Details

sample278.0ms

Algorithm

intervals

Results

61.0ms	46×	body	1280	valid
58.0ms	18×	body	320	valid
38.0ms	166×	body	80	valid
37.0ms	43×	body	640	valid
11.0ms	72×	body	80	nan
5.0ms	14×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5020
7	4228
6	1403
5	705
4	360
3	169
2	91
1	46
0	20

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.4b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
19.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

10.0ms	(/ x (tan B))
84.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
47.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
29.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series619.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ x (tan B))
134.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
225.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
117.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.6s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1400
1	458
0	199

prune784.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.4b	(* (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (/ 1 (sin B)))
19.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-r`
10×	`div-exp`
8×	`pow1` `associate-l`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 122

Calls

4 calls:

6.0ms	(/ 1 (sin B))
134.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
165.0ms	(* (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (/ 1 (sin B)))
19.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series408.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1 (sin B))
91.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
201.0ms	(* (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (/ 1 (sin B)))
91.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify2.3s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	1581
1	527
0	200

prune755.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.4b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
19.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
20×	`associate-l`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`times-frac`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-r`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-/r*` `pow-exp` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 101

Calls

4 calls:

15.0ms	(* (/ x (sin B)) (cos B))
113.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
56.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
35.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series594.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (/ x (sin B)) (cos B))
102.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
203.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
113.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1603
1	510
0	206

prune732.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.4b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
19.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (* x (cos B)) (sin B))
116.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
57.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
21.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series490.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (* x (cos B)) (sin B))
92.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
181.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
79.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5005
2	1563
1	469
0	185

prune664.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes258.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.1b

bsearch465.0ms

Steps

Iters	Range		Point
7	1127.9279929291722	170178.13541022167	11392.48259111127
9	-4.6204468068562855e+39	-1.5359199640650495e+32	-1.5555718098587194e+32

simplify8.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample10.3s

Algorithm

intervals

Results

3.9s	1676×	body	1280	valid
2.1s	1391×	body	640	valid
2.1s	4801×	body	80	valid
781.0ms	670×	body	320	valid
673.0ms	392×	body	160	valid
394.0ms	1595×	body	80	nan