Details

sample814.0ms

Algorithm

intervals

Results

583.0ms	150×	body	1280	valid
157.0ms	59×	body	640	valid
35.0ms	22×	body	320	valid
8.0ms	20×	body	80	valid
4.0ms	5×	body	160	valid

simplify45.0ms

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.3b	(cos (- lambda1 lambda2))
4.4b	(sin (- lambda1 lambda2))

rewrite115.0ms

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`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
62.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
18.0ms	(sin (- lambda1 lambda2))

series290.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (cos phi1) (sin phi2))
147.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	2028
3	2028
2	1053
1	463
0	226

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.5b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.3b	(cos (- lambda1 lambda2))

rewrite142.0ms

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:

23.0ms	(* (cos phi1) (sin phi2))
24.0ms	(* (sin lambda1) (cos lambda2))
62.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

series361.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (cos phi1) (sin phi2))
78.0ms	(* (sin lambda1) (cos lambda2))
164.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
36.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
3	2001
2	1211
1	494
0	230

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize136.0ms

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	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

rewrite217.0ms

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:

25.0ms	(* (sin lambda1) (cos lambda2))
26.0ms	(* (sin lambda1) (sin lambda2))
84.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
79.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin lambda1) (cos lambda2))
78.0ms	(* (sin lambda1) (sin lambda2))
161.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
205.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	2008
3	2008
2	1552
1	435
0	169

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize141.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

rewrite172.0ms

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×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `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:

0.0ms	(log1p (expm1 (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))))
21.0ms	(* (sin lambda1) (sin lambda2))
62.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
87.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series722.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(log1p (expm1 (* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))))
90.0ms	(* (sin lambda1) (sin lambda2))
147.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
202.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	1335
1	371
0	147

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample26.0s

Algorithm

intervals

Results

18.5s	4683×	body	1280	valid
5.7s	1903×	body	640	valid
922.0ms	548×	body	320	valid
353.0ms	644×	body	80	valid
177.0ms	222×	body	160	valid