Details

sample814.0ms

Algorithm

intervals

Results

573.0ms	153×	body	1280	valid
177.0ms	61×	body	640	valid
26.0ms	18×	body	320	valid
8.0ms	19×	body	80	valid
4.0ms	5×	body	160	valid

simplify108.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	80
4	80
3	77
2	47
1	28
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize45.0ms

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))

rewrite71.0ms

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:

11.0ms	(* (sin phi1) (cos phi2))
30.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))
18.0ms	(sin (- lambda1 lambda2))

series235.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin phi1) (cos phi2))
130.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
3	2844
2	925
1	422
0	212

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize128.0ms

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))

rewrite112.0ms

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))
11.0ms	(* (sin lambda1) (cos lambda2))
68.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series315.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos lambda1) (sin lambda2))
81.0ms	(* (sin lambda1) (cos lambda2))
135.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

101 → 101

Iterations

Iter	Nodes
3	3736
2	1198
1	478
0	228

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

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)))

rewrite140.0ms

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:

18.0ms	(* (sin lambda1) (cos lambda2))
57.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(* (sin lambda1) (sin lambda2))
45.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin lambda1) (cos lambda2))
107.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
67.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify2.4s

Counts

112 → 112

Iterations

Iter	Nodes
3	7633
2	1481
1	417
0	167

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize102.0ms

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)))

rewrite137.0ms

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))))
60.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (sin lambda1) (sin lambda2))
62.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(log1p (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
133.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
52.0ms	(* (sin lambda1) (sin lambda2))
154.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
3	6756
2	1344
1	367
0	150

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes812.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	39
1	39
0	29

end0.0ms

sample22.1s

Algorithm

intervals

Results

16.0s	4667×	body	1280	valid
4.5s	1913×	body	640	valid
789.0ms	511×	body	320	valid
306.0ms	689×	body	80	valid
199.0ms	220×	body	160	valid