Details

sample803.0ms

Algorithm

intervals

Results

615.0ms	142×	body	1280	valid
107.0ms	54×	body	640	valid
30.0ms	23×	body	320	valid
16.0ms	14×	body	160	valid
8.0ms	23×	body	80	valid

simplify75.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
4	95
3	78
2	47
1	28
0	17

prune405.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite118.0ms

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:

24.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
63.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(sin (- lambda1 lambda2))
10.0ms	(cos (- lambda1 lambda2))

series251.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
125.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(sin (- lambda1 lambda2))
25.0ms	(cos (- lambda1 lambda2))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1764
1	436
0	214

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.0b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite94.0ms

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

Counts

4 → 88

Calls

4 calls:

16.0ms	(* (cos phi1) (sin phi2))
11.0ms	(* (cos lambda1) (sin lambda2))
49.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos phi1) (sin phi2))
59.0ms	(* (cos lambda1) (sin lambda2))
147.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	2035
1	483
0	226

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin 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)))

rewrite159.0ms

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:

19.0ms	(* (cos lambda1) (sin lambda2))
20.0ms	(* (sin lambda1) (sin lambda2))
75.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
43.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos lambda1) (sin lambda2))
51.0ms	(* (sin lambda1) (sin lambda2))
116.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
153.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.3s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	2042
1	443
0	167

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

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)))
0.3b	(log1p (* (cos lambda1) (sin lambda2)))

rewrite121.0ms

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:

21.0ms	(* (sin lambda1) (sin lambda2))
56.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
41.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.0ms	(log1p (* (cos lambda1) (sin lambda2)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda1) (sin lambda2))
175.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
162.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
91.0ms	(log1p (* (cos lambda1) (sin lambda2)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1853
1	409
0	161

prune815.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes965.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	39
1	39
0	29

end0.0ms

sample22.6s

Algorithm

intervals

Results

16.9s	4601×	body	1280	valid
4.2s	1955×	body	640	valid
704.0ms	546×	body	320	valid
302.0ms	675×	body	80	valid
219.0ms	223×	body	160	valid