Details

sample292.0ms

Algorithm

intervals

Results

217.0ms	152×	body	1280	valid
38.0ms	53×	body	640	valid
12.0ms	23×	body	320	valid
3.0ms	24×	body	80	valid
1.0ms	4×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	88	24
done	88	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
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`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))
14.0ms	(sin (- lambda1 lambda2))

series188.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos phi1) (sin phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify4.8s

Counts

97 → 97

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	222	1711
1	430	1374
2	1059	1096
3	2652	1011
4	4517	847
done	5000	738

prune567.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
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` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* (cos lambda1) (sin (- lambda2)))
12.0ms	(* (sin lambda1) (cos lambda2))
37.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos lambda1) (sin (- lambda2)))
49.0ms	(* (sin lambda1) (cos lambda2))
100.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

98 → 98

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	228	1345
1	454	1167
2	1228	946
3	3073	855
done	5000	783

prune483.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

12.0ms	(* (sin lambda1) (cos lambda2))
12.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
47.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (cos lambda2))
50.0ms	(* (sin lambda1) (sin lambda2))
107.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
123.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.1s

Counts

108 → 108

Iterations

Useful iterations: 2 (224.0ms)

Iter	Nodes	Cost
0	165	1310
1	415	1283
2	1644	1023
done	5000	1023

prune556.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

45.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))

series413.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
100.0ms	(cbrt (cos lambda2))
95.0ms	(cbrt (cos lambda2))
95.0ms	(cbrt (cos lambda2))

simplify2.1s

Counts

78 → 78

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	94	757
1	219	735
2	780	598
3	3523	589
done	5001	586

prune439.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes412.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	54
1	42	54
done	42	54

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.3s	4646×	body	1280	valid
1.4s	1855×	body	640	valid
299.0ms	592×	body	320	valid
97.0ms	699×	body	80	valid
61.0ms	208×	body	160	valid