Details

sample263.0ms

Algorithm

intervals

Results

109.0ms	82×	body	1280	valid
48.0ms	67×	body	640	valid
41.0ms	264×	body	80	valid
21.0ms	22×	body	160	valid
19.0ms	37×	body	320	valid

simplify142.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize40.0ms

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))

rewrite91.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 180

Calls

4 calls:

30.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
24.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
16.0ms	(/ (cos th) (sqrt 2))

series435.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
149.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
80.0ms	(/ (cos th) (sqrt 2))
75.0ms	(/ (cos th) (sqrt 2))

simplify1.1s

Counts

192 → 192

Iterations

Iter	Nodes
done	2003
3	2003
2	1524
1	528
0	189

prune895.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ a2 (sqrt 2)) a2)
0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.4b	(/ a2 (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
25×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`

Counts

4 → 177

Calls

4 calls:

28.0ms	(* (/ a2 (sqrt 2)) a2)
45.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms	(/ a2 (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series370.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ a2 (sqrt 2)) a2)
132.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
93.0ms	(/ a2 (sqrt 2))
58.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

189 → 189

Iterations

Iter	Nodes
done	2001
3	2001
2	1685
1	546
0	219

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ a2 (sqrt 2)) a2)
0.3b	(* (/ (cos th) (sqrt 2)) a1)
0.4b	(/ a2 (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
76×	`times-frac`
62×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
18×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
8×	`pow1`
6×	`associate-r` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 174

Calls

4 calls:

12.0ms	(* (/ a2 (sqrt 2)) a2)
18.0ms	(* (/ (cos th) (sqrt 2)) a1)
5.0ms	(/ a2 (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series471.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (/ a2 (sqrt 2)) a2)
175.0ms	(* (/ (cos th) (sqrt 2)) a1)
137.0ms	(/ a2 (sqrt 2))
65.0ms	(/ (cos th) (sqrt 2))

simplify1.2s

Counts

186 → 186

Iterations

Iter	Nodes
done	2002
3	2002
2	1555
1	492
0	214

prune937.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
0.4b	(/ a2 (sqrt 2))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 756

Calls

4 calls:

50.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
5.0ms	(/ a2 (sqrt 2))
10.0ms	(/ (cos th) (sqrt (sqrt 2)))
27.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
97.0ms	(/ a2 (sqrt 2))
140.0ms	(/ (cos th) (sqrt (sqrt 2)))
96.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify1.7s

Counts

768 → 768

Iterations

Iter	Nodes
done	2014
2	2014
1	1650
0	589

prune3.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end2.0ms

sample8.7s

Algorithm

intervals

Results

3.0s	2553×	body	1280	valid
2.0s	2104×	body	640	valid
2.0s	8056×	body	80	valid
1.1s	1018×	body	320	valid
224.0ms	508×	body	160	valid