Details

sample342.0ms

Algorithm

intervals

Results

208.0ms	104×	body	1280	valid
79.0ms	86×	body	640	valid
13.0ms	19×	body	320	valid
8.0ms	19×	body	160	valid
5.0ms	28×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize73.0ms

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))))
3.6b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite29.0ms

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)))))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms	(sin (- lambda1 lambda2))
8.0ms	(cos (- lambda1 lambda2))

series250.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
156.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
40.0ms	(sin (- lambda1 lambda2))
32.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (426.0ms)

Iter	Nodes	Cost
0	97	18618
1	207	17405
2	528	17405
3	1502	17365
done	5000	17365

prune532.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.7b

localize63.0ms

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)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.8b	(cos (- lambda1 lambda2))

rewrite93.0ms

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×	`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 → 54

Calls

4 calls:

76.0ms	(* (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)))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))

series476.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
28.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
175.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify1.5s

Counts

66 → 66

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	124	32606
1	310	31232
2	1276	31232
done	5000	31112

prune743.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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

Counts

4 → 63

Calls

4 calls:

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))))))
46.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
9.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series658.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
218.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
61.0ms	(* (sin lambda1) (sin lambda2))
338.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.1s

Counts

75 → 75

Iterations

Useful iterations: 2 (588.0ms)

Iter	Nodes	Cost
0	144	38425
1	376	36991
2	1865	36831
done	5001	36831

prune823.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize249.0ms

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)))) (+ (* (cos phi1) (cos phi1)) (- (* (* (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))))))))
0.5b	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.5b	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.7b	(- (* (* (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))))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

660×	`associate-*r/`
266×	`frac-add` `cos-mult`
153×	`frac-times`
152×	`flip3-+` `flip-+`
150×	`sin-mult`
90×	`frac-sub`
82×	`pow1`
65×	`associate-/l/`
57×	`associate-*l/`
55×	`associate-/r/`
34×	`pow-prod-down`
30×	`add-cbrt-cube` `add-exp-log`
16×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `sub-div`
8×	`pow-sqr` `pow-prod-up`
6×	`add-log-exp`
4×	`pow-plus` `cube-unmult` `pow3` `associate--l+` `sum-cubes` `associate-/l*` `associate--r+`
3×	`associate-/r*`
2×	`pow2` `flip3--` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `distribute-rgt-out--` `diff-log` `div-exp` `div-inv`

Counts

4 → 329

Calls

4 calls:

1.4s	(/ (+ (* (* (* (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)))) (+ (* (cos phi1) (cos phi1)) (- (* (* (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))))))))
161.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
189.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
245.0ms	(- (* (* (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))))))

series6.6s

Counts

4 → 12

Calls

4 calls:

4.7s	(/ (+ (* (* (* (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)))) (+ (* (cos phi1) (cos phi1)) (- (* (* (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))))))))
270.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
282.0ms	(* (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.3s	(- (* (* (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))))))

simplify5.1s

Counts

341 → 341

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	756	431324
1	2452	376932
done	5001	376732

prune5.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes797.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	36	1544
1	53	1544
done	53	1544

end0.0ms

sample11.7s

Algorithm

intervals

Results

7.3s	3606×	body	1280	valid
2.9s	2359×	body	640	valid
680.0ms	900×	body	320	valid
264.0ms	429×	body	160	valid
126.0ms	706×	body	80	valid