Details

sample576.0ms

Algorithm

intervals

Results

214.0ms	65×	body	1280	valid
67.0ms	34×	body	640	valid
66.0ms	150×	body	80	valid
61.0ms	56×	body	80	nan
38.0ms	25×	body	320	valid
7.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.2b	(/ x (tan B))
5.2b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
17.0b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

181×	`times-frac`
106×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`sqr-pow`
13×	`add-cbrt-cube` `associate-/l*`
11×	`div-exp` `div-inv`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 206

Calls

4 calls:

15.0ms	(/ (sin B) F)
10.0ms	(/ x (tan B))
57.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
28.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series609.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (sin B) F)
195.0ms	(/ x (tan B))
262.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
116.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify786.0ms

Counts

218 → 218

Iterations

Iter	Nodes
done	2000
1	912
0	375

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
0.5b	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
17.0b	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

rewrite367.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`associate-l`
20×	`add-cbrt-cube`
18×	`times-frac`
9×	`unpow-prod-down` `div-exp`
7×	`pow1` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `associate-r` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/r/`

Counts

4 → 120

Calls

4 calls:

11.0ms	(/ x (tan B))
173.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
152.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
28.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

series725.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ x (tan B))
139.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
160.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
275.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

simplify1.3s

Counts

132 → 132

Iterations

Iter	Nodes
done	2004
2	1522
1	594
0	246

prune860.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.3b	(/ (/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B)) (/ 1 F))
0.3b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B))
17.0b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

883×	`times-frac`
408×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
141×	`unpow-prod-down`
56×	`add-exp-log`
47×	`sqr-pow`
43×	`div-inv`
40×	`div-exp`
35×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot` `associate-/l/`

Counts

4 → 489

Calls

4 calls:

5.0ms	(/ x (tan B))
68.0ms	(/ (/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B)) (/ 1 F))
93.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B))
38.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series589.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ x (tan B))
188.0ms	(/ (/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B)) (/ 1 F))
151.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B))
96.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify953.0ms

Counts

501 → 501

Iterations

Iter	Nodes
done	2000
0	816

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.2b	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
0.5b	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
17.0b	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
32×	`prod-exp`
23×	`add-sqr-sqrt` `add-cbrt-cube`
22×	`*-un-lft-identity`
21×	`associate-l`
18×	`add-cube-cbrt`
12×	`times-frac`
10×	`div-exp`
9×	`unpow-prod-down`
8×	`cbrt-unprod`
7×	`pow1`
6×	`pow-to-exp` `pow-exp`
4×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-/r*` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/ (* x (cos B)) (sin B))
151.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
205.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
41.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

series712.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (* x (cos B)) (sin B))
135.0ms	(* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F)
159.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ (* x 2) (* F F)) 2) -1/2) F))
272.0ms	(pow (+ (+ (* x 2) (* F F)) 2) -1/2)

simplify972.0ms

Counts

125 → 125

Iterations

Iter	Nodes
done	2004
2	1800
1	613
0	234

prune767.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes339.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.9b

bsearch758.0ms

Steps

Iters	Range		Point
10	5.946889120991019e+19	8.906366062612403e+30	6.013802817876398e+19
10	-5.62159838506386e+29	-3139973514407996.0	-4.183187481012982e+22

simplify8.0ms

Iterations

Iter	Nodes
done	37
1	37
0	31

end0.0ms

sample13.6s

Algorithm

intervals

Results

4.9s	1728×	body	1280	valid
4.0s	1338×	body	640	valid
2.2s	4735×	body	80	valid
1.0s	720×	body	320	valid
805.0ms	1709×	body	80	nan
323.0ms	357×	body	160	valid