Details

sample247.0ms

Algorithm

intervals

Results

105.0ms	82×	body	1280	valid
49.0ms	63×	body	640	valid
44.0ms	247×	body	80	valid
21.0ms	36×	body	320	valid
6.0ms	14×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

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))

rewrite120.0ms

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:

43.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
49.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series496.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
155.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
88.0ms	(/ (cos th) (sqrt 2))
90.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

192 → 192

Iterations

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

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ a1 (sqrt 2)) a1)
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.5b	(/ a1 (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite64.0ms

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:

17.0ms	(* (/ a1 (sqrt 2)) a1)
21.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
6.0ms	(/ a1 (sqrt 2))
15.0ms	(/ (cos th) (sqrt 2))

series426.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ a1 (sqrt 2)) a1)
157.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
93.0ms	(/ a1 (sqrt 2))
89.0ms	(/ (cos th) (sqrt 2))

simplify1.5s

Counts

189 → 189

Iterations

Iter	Nodes
done	2016
3	2016
2	1683
1	546
0	219

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* (/ a1 (sqrt 2)) a1))
0.1b	(* (/ a1 (sqrt 2)) a1)
0.3b	(/ (* a2 a2) (sqrt 2))
0.5b	(/ a1 (sqrt 2))

rewrite87.0ms

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` `associate-l` `add-exp-log`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`associate-*r/`

Counts

4 → 141

Calls

4 calls:

27.0ms	(* (cos th) (* (/ a1 (sqrt 2)) a1))
30.0ms	(* (/ a1 (sqrt 2)) a1)
19.0ms	(/ (* a2 a2) (sqrt 2))
9.0ms	(/ a1 (sqrt 2))

series427.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (cos th) (* (/ a1 (sqrt 2)) a1))
96.0ms	(* (/ a1 (sqrt 2)) a1)
89.0ms	(/ (* a2 a2) (sqrt 2))
73.0ms	(/ a1 (sqrt 2))

simplify1.4s

Counts

153 → 153

Iterations

Iter	Nodes
done	2003
3	2003
2	1714
1	461
0	183

prune952.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

33.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
31.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
9.0ms	(/ (* a1 a1) (sqrt 2))
10.0ms	(/ (* a2 a2) (sqrt 2))

series568.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
167.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
98.0ms	(/ (* a1 a1) (sqrt 2))
114.0ms	(/ (* a2 a2) (sqrt 2))

simplify983.0ms

Counts

142 → 142

Iterations

Iter	Nodes
done	2000
2	2000
1	517
0	180

prune732.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes486.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample9.6s

Algorithm

intervals

Results

4.1s	2595×	body	1280	valid
1.9s	1996×	body	640	valid
1.8s	8122×	body	80	valid
706.0ms	1010×	body	320	valid
616.0ms	547×	body	160	valid