Details

sample136.0ms

Algorithm

intervals

Results

39.0ms	286×	body	80	valid
34.0ms	77×	body	1280	valid
25.0ms	76×	body	640	valid
8.0ms	38×	body	320	valid
2.0ms	17×	body	160	valid

simplify138.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.8b	(/ (cos th) (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite157.0ms

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)) (* a2 a2))
76.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
20.0ms	(/ (cos th) (sqrt 2.0))
20.0ms	(/ (cos th) (sqrt 2.0))

series529.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
197.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
80.0ms	(/ (cos th) (sqrt 2.0))
81.0ms	(/ (cos th) (sqrt 2.0))

simplify884.0ms

Counts: 180 → 180

prune774.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite355.0ms

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:

160.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
54.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
36.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
22.0ms	(/ (cos th) (sqrt 2.0))

series503.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
78.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
168.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
89.0ms	(/ (cos th) (sqrt 2.0))

simplify1.1s

Counts: 756 → 756

prune3.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))

rewrite227.0ms

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:

59.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
29.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
23.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
23.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
109.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
165.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
168.0ms	(/ (cos th) (sqrt (sqrt 2.0)))

simplify1.3s

Counts: 782 → 782

prune3.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite737.0ms

Algorithm

rewrite-expression-head

Rules

2070×	`sqrt-prod`
1711×	`times-frac`
1318×	`add-sqr-sqrt`
772×	`*-un-lft-identity`
712×	`add-cube-cbrt`
376×	`associate-r`
145×	`unswap-sqr`
50×	`add-exp-log`
40×	`associate-l`
37×	`associate-/l*`
34×	`add-cbrt-cube`
27×	`associate-/r*` `div-inv`
23×	`div-exp`
14×	`cbrt-undiv`
10×	`prod-exp`
9×	`pow1`
6×	`cbrt-unprod`
5×	`pow-flip`
4×	`sqrt-pow1` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
2×	`pow1/2`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 1033

Calls

4 calls:

37.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
517.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
30.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
19.0ms	(/ 1 (sqrt (sqrt 2.0)))

series338.0ms

Counts

4 → 10

Calls

4 calls:

97.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
93.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
147.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify1.7s

Counts: 1043 → 1043

prune5.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes585.0ms

Accuracy

-11.8% (0.5b remaining)

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

bsearch0.0ms

simplify602.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	2606×	body	1280	valid
1.4s	8026×	body	80	valid
998.0ms	2070×	body	640	valid
427.0ms	1022×	body	320	valid
106.0ms	514×	body	160	valid