Details

sample804.0ms

Algorithm

intervals

Results

579.0ms	153×	body	1280	valid
141.0ms	61×	body	640	valid
43.0ms	18×	body	320	valid
9.0ms	19×	body	80	valid
4.0ms	5×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
4	80
3	77
2	47
1	28
0	17

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite92.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

15.0ms	(* (sin phi1) (cos phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

series251.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin phi1) (cos phi2))
120.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))
44.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	2016
3	2016
2	969
1	433
0	212

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize101.0ms

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)))
3.1b	(cos (- lambda1 lambda2))

rewrite67.0ms

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` `insert-posit16` `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/`

Counts

4 → 89

Calls

4 calls:

11.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(* (sin lambda1) (cos lambda2))
34.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series288.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos lambda1) (sin lambda2))
72.0ms	(* (sin lambda1) (cos lambda2))
134.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	2002
3	2002
2	1212
1	490
0	228

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

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`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

19.0ms	(* (sin lambda1) (cos lambda2))
50.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
11.0ms	(* (sin lambda1) (sin lambda2))
44.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin lambda1) (cos lambda2))
138.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
78.0ms	(* (sin lambda1) (sin lambda2))
178.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	2004
3	2004
2	1445
1	418
0	167

prune2.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.2b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`expm1-log1p-u` `associate-r` `associate-l`
4×	`insert-posit16` `log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult`
1×	`log1p-udef` `log1p-expm1` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

1.0ms	(log1p (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
67.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
19.0ms	(* (sin lambda1) (sin lambda2))
79.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(log1p (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
119.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
65.0ms	(* (sin lambda1) (sin lambda2))
151.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	1341
1	368
0	150

prune2.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes788.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample24.3s

Algorithm

intervals

Results

17.1s	4667×	body	1280	valid
5.7s	1913×	body	640	valid
709.0ms	511×	body	320	valid
251.0ms	689×	body	80	valid
209.0ms	220×	body	160	valid