Details

sample735.0ms

Algorithm

intervals

Results

171.0ms	55×	body	1280	valid
91.0ms	19×	body	320	valid
91.0ms	37×	body	640	valid
75.0ms	155×	body	80	valid
58.0ms	61×	body	80	nan
49.0ms	17×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.1b	(/ x (tan B))
5.6b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
14.1b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite132.0ms

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:

8.0ms	(/ (sin B) F)
5.0ms	(/ x (tan B))
74.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
36.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series570.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (sin B) F)
175.0ms	(/ x (tan B))
225.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) (/ (sin B) F))
120.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.2s

Counts

218 → 218

Iterations

Iter	Nodes
done	2000
2	2000
1	912
0	375

prune3.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B)) (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (/ 1 F)))
0.4b	(/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (/ 1 F))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

446×	`times-frac`
330×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
203×	`add-exp-log`
194×	`add-cube-cbrt`
129×	`div-exp`
118×	`unpow-prod-down`
96×	`associate-r`
54×	`sqr-pow`
52×	`prod-exp`
40×	`unswap-sqr`
35×	`pow-to-exp` `pow-exp`
30×	`add-cbrt-cube`
26×	`pow-unpow`
25×	`associate-l`
20×	`div-inv`
15×	`rec-exp` `1-exp`
13×	`associate-/r*`
12×	`cbrt-undiv`
8×	`pow1`
7×	`associate-/l*`
6×	`cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
2×	`pow-pow` `associate-/r/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 425

Calls

4 calls:

212.0ms	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B)) (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (/ 1 F)))
76.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (/ 1 F))
43.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
39.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

series586.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (sin B)) (/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (/ 1 F)))
142.0ms	(/ (pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2)) (/ 1 F))
124.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
111.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

simplify1.7s

Counts

437 → 437

Iterations

Iter	Nodes
done	2002
2	2002
1	1933
0	565

prune8.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow-unpow`
36×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
12×	`unpow-prod-down`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `insert-posit16` `div-inv` `add-log-exp` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

21.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
24.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
39.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
23.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

series491.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
137.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
109.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
136.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

simplify1.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	2001
3	2001
2	673
1	247
0	91

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize101.0ms

Local error

Found 4 expressions with local error:

11.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
14.4b	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

46×	`pow-unpow`
31×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`times-frac`
12×	`unpow-prod-down`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `insert-posit16` `div-inv` `add-log-exp` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

21.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
21.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
25.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
24.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

series781.0ms

Counts

4 → 12

Calls

4 calls:

370.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ 1 (* (cbrt 2) (cbrt 2))))
147.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
140.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))
124.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) (/ -1/2 2))

simplify1.4s

Counts

118 → 118

Iterations

Iter	Nodes
done	2003
3	2003
2	1074
1	401
0	148

prune2.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes519.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.7b

bsearch500.0ms

Steps

Iters	Range		Point
8	657359.5389414565	1775159043.1692293	59636856.48207364
6	-8748.371804340544	-1395.4681145621753	-8575.24190677927

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample13.0s

Algorithm

intervals

Results

4.8s	1648×	body	1280	valid
2.9s	4834×	body	80	valid
2.6s	1385×	body	640	valid
1.1s	1778×	body	80	nan
967.0ms	690×	body	320	valid
383.0ms	360×	body	160	valid