Details

sample798.0ms

Algorithm

intervals

Results

296.0ms	54×	body	640	valid
164.0ms	46×	body	1280	valid
107.0ms	143×	body	80	valid
47.0ms	18×	body	160	valid
30.0ms	19×	body	320	valid
20.0ms	48×	body	80	nan

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2007
7	2007
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ (sin B) F)
6.8b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
17.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite181.0ms

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:

9.0ms	(/ x (tan B))
15.0ms	(/ (sin B) F)
111.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
41.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series596.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ x (tan B))
50.0ms	(/ (sin B) F)
225.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
127.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.2s

Counts

218 → 218

Iterations

Iter	Nodes
done	2001
2	2001
1	912
0	375

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B)) F)
0.4b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B))
17.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
54×	`times-frac`
45×	`*-un-lft-identity` `add-cube-cbrt`
25×	`unpow-prod-down` `associate-l`
22×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`sqr-pow`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`prod-exp` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `div-inv`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-/r/` `-commutative`

Counts

4 → 142

Calls

4 calls:

9.0ms	(/ x (tan B))
127.0ms	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B)) F)
60.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B))
30.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series651.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ x (tan B))
221.0ms	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B)) F)
181.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (sin B))
92.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.4s

Counts

154 → 154

Iterations

Iter	Nodes
done	2007
3	2007
2	1669
1	585
0	252

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B))
0.3b	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) 1) (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B)))
18.0b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
18.0b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
126×	`times-frac`
85×	`add-exp-log`
76×	`*-un-lft-identity`
64×	`add-cube-cbrt`
51×	`unpow-prod-down`
48×	`div-exp`
28×	`prod-exp` `unswap-sqr`
27×	`sqr-pow`
26×	`pow-unpow`
25×	`associate-r` `associate-l`
18×	`pow-to-exp` `add-cbrt-cube` `pow-exp`
12×	`1-exp`
8×	`pow1`
7×	`associate-/l*`
5×	`cbrt-undiv` `div-inv`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`pow-pow`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 225

Calls

4 calls:

76.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B))
160.0ms	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) 1) (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B)))
36.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
43.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

series670.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B))
194.0ms	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) 1) (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B)))
141.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
132.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

simplify1.3s

Counts

237 → 237

Iterations

Iter	Nodes
done	2000
2	2000
1	1036
0	329

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F))
0.4b	(* (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (sin B)) (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F)))
17.4b	(sqrt (+ (+ 2 (* F F)) (* x 2)))
17.4b	(sqrt (+ (+ 2 (* F F)) (* x 2)))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

631×	`times-frac`
491×	`add-sqr-sqrt`
275×	`*-un-lft-identity`
255×	`add-cube-cbrt`
236×	`unpow-prod-down`
201×	`add-exp-log`
135×	`associate-r`
129×	`div-exp`
124×	`sqrt-prod`
65×	`unswap-sqr`
58×	`sqr-pow`
52×	`prod-exp`
34×	`associate-l`
33×	`pow-to-exp` `pow-exp`
30×	`add-cbrt-cube`
24×	`div-inv`
15×	`rec-exp` `1-exp`
13×	`associate-/r*`
12×	`cbrt-undiv`
10×	`associate-/l*`
8×	`pow1`
6×	`cbrt-unprod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 516

Calls

4 calls:

76.0ms	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F))
210.0ms	(* (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (sin B)) (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F)))
17.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
35.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F))
229.0ms	(* (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (sin B)) (/ (pow (sqrt (+ (+ 2 (* F F)) (* x 2))) -1/2) (/ 1 F)))
67.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))
73.0ms	(sqrt (+ (+ 2 (* F F)) (* x 2)))

simplify1.4s

Counts

528 → 528

Iterations

Iter	Nodes
done	2000
1	2000
0	615

prune3.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.6b

bsearch636.0ms

Steps

Iters	Range		Point
11	1.2035886760163307e-31	3231.8276777318033	3174.6489492657015
6	-28834360.271521915	-6838974.188497498	-7181092.308785896

simplify20.0ms

Iterations

Iter	Nodes
done	44
1	44
0	35

end0.0ms

sample13.8s

Algorithm

intervals

Results

5.1s	1632×	body	1280	valid
2.8s	1351×	body	640	valid
2.6s	4817×	body	80	valid
1.5s	685×	body	320	valid
1.1s	1676×	body	80	nan
319.0ms	377×	body	160	valid