Details

sample73.0ms

Algorithm

intervals

Results

25.0ms	80×	body	1280	valid
12.0ms	253×	body	80	valid
10.0ms	51×	body	640	valid
4.0ms	30×	body	320	valid
2.0ms	19×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	12	19
1	25	13
2	49	13
3	76	13
4	95	13
5	111	13
6	125	13
7	139	13
done	139	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

30.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
33.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
10.0ms	(/ (cos th) (sqrt 2.0))
10.0ms	(/ (cos th) (sqrt 2.0))

series344.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
113.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms	(/ (cos th) (sqrt 2.0))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts

180 → 180

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	181	2118
1	466	2012
2	1390	1832
done	5000	1812

prune501.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(* (/ (cos th) (sqrt 2.0)) a2)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 165

Calls

4 calls:

30.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
22.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
10.0ms	(/ (cos th) (sqrt 2.0))
10.0ms	(/ (cos th) (sqrt 2.0))

series338.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
110.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
55.0ms	(/ (cos th) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify2.5s

Counts

177 → 177

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	175	1959
1	424	1860
2	1261	1720
3	4213	1704
done	5000	1704

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 1 (/ (* (cos th) a2) (sqrt 2.0))) a2)
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(/ (* (cos th) a2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
44×	`times-frac`
42×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
28×	`sqrt-prod`
23×	`associate-l`
22×	`prod-exp`
15×	`cbrt-unprod`
14×	`pow1`
12×	`associate-/r*`
9×	`div-exp`
7×	`cbrt-undiv`
6×	`pow-prod-down`
4×	`associate-r` `associate-/l*` `add-log-exp`
3×	`1-exp` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`associate-*r/`

Counts

4 → 137

Calls

4 calls:

54.0ms	(* (* 1 (/ (* (cos th) a2) (sqrt 2.0))) a2)
33.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
13.0ms	(/ (* (cos th) a2) (sqrt 2.0))
10.0ms	(/ (cos th) (sqrt 2.0))

series387.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (* 1 (/ (* (cos th) a2) (sqrt 2.0))) a2)
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
103.0ms	(/ (* (cos th) a2) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify1.3s

Counts

149 → 149

Iterations

Useful iterations: 2 (277.0ms)

Iter	Nodes	Cost
0	221	1850
1	526	1678
2	1708	1480
done	5000	1480

prune396.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos th) a2) (sqrt (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (/ (* (cos th) a2) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

256×	`sqrt-prod`
254×	`times-frac`
125×	`add-sqr-sqrt`
120×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
17×	`associate-/l*`
14×	`div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

13.0ms	(/ (* (cos th) a2) (sqrt (sqrt 2.0)))
32.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
22.0ms	(/ (/ (* (cos th) a2) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
10.0ms	(/ (cos th) (sqrt 2.0))

series441.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (* (cos th) a2) (sqrt (sqrt 2.0)))
107.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
102.0ms	(/ (/ (* (cos th) a2) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
61.0ms	(/ (cos th) (sqrt 2.0))

simplify859.0ms

Counts

285 → 285

Iterations

Useful iterations: done (850.0ms)

Iter	Nodes	Cost
0	337	4974
1	821	4327
2	2152	3962
done	5000	3894

prune626.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes259.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	24	35
1	30	33
done	30	33

end0.0ms

sample2.3s

Algorithm

intervals

Results

770.0ms	2438×	body	1280	valid
430.0ms	2009×	body	640	valid
401.0ms	8039×	body	80	valid
155.0ms	1046×	body	320	valid
62.0ms	569×	body	160	valid