Details

sample156.0ms

Algorithm

intervals

Results

46.0ms	78×	body	1280	valid
39.0ms	242×	body	80	valid
28.0ms	68×	body	640	valid
13.0ms	39×	body	320	valid
2.0ms	12×	body	160	valid

simplify155.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

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))
0.8b	(/ (cos th) (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite106.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 176

Calls

4 calls:

27.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
44.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
15.0ms	(/ (cos th) (sqrt 2.0))
11.0ms	(/ (cos th) (sqrt 2.0))

series476.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
130.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
86.0ms	(/ (cos th) (sqrt 2.0))
81.0ms	(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts

188 → 188

Iterations

Iter	Nodes
done	5002
2	1722
1	533
0	187

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (* a2 a2) (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (* a2 a2) (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

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×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 151

Calls

4 calls:

26.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2.0)))
34.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
9.0ms	(/ (* a2 a2) (sqrt 2.0))
11.0ms	(/ (cos th) (sqrt 2.0))

series487.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2.0)))
164.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
76.0ms	(/ (* a2 a2) (sqrt 2.0))
85.0ms	(/ (cos th) (sqrt 2.0))

simplify1.7s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	1955
1	578
0	210

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ a1 (/ (sqrt 2.0) a1)))
0.2b	(/ a1 (/ (sqrt 2.0) a1))
0.3b	(/ (* a2 a2) (sqrt 2.0))
0.5b	(/ (sqrt 2.0) a1)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

287×	`times-frac`
174×	`add-sqr-sqrt`
161×	`*-un-lft-identity` `add-cube-cbrt`
82×	`sqrt-prod`
71×	`associate-r`
31×	`associate-/r*`
25×	`add-cbrt-cube` `add-exp-log`
11×	`div-inv`
10×	`associate-/l*`
9×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`associate-/r/`
1×	`pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 274

Calls

4 calls:

67.0ms	(* (cos th) (/ a1 (/ (sqrt 2.0) a1)))
18.0ms	(/ a1 (/ (sqrt 2.0) a1))
18.0ms	(/ (* a2 a2) (sqrt 2.0))
5.0ms	(/ (sqrt 2.0) a1)

series461.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (cos th) (/ a1 (/ (sqrt 2.0) a1)))
93.0ms	(/ a1 (/ (sqrt 2.0) a1))
95.0ms	(/ (* a2 a2) (sqrt 2.0))
78.0ms	(/ (sqrt 2.0) a1)

simplify2.3s

Counts

286 → 286

Iterations

Iter	Nodes
done	5036
2	3661
1	961
0	342

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* (/ a1 (sqrt 2.0)) a1))
0.2b	(* (/ a1 (sqrt 2.0)) a1)
0.3b	(/ (* a2 a2) (sqrt 2.0))
0.4b	(/ a1 (sqrt 2.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
44×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
28×	`sqrt-prod`
25×	`add-cbrt-cube` `associate-l` `add-exp-log`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`associate-*r/`

Counts

4 → 137

Calls

4 calls:

49.0ms	(* (cos th) (* (/ a1 (sqrt 2.0)) a1))
21.0ms	(* (/ a1 (sqrt 2.0)) a1)
9.0ms	(/ (* a2 a2) (sqrt 2.0))
10.0ms	(/ a1 (sqrt 2.0))

series394.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (cos th) (* (/ a1 (sqrt 2.0)) a1))
73.0ms	(* (/ a1 (sqrt 2.0)) a1)
88.0ms	(/ (* a2 a2) (sqrt 2.0))
79.0ms	(/ a1 (sqrt 2.0))

simplify1.5s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	1503
1	453
0	180

prune848.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes564.0ms

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	17
1	17
0	13

end0.0ms

sample5.6s

Algorithm

intervals

Results

1.7s	2508×	body	1280	valid
1.6s	2077×	body	640	valid
1.5s	7978×	body	80	valid
285.0ms	1041×	body	320	valid
102.0ms	518×	body	160	valid