Details

sample220.0ms

Algorithm

intervals

Results

72.0ms	82×	body	1280	valid
46.0ms	37×	body	320	valid
38.0ms	67×	body	640	valid
38.0ms	264×	body	80	valid
7.0ms	22×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

43.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
22.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
11.0ms	(/ (cos th) (sqrt 2))
24.0ms	(/ (cos th) (sqrt 2))

series447.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
147.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
102.0ms	(/ (cos th) (sqrt 2))
67.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

184 → 184

Iterations

Iter	Nodes
done	2000
3	2000
2	1563
1	533
0	183

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (* a2 a2) (sqrt 2)))
0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(/ (* a2 a2) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
51×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 147

Calls

4 calls:

21.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
23.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
10.0ms	(/ (* a2 a2) (sqrt 2))
13.0ms	(/ (cos th) (sqrt 2))

series490.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
158.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
107.0ms	(/ (* a2 a2) (sqrt 2))
64.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

159 → 159

Iterations

Iter	Nodes
done	2000
3	2000
2	1971
1	563
0	205

prune803.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ (cos th) (sqrt 2)) a1) a1)
0.3b	(* (/ (cos th) (sqrt 2)) a1)
0.3b	(/ (* a2 a2) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
28×	`sqrt-prod`
25×	`add-cbrt-cube` `add-exp-log`
23×	`associate-l`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-r`
5×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`associate-*l/` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`

Counts

4 → 133

Calls

4 calls:

46.0ms	(* (* (/ (cos th) (sqrt 2)) a1) a1)
13.0ms	(* (/ (cos th) (sqrt 2)) a1)
11.0ms	(/ (* a2 a2) (sqrt 2))
27.0ms	(/ (cos th) (sqrt 2))

series492.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (* (/ (cos th) (sqrt 2)) a1) a1)
179.0ms	(* (/ (cos th) (sqrt 2)) a1)
90.0ms	(/ (* a2 a2) (sqrt 2))
75.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

145 → 145

Iterations

Iter	Nodes
done	2007
3	2007
2	1512
1	495
0	193

prune726.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* a2 a2) (sqrt (sqrt 2)))
0.2b	(/ (/ (* a2 a2) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.3b	(* (/ (cos th) (sqrt 2)) a1)
0.7b	(/ (cos th) (sqrt 2))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

256×	`sqrt-prod`
254×	`times-frac`
129×	`add-sqr-sqrt`
121×	`*-un-lft-identity` `add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
17×	`associate-/l*`
14×	`div-inv`
9×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 274

Calls

4 calls:

17.0ms	(/ (* a2 a2) (sqrt (sqrt 2)))
36.0ms	(/ (/ (* a2 a2) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
25.0ms	(* (/ (cos th) (sqrt 2)) a1)
18.0ms	(/ (cos th) (sqrt 2))

series521.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* a2 a2) (sqrt (sqrt 2)))
111.0ms	(/ (/ (* a2 a2) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
143.0ms	(* (/ (cos th) (sqrt 2)) a1)
85.0ms	(/ (cos th) (sqrt 2))

simplify1.1s

Counts

286 → 286

Iterations

Iter	Nodes
done	2002
2	2002
1	807
0	326

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes421.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.2s	2553×	body	1280	valid
1.9s	8056×	body	80	valid
1.7s	2104×	body	640	valid
959.0ms	1018×	body	320	valid
171.0ms	508×	body	160	valid