Details

sample800.0ms

Algorithm

intervals

Results

577.0ms	145×	body	1280	valid
160.0ms	70×	body	640	valid
31.0ms	19×	body	320	valid
7.0ms	17×	body	80	valid
5.0ms	5×	body	160	valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.2b	(cos (- lambda1 lambda2))
2.4b	(sin (- lambda1 lambda2))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (sin phi1) (cos phi2))
54.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series231.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin phi1) (cos phi2))
98.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
43.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	2001
3	2001
2	783
1	272
0	118

prune661.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize78.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.2b	(cos (- lambda1 lambda2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 72

Calls

4 calls:

10.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (sin phi1) (cos phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series330.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (cos phi1) (sin phi2))
79.0ms	(* (sin phi1) (cos phi2))
140.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))

simplify1.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	2003
3	2003
2	918
1	325
0	138

prune835.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize117.0ms

Local error

Found 4 expressions with local error:

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

rewrite168.0ms

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

Counts

4 → 92

Calls

4 calls:

22.0ms	(* (sin phi1) (cos phi2))
21.0ms	(* (sin lambda1) (sin lambda2))
66.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
58.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin phi1) (cos phi2))
68.0ms	(* (sin lambda1) (sin lambda2))
157.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
144.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
done	2002
3	2002
2	1509
1	414
0	155

prune995.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

15.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (sin lambda1) (sin lambda2))
63.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
50.0ms	(* (* (cos lambda1) (cos lambda2)) (sin phi1))

series392.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin phi1) (cos phi2))
72.0ms	(* (sin lambda1) (sin lambda2))
159.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
105.0ms	(* (* (cos lambda1) (cos lambda2)) (sin phi1))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	2003
3	2003
2	1308
1	387
0	151

prune884.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes524.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample25.1s

Algorithm

intervals

Results

18.2s	4596×	body	1280	valid
4.8s	1983×	body	640	valid
1.3s	548×	body	320	valid
318.0ms	660×	body	80	valid
195.0ms	213×	body	160	valid