Details

sample675.0ms

Algorithm

intervals

Results

444.0ms	148×	body	1280	valid
180.0ms	64×	body	640	valid
20.0ms	17×	body	320	valid
8.0ms	23×	body	80	valid
2.0ms	4×	body	160	valid

simplify76.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b	(cos (- lambda1 lambda2))
5.2b	(sin (- lambda1 lambda2))

rewrite90.0ms

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:

25.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
29.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

simplify942.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2005
3	2005
2	1034
1	436
0	214

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.9b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b	(cos (- lambda1 lambda2))

rewrite162.0ms

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` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 90

Calls

4 calls:

84.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
11.0ms	(* (cos lambda1) (sin lambda2))
53.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))

series355.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
50.0ms	(* (cos lambda1) (sin lambda2))
136.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	2000
3	2000
2	1362
1	492
0	225

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

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:

42.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
12.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (cos lambda1) (sin lambda2))
44.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
63.0ms	(* (sin lambda1) (sin lambda2))
52.0ms	(* (cos lambda1) (sin lambda2))
121.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	2006
3	2006
2	1562
1	442
0	167

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (cos lambda1) (sin lambda2))
88.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
59.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin lambda1) (sin lambda2))
62.0ms	(* (cos lambda1) (sin lambda2))
149.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
131.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	2004
3	2004
2	1530
1	440
0	172

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes578.0ms

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	41
1	41
0	29

end0.0ms

sample22.5s

Algorithm

intervals

Results

15.7s	4509×	body	1280	valid
4.9s	2043×	body	640	valid
1.1s	555×	body	320	valid
286.0ms	664×	body	80	valid
196.0ms	229×	body	160	valid