Details

sample525.0ms

Algorithm

intervals

Results

397.0ms	143×	body	1280	valid
78.0ms	62×	body	640	valid
20.0ms	24×	body	320	valid
5.0ms	10×	body	160	valid
4.0ms	17×	body	80	valid

simplify38.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite94.0ms

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:

29.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(sin (- lambda1 lambda2))
13.0ms	(cos (- lambda1 lambda2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
126.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3650
2	1063
1	436
0	214

prune851.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.3b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(cos (- lambda1 lambda2))

rewrite72.0ms

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	(* (sin phi1) (cos phi2))
14.0ms	(* (cos lambda1) (sin lambda2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series478.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin phi1) (cos phi2))
52.0ms	(* (cos lambda1) (sin lambda2))
355.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify2.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
3	3739
2	1096
1	449
0	212

prune910.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

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

Counts

4 → 99

Calls

4 calls:

18.0ms	(* (cos lambda1) (sin lambda2))
55.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
18.0ms	(* (sin lambda1) (sin lambda2))
67.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos lambda1) (sin lambda2))
109.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
49.0ms	(* (sin lambda1) (sin lambda2))
172.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	1534
1	442
0	167

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

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:

67.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.0ms	(log1p (* (cos lambda1) (sin lambda2)))
12.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
91.0ms	(log1p (* (cos lambda1) (sin lambda2)))
66.0ms	(* (sin lambda1) (sin lambda2))
139.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1464
1	409
0	161

prune886.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes883.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample19.9s

Algorithm

intervals

Results

15.5s	4582×	body	1280	valid
2.9s	1943×	body	640	valid
703.0ms	583×	body	320	valid
225.0ms	688×	body	80	valid
121.0ms	204×	body	160	valid