Details

sample153.0ms

Algorithm

intervals

Results

43.0ms	66×	body	1280	valid
33.0ms	63×	body	640	valid
24.0ms	236×	body	80	valid
14.0ms	43×	body	320	valid
5.0ms	21×	body	160	valid

simplify132.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

53.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
68.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
22.0ms	(/ (cos th) (sqrt 2.0))
68.0ms	(/ (cos th) (sqrt 2.0))

series479.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
168.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
69.0ms	(/ (cos th) (sqrt 2.0))
81.0ms	(/ (cos th) (sqrt 2.0))

simplify925.0ms

Counts: 180 → 180

prune747.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 744

Calls

4 calls:

197.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
28.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
35.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
11.0ms	(/ (cos th) (sqrt 2.0))

series531.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
152.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
108.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
78.0ms	(/ (cos th) (sqrt 2.0))

simplify1.0s

Counts: 756 → 756

prune3.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

867×	`sqrt-prod`
750×	`times-frac`
403×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
102×	`cbrt-prod`
34×	`associate-/l*`
21×	`associate-/r*`
17×	`add-exp-log`
15×	`div-inv`
11×	`sqrt-pow1` `add-cbrt-cube`
8×	`pow1` `div-exp`
7×	`pow-flip`
4×	`cbrt-undiv` `pow1/3` `add-log-exp`
3×	`pow1/2`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `pow-div`
1×	`associate-/l/` `inv-pow`

Counts

4 → 515

Calls

4 calls:

2.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)
16.0ms	(/ 1 (sqrt (sqrt 2.0)))
39.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

simplify765.0ms

Counts: 519 → 519

prune3.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

1188×	`sqrt-prod`
1152×	`times-frac`
620×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
68×	`associate-/l*`
36×	`associate-/r*`
24×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 770

Calls

4 calls:

12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
21.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
31.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
140.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
83.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
105.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.3s

Counts: 782 → 782

prune2.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes308.0ms

Accuracy

1.6% (0.4b remaining)

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

bsearch0.0ms

simplify1.2s

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.0s	2492×	body	1280	valid
1.7s	2043×	body	640	valid
1.1s	7881×	body	80	valid
367.0ms	1066×	body	320	valid
151.0ms	511×	body	160	valid