Details

sample148.0ms

Algorithm

intervals

Results

64.0ms	81×	body	1280	valid
28.0ms	260×	body	80	valid
26.0ms	55×	body	640	valid
10.0ms	28×	body	320	valid
3.0ms	13×	body	160	valid

simplify136.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	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: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

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:

41.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
26.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
9.0ms	(/ (cos th) (sqrt 2))
13.0ms	(/ (cos th) (sqrt 2))

series455.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
149.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
77.0ms	(/ (cos th) (sqrt 2))
105.0ms	(/ (cos th) (sqrt 2))

simplify890.0ms

Counts

184 → 184

Iterations

Iter	Nodes
done	2000
2	1563
1	533
0	183

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (* a2 a2) (sqrt 2)))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(/ (* a2 a2) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
51×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 147

Calls

4 calls:

27.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
22.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
15.0ms	(/ (* a2 a2) (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series514.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
123.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
118.0ms	(/ (* a2 a2) (sqrt 2))
83.0ms	(/ (cos th) (sqrt 2))

simplify972.0ms

Counts

159 → 159

Iterations

Iter	Nodes
done	2000
2	1971
1	563
0	205

prune844.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
0.3b	(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
0.3b	(/ (* a2 a2) (sqrt 2))
0.6b	(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

201×	`times-frac`
107×	`add-sqr-sqrt`
94×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
67×	`associate-l`
55×	`add-exp-log`
53×	`sqrt-prod`
38×	`add-cbrt-cube`
23×	`div-inv`
19×	`cbrt-undiv` `div-exp`
17×	`prod-exp` `cbrt-unprod`
16×	`associate-/r*`
11×	`associate-/l*`
9×	`pow1`
7×	`unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 250

Calls

4 calls:

24.0ms	(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
95.0ms	(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
19.0ms	(/ (* a2 a2) (sqrt 2))
24.0ms	(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

series796.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2)))
162.0ms	(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt 2))) (* a1 a1))
95.0ms	(/ (* a2 a2) (sqrt 2))
428.0ms	(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

simplify647.0ms

Counts

262 → 262

Iterations

Iter	Nodes
done	2000
1	940
0	328

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2)))) (* a1 a1)))
0.2b	(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2)))) (* a1 a1))
0.3b	(/ (* a2 a2) (sqrt 2))
0.6b	(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

385×	`add-exp-log`
204×	`prod-exp`
144×	`times-frac`
139×	`add-cbrt-cube`
120×	`div-exp`
115×	`cbrt-prod`
95×	`associate-l`
94×	`cbrt-unprod`
82×	`add-sqr-sqrt`
65×	`*-un-lft-identity` `add-cube-cbrt`
62×	`cbrt-undiv`
29×	`sqrt-prod`
18×	`pow1` `rec-exp` `1-exp`
16×	`div-inv`
9×	`pow-prod-down` `unswap-sqr`
7×	`associate-/r*`
4×	`associate-l/` `insert-posit16` `associate-/l` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 289

Calls

4 calls:

167.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2)))) (* a1 a1)))
83.0ms	(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2)))) (* a1 a1))
27.0ms	(/ (* a2 a2) (sqrt 2))
25.0ms	(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (/ 1 (* (cbrt (cbrt (sqrt 2))) (cbrt (cbrt (sqrt 2))))) (* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2)))) (* a1 a1)))
735.0ms	(* (/ (/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt 2)))) (* a1 a1))
96.0ms	(/ (* a2 a2) (sqrt 2))
441.0ms	(/ (cos th) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

simplify1.0s

Counts

301 → 301

Iterations

Iter	Nodes
done	2002
1	1224
0	413

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes474.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.6s	2512×	body	1280	valid
2.4s	2103×	body	640	valid
1.4s	7892×	body	80	valid
601.0ms	1035×	body	320	valid
204.0ms	536×	body	160	valid