Details

sample522.0ms

Algorithm

intervals

Results

313.0ms	146×	body	1280	valid
97.0ms	64×	body	640	valid
75.0ms	20×	body	320	valid
4.0ms	18×	body	80	valid
4.0ms	8×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	83	24
5	84	24
done	84	24

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

18.0ms	(* (sin phi1) (cos phi2))
41.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin phi1) (cos phi2))
154.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify1.0s

Counts

72 → 72

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	114	718
1	268	706
2	1417	618
done	5000	608

prune418.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
48.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))

series365.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin phi1) (cos phi2))
167.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
118.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	137	1068
1	370	1054
2	2152	910
done	5001	904

prune747.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

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

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `flip-+` `sin-mult` `unswap-sqr`
2×	`frac-add` `cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
75.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
13.0ms	(* (sin lambda2) (sin lambda1))
117.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin phi1) (cos phi2))
188.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
52.0ms	(* (sin lambda2) (sin lambda1))
244.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1))))

simplify2.2s

Counts

97 → 97

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	189	1541
1	568	1506
2	3511	1318
done	5000	1314

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda2) (sin lambda1))))))
4.1b	(log (exp (* (sin lambda2) (sin lambda1))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`log-prod` `flip3-+` `associate-l/` `log-pow` `-commutative` `sin-cos-mult` `flip-+`
2×	`frac-times` `associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `exp-prod` `exp-to-pow` `distribute-lft-in` `rem-log-exp` `sin-mult`

Counts

4 → 78

Calls

4 calls:

72.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
20.0ms	(* (sin lambda2) (sin lambda1))
104.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda2) (sin lambda1))))))
7.0ms	(log (exp (* (sin lambda2) (sin lambda1))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
56.0ms	(* (sin lambda2) (sin lambda1))
196.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda2) (cos lambda1)) (log (exp (* (sin lambda2) (sin lambda1))))))
53.0ms	(log (exp (* (sin lambda2) (sin lambda1))))

simplify1.7s

Counts

90 → 90

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	177	1531
1	491	1390
2	2850	1212
done	5000	1210

prune658.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	53
1	44	53
done	44	53

end0.0ms

sample17.6s

Algorithm

intervals

Results

13.3s	4608×	body	1280	valid
2.9s	1915×	body	640	valid
535.0ms	575×	body	320	valid
186.0ms	211×	body	160	valid
156.0ms	691×	body	80	valid