Details

sample828.0ms

Algorithm

intervals

Results

322.0ms	68×	body	80	nan
210.0ms	47×	body	1280	valid
62.0ms	47×	body	640	valid
59.0ms	26×	body	320	valid
55.0ms	167×	body	80	valid
6.0ms	8×	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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.6b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
16.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite231.0ms

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:

6.0ms	(/ x (tan B))
94.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
74.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
53.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series548.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ x (tan B))
106.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
204.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
110.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.6s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1400
1	458
0	199

prune704.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
0.5b	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F))
0.5b	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)))
16.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

117.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
58.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F))
63.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)))
31.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series640.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
204.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F))
225.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)))
113.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.7s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	1790
1	589
0	233

prune983.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F))
0.3b	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
1.0b	(/ (/ 1 (sin B)) (/ 1 (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)))
16.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite349.0ms

Algorithm

rewrite-expression-head

Rules

208×	`times-frac`
189×	`add-exp-log`
118×	`div-exp`
100×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
48×	`prod-exp`
33×	`rec-exp` `1-exp`
32×	`add-cbrt-cube`
24×	`div-inv`
17×	`pow-to-exp` `pow-exp`
16×	`associate-/l*`
15×	`cbrt-undiv`
8×	`associate-/r*`
7×	`unpow-prod-down` `associate-l`
6×	`pow1`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-r` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 260

Calls

4 calls:

60.0ms	(/ 1 (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F))
133.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
90.0ms	(/ (/ 1 (sin B)) (/ 1 (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)))
50.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series513.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ 1 (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F))
101.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
228.0ms	(/ (/ 1 (sin B)) (/ 1 (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)))
95.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify2.2s

Counts

272 → 272

Iterations

Iter	Nodes
done	5006
2	2561
1	1107
0	397

prune1.7s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.0b

localize82.0ms

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)
0.6b	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
16.4b	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

rewrite270.0ms

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:

29.0ms	(* (/ x (sin B)) (cos B))
126.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
84.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
26.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

series554.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (/ x (sin B)) (cos B))
125.0ms	(* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F)
193.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* x 2)) -1/2) F) (sin B))
103.0ms	(pow (+ (+ 2 (* F F)) (* x 2)) -1/2)

simplify1.5s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1603
1	510
0	206

prune751.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 0.0b

regimes474.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.5b

bsearch476.0ms

Steps

Iters	Range		Point
9	443.57959014112146	38910778292.312386	107303683.05601409
6	-2.4189380706844988e+60	-1.9938791164796219e+59	-2.034324775890907e+59

simplify22.0ms

Iterations

Iter	Nodes
done	53
3	53
2	50
1	46
0	34

end0.0ms

sample10.1s

Algorithm

intervals

Results

3.6s	1607×	body	1280	valid
2.9s	1355×	body	640	valid
1.8s	4862×	body	80	valid
680.0ms	689×	body	320	valid
492.0ms	1636×	body	80	nan
231.0ms	361×	body	160	valid