	662	22285
3	2083	22205
done	5000	22205

prune657.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize100.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite31.0ms

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`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `flip-+` `sin-mult`

Counts

4 → 57

Calls

4 calls:

11.0ms	(* (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)) (* (sin lambda1) (sin lambda2))))))
10.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos lambda1) (sin lambda2))
34.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
53.0ms	(* (sin lambda1) (sin lambda2))
396.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify4.8s

Counts

69 → 69

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	133	29599
1	328	28124
2	964	27964
3	4076	27924
done	5002	27924

prune789.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize304.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

468×	`associate-*r/`
170×	`frac-add` `cos-mult`
126×	`frac-times`
108×	`flip3-+` `flip-+`
107×	`sin-mult`
82×	`pow1`
45×	`associate-*l/` `frac-sub`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up` `add-log-exp`
6×	`sub-div`
4×	`add-sqr-sqrt` `associate-+l+` `*-un-lft-identity` `pow-plus` `associate--l+` `add-cube-cbrt` `associate--r+`
2×	`pow2` `sqr-cos` `associate-+r+` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `cube-unmult` `pow3` `sum-cubes` `flip--`

Counts

4 → 259

Calls

4 calls:

494.0ms	(+ (* (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
125.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
192.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
272.0ms	(- (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series3.6s

Counts

4 → 12

Calls

4 calls:

1.7s	(+ (* (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi1) (cos phi1))))
240.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
246.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.4s	(- (* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Iterations

Useful iterations: 0 (830.0ms)

Iter	Nodes	Cost
0	701	369825