Details

sample191.0ms

Algorithm

intervals

Results

65.0ms	91×	body	1280	valid
52.0ms	262×	body	80	valid
29.0ms	60×	body	640	valid
13.0ms	38×	body	320	valid
4.0ms	20×	body	160	valid

simplify143.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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))

rewrite119.0ms

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:

45.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
44.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series463.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
148.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
82.0ms	(/ (cos th) (sqrt 2))
66.0ms	(/ (cos th) (sqrt 2))

simplify1.7s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	1524
1	528
0	189

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite99.0ms

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))
19.0ms	(/ (cos th) (sqrt (sqrt 2)))
21.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms	(/ (cos th) (sqrt 2))

series479.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
147.0ms	(/ (cos th) (sqrt (sqrt 2)))
84.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
86.0ms	(/ (cos th) (sqrt 2))

simplify1.7s

Counts

493 → 493

Iterations

Iter	Nodes
done	5002
2	2744
1	1155
0	488

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 478

Calls

4 calls:

13.0ms	(* (/ (cos th) (sqrt 2)) a2)
15.0ms	(/ (cos th) (sqrt (sqrt 2)))
33.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
26.0ms	(/ (cos th) (sqrt 2))

series401.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (/ (cos th) (sqrt 2)) a2)
98.0ms	(/ (cos th) (sqrt (sqrt 2)))
89.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
78.0ms	(/ (cos th) (sqrt 2))

simplify1.8s

Counts

490 → 490

Iterations

Iter	Nodes
done	5029
2	2570
1	1092
0	482

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
0.5b	(/ a2 (sqrt 2))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite170.0ms

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:

77.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
10.0ms	(/ a2 (sqrt 2))
20.0ms	(/ (cos th) (sqrt (sqrt 2)))
31.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
95.0ms	(/ a2 (sqrt 2))
113.0ms	(/ (cos th) (sqrt (sqrt 2)))
93.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify3.0s

Counts

768 → 768

Iterations

Iter	Nodes
done	5007
2	4562
1	1650
0	589

prune3.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes352.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.8s	2537×	body	1280	valid
1.6s	2109×	body	640	valid
1.1s	8110×	body	80	valid
535.0ms	1084×	body	320	valid
209.0ms	503×	body	160	valid