Details

sample273.0ms

Algorithm

intervals

Results

140.0ms	89×	body	1280	valid
51.0ms	69×	body	640	valid
42.0ms	248×	body	80	valid
12.0ms	23×	body	320	valid
7.0ms	20×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.2b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite86.0ms

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×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

24.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
28.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
14.0ms	(/ (cos th) (sqrt 2))
17.0ms	(/ (cos th) (sqrt 2))

series401.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
126.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
72.0ms	(/ (cos th) (sqrt 2))
74.0ms	(/ (cos th) (sqrt 2))

simplify3.0s

Counts

184 → 184

Iterations

Iter	Nodes
3	7244
2	1771
1	523
0	183

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite137.0ms

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×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 748

Calls

4 calls:

59.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
10.0ms	(/ (cos th) (sqrt (sqrt 2)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
10.0ms	(/ (cos th) (sqrt 2))

series537.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
156.0ms	(/ (cos th) (sqrt (sqrt 2)))
91.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
118.0ms	(/ (cos th) (sqrt 2))

simplify2.1s

Counts

760 → 760

Iterations

Iter	Nodes
2	5002
1	1615
0	563

prune12.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

1188×	`sqrt-prod`
1152×	`times-frac`
620×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
68×	`associate-/l*`
36×	`associate-/r*`
24×	`div-inv`
18×	`add-cbrt-cube` `add-exp-log`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 774

Calls

4 calls:

16.0ms	(/ (cos th) (sqrt (sqrt 2)))
11.0ms	(/ (cos th) (sqrt (sqrt 2)))
21.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
27.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (cos th) (sqrt (sqrt 2)))
168.0ms	(/ (cos th) (sqrt (sqrt 2)))
78.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
68.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify3.6s

Counts

786 → 786

Iterations

Iter	Nodes
3	9890
2	1909
1	866
0	394

prune12.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
1.0b	(/ 1 (sqrt (sqrt 2)))

rewrite182.0ms

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` `insert-posit16` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
2×	`pow1/2`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `inv-pow` `associate-/l/`

Counts

4 → 1037

Calls

4 calls:

11.0ms	(/ (cos th) (sqrt (sqrt 2)))
75.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
24.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
7.0ms	(/ 1 (sqrt (sqrt 2)))

series341.0ms

Counts

4 → 10

Calls

4 calls:

153.0ms	(/ (cos th) (sqrt (sqrt 2)))
99.0ms	(* (/ (cos th) (sqrt (sqrt (sqrt 2)))) (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt (sqrt 2)))))
88.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms	(/ 1 (sqrt (sqrt 2)))

simplify2.9s

Counts

1047 → 1047

Iterations

Iter	Nodes
1	3106
0	963

prune19.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes627.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.7s	2563×	body	1280	valid
1.8s	2080×	body	640	valid
1.4s	7943×	body	80	valid
1.0s	1057×	body	320	valid
200.0ms	569×	body	160	valid