Details

sample187.0ms

Algorithm

intervals

Results

77.0ms	88×	body	1280	valid
36.0ms	73×	body	640	valid
30.0ms	258×	body	80	valid
11.0ms	30×	body	320	valid
2.0ms	11×	body	160	valid

simplify451.0ms

Counts

1 → 1

Iterations

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

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize156.0ms

Local error

Found 4 expressions with local error:

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

rewrite337.0ms

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:

118.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
132.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
42.0ms	(/ (cos th) (sqrt 2.0))
30.0ms	(/ (cos th) (sqrt 2.0))

series639.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
213.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
119.0ms	(/ (cos th) (sqrt 2.0))
99.0ms	(/ (cos th) (sqrt 2.0))

simplify4.0s

Counts

192 → 192

Iterations

Iter	Nodes
done	5000
2	1737
1	526
0	190

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize165.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 481

Calls

4 calls:

107.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
44.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
70.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
44.0ms	(/ (cos th) (sqrt 2.0))

series608.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
162.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
128.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
121.0ms	(/ (cos th) (sqrt 2.0))

simplify5.8s

Counts

493 → 493

Iterations

Iter	Nodes
done	5012
2	2844
1	1147
0	489

prune4.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize155.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.5b	(/ (sqrt 2.0) a1)
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite592.0ms

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`
40×	`associate-/l*`
34×	`add-cbrt-cube` `add-exp-log`
23×	`div-inv`
21×	`associate-/r*`
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:

265.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
14.0ms	(/ (sqrt 2.0) a1)
45.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
80.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
87.0ms	(/ (sqrt 2.0) a1)
151.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
91.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify4.3s

Counts

768 → 768

Iterations

Iter	Nodes
done	5000
1	1707
0	592

prune7.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize204.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (sqrt 2.0)) a1)
0.3b	(* (sqrt (sqrt 2.0)) (/ (sqrt (sqrt 2.0)) a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite339.0ms

Algorithm

rewrite-expression-head

Rules

687×	`sqrt-prod`
639×	`times-frac`
389×	`add-sqr-sqrt`
356×	`*-un-lft-identity` `add-cube-cbrt`
43×	`associate-/l*`
31×	`associate-r`
21×	`associate-/r*`
18×	`add-cbrt-cube` `add-exp-log`
14×	`div-inv`
12×	`unswap-sqr`
9×	`associate-l`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 514

Calls

4 calls:

33.0ms	(/ (sqrt (sqrt 2.0)) a1)
84.0ms	(* (sqrt (sqrt 2.0)) (/ (sqrt (sqrt 2.0)) a1))
36.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
63.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (sqrt (sqrt 2.0)) a1)
76.0ms	(* (sqrt (sqrt 2.0)) (/ (sqrt (sqrt 2.0)) a1))
179.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
107.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify7.6s

Counts

526 → 526

Iterations

Iter	Nodes
done	5000
2	3095
1	1227
0	508

prune4.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes2.0s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.3s	2574×	body	1280	valid
1.9s	2182×	body	640	valid
1.0s	8046×	body	80	valid
603.0ms	565×	body	160	valid
527.0ms	1051×	body	320	valid