Details

sample187.0ms

Algorithm

intervals

Results

83.0ms	77×	body	1280	valid
31.0ms	56×	body	640	valid
27.0ms	227×	body	80	valid
9.0ms	25×	body	320	valid
3.0ms	14×	body	160	valid

simplify116.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (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))

rewrite464.0ms

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:

32.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
394.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
11.0ms	(/ (cos th) (sqrt 2.0))
11.0ms	(/ (cos th) (sqrt 2.0))

series463.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
139.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
77.0ms	(/ (cos th) (sqrt 2.0))
93.0ms	(/ (cos th) (sqrt 2.0))

simplify742.0ms

Counts: 180 → 180

prune747.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (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))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 469

Calls

4 calls:

68.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
33.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
16.0ms	(/ (cos th) (sqrt 2.0))

series558.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
170.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
113.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
101.0ms	(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts: 481 → 481

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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)))

rewrite187.0ms

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)))
12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
30.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
132.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
75.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
70.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.4s

Counts: 782 → 782

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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	(* (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

5324×	`sqrt-prod`
4187×	`times-frac`
4082×	`add-sqr-sqrt`
1448×	`*-un-lft-identity`
1040×	`add-cube-cbrt`
629×	`unswap-sqr`
376×	`associate-r` `associate-l`
73×	`add-exp-log`
49×	`add-cbrt-cube`
39×	`div-inv`
38×	`div-exp`
37×	`associate-/l*`
27×	`associate-/r*`
23×	`cbrt-undiv`
15×	`prod-exp`
9×	`cbrt-unprod`
6×	`pow1`
4×	`add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/`

Counts

4 → 1853

Calls

4 calls:

12.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
17.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
28.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
2.4s	(* (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
126.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
78.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
105.0ms	(* (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))

simplify2.8s

Counts: 1865 → 1865

prune7.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes477.0ms

Accuracy

-12.2% (0.5b remaining)

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

bsearch0.0ms

simplify908.0ms

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.3s	2525×	body	1280	valid
1.6s	2049×	body	640	valid
1.1s	7986×	body	80	valid
374.0ms	1057×	body	320	valid
104.0ms	503×	body	160	valid