Details

sample196.0ms

Algorithm

intervals

Results

64.0ms	82×	body	1280	valid
38.0ms	48×	body	320	valid
38.0ms	66×	body	640	valid
31.0ms	240×	body	80	valid
6.0ms	23×	body	160	valid

simplify130.0ms

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize46.0ms

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))

rewrite97.0ms

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:

23.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
35.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series446.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
165.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
82.0ms	(/ (cos th) (sqrt 2))
80.0ms	(/ (cos th) (sqrt 2))

simplify1.2s

Counts

192 → 192

Iterations

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

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite83.0ms

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:

36.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
14.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms	(/ (cos th) (sqrt (sqrt 2)))
12.0ms	(/ (cos th) (sqrt 2))

series421.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
76.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
125.0ms	(/ (cos th) (sqrt (sqrt 2)))
62.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

493 → 493

Iterations

Iter	Nodes
done	2001
2	2001
1	1148
0	488

prune7.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.6b	(/ 1 (/ (sqrt (sqrt 2)) (/ (cos th) (sqrt (sqrt 2)))))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

3005×	`times-frac`
2146×	`sqrt-prod`
1404×	`add-sqr-sqrt`
1399×	`*-un-lft-identity` `add-cube-cbrt`
299×	`associate-/r*`
44×	`div-inv`
41×	`add-exp-log`
29×	`add-cbrt-cube`
22×	`associate-l`
19×	`div-exp`
10×	`pow1` `cbrt-undiv`
9×	`associate-/l*`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1311

Calls

4 calls:

44.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
14.0ms	(/ 1 (/ (sqrt (sqrt 2)) (/ (cos th) (sqrt (sqrt 2)))))
9.0ms	(/ (cos th) (sqrt (sqrt 2)))
13.0ms	(/ (cos th) (sqrt 2))

series525.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
107.0ms	(/ 1 (/ (sqrt (sqrt 2)) (/ (cos th) (sqrt (sqrt 2)))))
173.0ms	(/ (cos th) (sqrt (sqrt 2)))
100.0ms	(/ (cos th) (sqrt 2))

simplify2.1s

Counts

1323 → 1323

Iterations

Iter	Nodes
done	2001
1	2001
0	1315

prune23.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (cos th) (sqrt 2)) a2)
0.6b	(/ 1 (/ (sqrt (sqrt 2)) (/ (cos th) (sqrt (sqrt 2)))))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

3005×	`times-frac`
2146×	`sqrt-prod`
1408×	`add-sqr-sqrt`
1400×	`*-un-lft-identity` `add-cube-cbrt`
299×	`associate-/r*`
44×	`div-inv`
34×	`add-exp-log`
22×	`add-cbrt-cube` `associate-l`
18×	`div-exp`
9×	`cbrt-undiv` `associate-/l*`
7×	`pow1`
5×	`associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-r` `unswap-sqr`
2×	`prod-exp` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1308

Calls

4 calls:

31.0ms	(* (/ (cos th) (sqrt 2)) a2)
28.0ms	(/ 1 (/ (sqrt (sqrt 2)) (/ (cos th) (sqrt (sqrt 2)))))
11.0ms	(/ (cos th) (sqrt (sqrt 2)))
9.0ms	(/ (cos th) (sqrt 2))

series404.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (/ (cos th) (sqrt 2)) a2)
77.0ms	(/ 1 (/ (sqrt (sqrt 2)) (/ (cos th) (sqrt (sqrt 2)))))
142.0ms	(/ (cos th) (sqrt (sqrt 2)))
68.0ms	(/ (cos th) (sqrt 2))

simplify2.2s

Counts

1320 → 1320

Iterations

Iter	Nodes
done	2001
1	2001
0	1309

prune22.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes771.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample8.4s

Algorithm

intervals

Results

3.4s	2567×	body	1280	valid
1.8s	2034×	body	640	valid
1.5s	8063×	body	80	valid
1.1s	1071×	body	320	valid
178.0ms	528×	body	160	valid