Details

sample596.0ms

Algorithm

intervals

Results

444.0ms	149×	body	1280	valid
88.0ms	59×	body	640	valid
18.0ms	18×	body	320	valid
7.0ms	25×	body	80	valid
3.0ms	5×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	95	24
done	95	24

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(sin (- lambda1 lambda2))
3.7b	(cos (- lambda1 lambda2))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

48.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
39.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

series285.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
131.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(sin (- lambda1 lambda2))
31.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

98 → 98

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	210	1766
1	434	1442
2	1802	1150
done	5000	1095

prune796.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.3b

localize85.0ms

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)))
3.7b	(cos (- lambda1 lambda2))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 87

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
55.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
46.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

series497.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin phi1) (cos phi2))
224.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
175.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

99 → 99

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	209	1587
1	469	1417
2	2064	1181
done	5000	1150

prune954.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 97

Calls

4 calls:

54.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
65.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
56.0ms	(* (sin lambda1) (sin lambda2))
179.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
127.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.6s

Counts

109 → 109

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	1576
1	463	1550
2	2211	1261
done	5001	1253

prune997.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-l`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-r/` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`cos-mult` `sin-cos-mult`
1×	`frac-times` `associate-*l/` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

10.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
45.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
51.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (sin lambda1) (sin lambda2))
134.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
152.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
177.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.1s

Counts

105 → 105

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	155	1320
1	398	1296
2	1787	1037
done	5000	1028

prune985.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes794.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	46
1	37	46
done	37	46

end0.0ms

sample20.5s

Algorithm

intervals

Results

13.6s	4571×	body	1280	valid
4.9s	1969×	body	640	valid
643.0ms	558×	body	320	valid
627.0ms	685×	body	80	valid
122.0ms	217×	body	160	valid