Details

sample652.0ms

Algorithm

intervals

Results

443.0ms	153×	body	1280	valid
104.0ms	61×	body	640	valid
52.0ms	18×	body	320	valid
32.0ms	19×	body	80	valid
3.0ms	5×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	73
4	73
3	69
2	45
1	27
0	17

prune25.0ms

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))

rewrite66.0ms

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:

10.0ms	(* (sin phi1) (cos phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series205.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin phi1) (cos phi2))
96.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))
32.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
3	2578
2	766
1	270
0	118

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.2b

localize66.0ms

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))

rewrite81.0ms

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:

15.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series276.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cos lambda1) (sin lambda2))
54.0ms	(* (sin lambda1) (cos lambda2))
137.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))

simplify2.2s

Counts

84 → 84

Iterations

Iter	Nodes
3	3375
2	1023
1	362
0	152

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

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

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`
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:

14.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
11.0ms	(* (sin lambda1) (sin lambda2))
41.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series453.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin lambda1) (cos lambda2))
160.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
62.0ms	(* (sin lambda1) (sin lambda2))
160.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify2.8s

Counts

104 → 104

Iterations

Iter	Nodes
3	7414
2	1521
1	428
0	161

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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-l`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r`
4×	`*-commutative` `insert-posit16` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`associate-*r/` `unswap-sqr`
1×	`frac-times` `associate-*l/`

Counts

4 → 86

Calls

4 calls:

10.0ms	(* (sin lambda1) (cos lambda2))
23.0ms	(* (cos lambda2) (* (sin phi1) (cos phi2)))
82.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
11.0ms	(* (sin lambda1) (sin lambda2))

series346.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (cos lambda2))
123.0ms	(* (cos lambda2) (* (sin phi1) (cos phi2)))
113.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
48.0ms	(* (sin lambda1) (sin lambda2))

simplify1.9s

Counts

98 → 98

Iterations

Iter	Nodes
3	5335
2	1184
1	364
0	145

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes785.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	39
1	39
0	28

end0.0ms

sample25.5s

Algorithm

intervals

Results

18.9s	4667×	body	1280	valid
4.4s	1913×	body	640	valid
1.3s	511×	body	320	valid
298.0ms	689×	body	80	valid
216.0ms	220×	body	160	valid