Details

sample416.0ms

Algorithm

intervals

Results

283.0ms	136×	body	1280	valid
88.0ms	75×	body	640	valid
15.0ms	23×	body	320	valid
3.0ms	18×	body	80	valid
2.0ms	4×	body	160	valid

simplify482.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	72	24
done	72	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.5b	(sin (- lambda1 lambda2))
6.0b	(cos (- lambda1 lambda2))

rewrite130.0ms

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:

30.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
43.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
36.0ms	(cos (- lambda1 lambda2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
132.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

simplify6.8s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	116	760
1	258	748
2	816	644
3	2177	642
4	3715	642
done	5000	642

prune545.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.5b

localize73.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0b	(cos (- lambda1 lambda2))

rewrite103.0ms

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

Counts

4 → 64

Calls

4 calls:

18.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
24.0ms	(* (sin lambda1) (cos lambda2))
48.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms	(cos (- lambda1 lambda2))

series438.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
70.0ms	(* (sin lambda1) (cos lambda2))
126.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify4.0s

Counts

76 → 76

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	141	1015
1	337	973
2	1122	873
3	3753	871
done	5000	871

prune670.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

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×	`*-commutative` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

12.0ms	(* (sin lambda1) (cos lambda2))
25.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
64.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda1) (cos lambda2))
70.0ms	(* (sin lambda1) (sin lambda2))
170.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
173.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.5s

Counts

100 → 100

Iterations

Useful iterations: 2 (329.0ms)

Iter	Nodes	Cost
0	161	1238
1	408	1212
2	1624	952
done	5000	952

prune739.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin phi1) (cos phi2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3)))
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(pow (* (sin lambda2) (sin lambda1)) 3)
29.9b	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1` `add-exp-log`
22×	`add-cbrt-cube`
16×	`cbrt-prod`
12×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`cube-div` `sin-cos-mult` `sin-mult` `add-log-exp`
3×	`cube-mult` `unpow-prod-down` `pow-unpow` `cbrt-div` `unpow3` `cube-prod` `sqr-pow`
2×	`frac-times` `pow-pow` `associate-r/` `associate-l` `associate-l/` `pow-exp` `cos-mult` `*-commutative` `rem-cube-cbrt`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube`

Counts

4 → 95

Calls

4 calls:

43.0ms	(* (* (sin phi1) (cos phi2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3)))
49.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
15.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
5.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

series448.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (* (sin phi1) (cos phi2)) (cbrt (pow (* (sin lambda2) (sin lambda1)) 3)))
164.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
107.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
62.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

simplify1.3s

Counts

107 → 107

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	173	1474
1	433	1263
2	1814	1071
done	5000	1067

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes741.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	48
1	40	48
done	40	48

end0.0ms

sample19.6s

Algorithm

intervals

Results

14.4s	4619×	body	1280	valid
3.7s	1988×	body	640	valid
696.0ms	570×	body	320	valid
163.0ms	634×	body	80	valid
97.0ms	189×	body	160	valid