Details

sample285.0ms

Algorithm

intervals

Results

102.0ms	104×	body	1280	valid
77.0ms	65×	body	640	valid
60.0ms	290×	body	80	valid
18.0ms	36×	body	320	valid
6.0ms	18×	body	160	valid

simplify102.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.5b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite90.0ms

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:

39.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
29.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series405.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
137.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
60.0ms	(/ (cos th) (sqrt 2))
74.0ms	(/ (cos th) (sqrt 2))

simplify4.2s

Counts

184 → 184

Iterations

Iter	Nodes
3	7109
2	1765
1	523
0	183

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2)) a1)
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
25×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`

Counts

4 → 169

Calls

4 calls:

33.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms	(* (/ (cos th) (sqrt 2)) a1)
16.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series479.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
149.0ms	(* (/ (cos th) (sqrt 2)) a1)
72.0ms	(/ (cos th) (sqrt 2))
84.0ms	(/ (cos th) (sqrt 2))

simplify3.6s

Counts

181 → 181

Iterations

Iter	Nodes
3	5111
2	1553
1	475
0	178

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) a1)
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite94.0ms

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×	`insert-posit16` `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 → 470

Calls

4 calls:

19.0ms	(* (/ (cos th) (sqrt 2)) a1)
17.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms	(/ (cos th) (sqrt (sqrt 2)))
18.0ms	(/ (cos th) (sqrt 2))

series824.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ (cos th) (sqrt 2)) a1)
90.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
531.0ms	(/ (cos th) (sqrt (sqrt 2)))
90.0ms	(/ (cos th) (sqrt 2))

simplify1.1s

Counts

482 → 482

Iterations

Iter	Nodes
2	2494
1	1069
0	475

prune3.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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:

15.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
15.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
19.0ms	(/ (cos th) (sqrt (sqrt 2)))
14.0ms	(/ (cos th) (sqrt (sqrt 2)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
106.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
125.0ms	(/ (cos th) (sqrt (sqrt 2)))
170.0ms	(/ (cos th) (sqrt (sqrt 2)))

simplify3.8s

Counts

786 → 786

Iterations

Iter	Nodes
3	8437
2	1841
1	855
0	394

prune5.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes491.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	23
1	23
0	19

end0.0ms

sample8.8s

Algorithm

intervals

Results

3.9s	2578×	body	1280	valid
1.9s	2062×	body	640	valid
1.7s	8121×	body	80	valid
569.0ms	1010×	body	320	valid
262.0ms	523×	body	160	valid