Details

sample181.0ms

Algorithm

intervals

Results

61.0ms	67×	body	640	valid
45.0ms	73×	body	1280	valid
24.0ms	246×	body	80	valid
13.0ms	44×	body	320	valid
4.0ms	20×	body	160	valid

simplify106.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	126
5	111
4	95
3	76
2	49
1	25
0	12

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (sqrt 2.0) (cos th))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
93×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `associate-/r/`

Counts

3 → 158

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
5.0ms	(/ (sqrt 2.0) (cos th))
46.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series351.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ (* a1 a1) (* a2 a2))
69.0ms	(/ (sqrt 2.0) (cos th))
230.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify1.6s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	4529
1	680
0	250

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 2.0) (cos th))
0.4b	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (pow a2 2))))
5.1b	(sqrt (+ (* a1 a1) (pow a2 2)))
5.1b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
28×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`pow1` `sqrt-div`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`associate-/l/`

Counts

4 → 246

Calls

4 calls:

6.0ms	(/ (sqrt 2.0) (cos th))
51.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (pow a2 2))))
18.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
7.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (sqrt 2.0) (cos th))
169.0ms	(/ (/ (sqrt 2.0) (cos th)) (sqrt (+ (* a1 a1) (pow a2 2))))
67.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
59.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify1.2s

Counts

258 → 258

Iterations

Iter	Nodes
done	5000
2	2982
1	762
0	327

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 1) (/ (cos th) (sqrt 2.0))))
0.6b	(/ (sqrt 1) (/ (cos th) (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

1647×	`times-frac`
786×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
624×	`sqrt-prod`
165×	`associate-/r*`
38×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/l*`
10×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
4×	`pow1`
3×	`clear-num` `frac-2neg`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log`

Counts

4 → 795

Calls

4 calls:

11.0ms	(+ (* a1 a1) (* a2 a2))
57.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 1) (/ (cos th) (sqrt 2.0))))
13.0ms	(/ (sqrt 1) (/ (cos th) (sqrt 2.0)))
9.0ms	(/ (cos th) (sqrt 2.0))

series430.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (* a1 a1) (* a2 a2))
224.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 1) (/ (cos th) (sqrt 2.0))))
72.0ms	(/ (sqrt 1) (/ (cos th) (sqrt 2.0)))
80.0ms	(/ (cos th) (sqrt 2.0))

simplify1.6s

Counts

807 → 807

Iterations

Iter	Nodes
done	5001
1	2705
0	897

prune2.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ (* a1 a1) (pow a2 2)) 1) (cos th))
0.5b	(/ (* (/ (+ (* a1 a1) (pow a2 2)) 1) (cos th)) (/ (sqrt 1) (/ 1 (sqrt 2.0))))
1.0b	(/ 1 (sqrt 2.0))
1.0b	(/ (sqrt 1) (/ 1 (sqrt 2.0)))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

904×	`times-frac`
417×	`add-sqr-sqrt`
411×	`*-un-lft-identity`
410×	`add-cube-cbrt`
384×	`sqrt-prod`
165×	`associate-/r*`
104×	`add-exp-log`
64×	`div-exp`
52×	`add-cbrt-cube`
26×	`cbrt-undiv`
25×	`div-inv`
18×	`prod-exp`
13×	`associate-l`
12×	`1-exp`
10×	`associate-/l*`
8×	`pow1` `cbrt-unprod`
6×	`rec-exp`
4×	`associate-/r/` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-flip` `unswap-sqr`
2×	`associate-*l/`
1×	`sqrt-pow1` `pow1/2` `pow-prod-down` `*-commutative` `inv-pow` `associate-/l/`

Counts

4 → 572

Calls

4 calls:

49.0ms	(* (/ (+ (* a1 a1) (pow a2 2)) 1) (cos th))
74.0ms	(/ (* (/ (+ (* a1 a1) (pow a2 2)) 1) (cos th)) (/ (sqrt 1) (/ 1 (sqrt 2.0))))
11.0ms	(/ 1 (sqrt 2.0))
27.0ms	(/ (sqrt 1) (/ 1 (sqrt 2.0)))

series360.0ms

Counts

4 → 8

Calls

4 calls:

128.0ms	(* (/ (+ (* a1 a1) (pow a2 2)) 1) (cos th))
231.0ms	(/ (* (/ (+ (* a1 a1) (pow a2 2)) 1) (cos th)) (/ (sqrt 1) (/ 1 (sqrt 2.0))))
0.0ms	(/ 1 (sqrt 2.0))
0.0ms	(/ (sqrt 1) (/ 1 (sqrt 2.0)))

simplify1.5s

Counts

580 → 580

Iterations

Iter	Nodes
done	5002
1	2052
0	600

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes594.0ms

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
done	17
1	17
0	14

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.7s	2451×	body	1280	valid
1.1s	2027×	body	640	valid
870.0ms	8056×	body	80	valid
374.0ms	997×	body	320	valid
199.0ms	526×	body	160	valid