Details

sample396.0ms

Algorithm

intervals

Results

246.0ms	117×	body	1280	valid
84.0ms	73×	body	640	valid
19.0ms	27×	body	320	valid
8.0ms	15×	body	160	valid
5.0ms	24×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
0.6b	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
4.6b	(cos (- lambda1 lambda2))
4.6b	(sin (- lambda1 lambda2))

rewrite44.0ms

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×	`associate-+l+` `cos-sum` `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 phi2) (cos (- lambda1 lambda2))) (cos phi1)))
14.0ms	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
14.0ms	(cos (- lambda1 lambda2))
15.0ms	(sin (- lambda1 lambda2))

series239.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
162.0ms	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
20.0ms	(cos (- lambda1 lambda2))
38.0ms	(sin (- lambda1 lambda2))

simplify1.2s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	2243
2	591
1	201
0	95

prune481.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
0.2b	(* (sin lambda2) (sin lambda1))
0.6b	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
4.6b	(sin (- lambda1 lambda2))

rewrite53.0ms

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

Counts

4 → 49

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
13.0ms	(* (sin lambda2) (sin lambda1))
22.0ms	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
17.0ms	(sin (- lambda1 lambda2))

series501.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
77.0ms	(* (sin lambda2) (sin lambda1))
354.0ms	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
37.0ms	(sin (- lambda1 lambda2))

simplify595.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
2	1010
1	273
0	121

prune741.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
0.2b	(* (sin lambda2) (sin lambda1))
0.6b	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))

rewrite54.0ms

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

Counts

4 → 58

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
15.0ms	(* (sin lambda2) (sin lambda1))
28.0ms	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))

series524.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (cos lambda2))
42.0ms	(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (- (* (cos lambda1) (sin lambda2))))) (+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
98.0ms	(* (sin lambda2) (sin lambda1))
320.0ms	(+ (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda2) (sin lambda1)))) (cos phi1))

simplify875.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1438
1	345
0	140

prune895.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize159.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow (cos phi1) 3) (pow (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3)
1.1b	(- (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

25.0ms	(+ (pow (cos phi1) 3) (pow (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3))
5.0ms	(pow (cos phi1) 3)
18.0ms	(pow (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3)
54.0ms	(- (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.8s	(+ (pow (cos phi1) 3) (pow (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3))
31.0ms	(pow (cos phi1) 3)
266.0ms	(pow (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) 3)
314.0ms	(- (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (cos phi2)) (cos phi1))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	3911
1	726
0	209

prune996.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes1.5s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	40
2	40
1	38
0	24

end0.0ms

sample12.8s

Algorithm

intervals

Results

7.4s	3483×	body	1280	valid
3.6s	2411×	body	640	valid
910.0ms	973×	body	320	valid
227.0ms	424×	body	160	valid
132.0ms	709×	body	80	valid