Details

sample156.0ms

Algorithm

intervals

Results

50.0ms	72×	body	640	valid
41.0ms	81×	body	1280	valid
22.0ms	271×	body	80	valid
9.0ms	38×	body	320	valid
3.0ms	15×	body	160	valid

simplify154.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

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)))

rewrite58.0ms

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:

7.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(/ (sqrt 2.0) (cos th))
39.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

series336.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* a1 a1) (* a2 a2))
74.0ms	(/ (sqrt 2.0) (cos th))
222.0ms	(/ (+ (* a1 a1) (* a2 a2)) (/ (sqrt 2.0) (cos th)))

simplify1.7s

Counts

167 → 167

Iterations

Iter	Nodes
done	5000
2	4529
1	680
0	250

prune991.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt 2.0)) (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)))
0.5b	(/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt 2.0))
5.6b	(sqrt (+ (* a1 a1) (pow a2 2)))
5.6b	(sqrt (+ (* a1 a1) (pow a2 2)))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
72×	`times-frac`
61×	`add-sqr-sqrt`
59×	`*-un-lft-identity` `add-cube-cbrt`
40×	`associate-l`
18×	`add-cbrt-cube` `add-exp-log`
11×	`pow1`
10×	`sqrt-div`
6×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `pow-prod-down`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `div-inv` `associate-/l/`
1×	`sqrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative`

Counts

4 → 157

Calls

4 calls:

135.0ms	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt 2.0)) (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)))
47.0ms	(/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt 2.0))
23.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
25.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt 2.0)) (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)))
153.0ms	(/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt 2.0))
74.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
65.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))

simplify1.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	2074
1	455
0	178

prune991.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* a1 a1) (pow a2 2))) (/ (sqrt (sqrt 2.0)) (cos th)))
0.4b	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt (sqrt 2.0))) (/ (sqrt (+ (* a1 a1) (pow a2 2))) (/ (sqrt (sqrt 2.0)) (cos th))))
5.6b	(sqrt (+ (* a1 a1) (pow a2 2)))
5.6b	(sqrt (+ (* a1 a1) (pow a2 2)))

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

929×	`times-frac`
778×	`sqrt-prod`
697×	`add-sqr-sqrt`
417×	`*-un-lft-identity` `add-cube-cbrt`
191×	`associate-r`
63×	`unswap-sqr`
58×	`associate-l`
31×	`associate-/r*`
30×	`add-cbrt-cube` `add-exp-log`
16×	`div-inv`
12×	`cbrt-undiv` `div-exp`
8×	`pow1`
6×	`sqrt-div` `prod-exp` `cbrt-unprod` `associate-/l*`
4×	`add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 606

Calls

4 calls:

40.0ms	(/ (sqrt (+ (* a1 a1) (pow a2 2))) (/ (sqrt (sqrt 2.0)) (cos th)))
354.0ms	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt (sqrt 2.0))) (/ (sqrt (+ (* a1 a1) (pow a2 2))) (/ (sqrt (sqrt 2.0)) (cos th))))
13.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
24.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(/ (sqrt (+ (* a1 a1) (pow a2 2))) (/ (sqrt (sqrt 2.0)) (cos th)))
253.0ms	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (sqrt (sqrt 2.0))) (/ (sqrt (+ (* a1 a1) (pow a2 2))) (/ (sqrt (sqrt 2.0)) (cos th))))
45.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
47.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))

simplify1.0s

Counts

618 → 618

Iterations

Iter	Nodes
done	5001
1	1964
0	565

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0)))
0.3b	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0))))
5.6b	(sqrt (+ (* a1 a1) (pow a2 2)))
5.6b	(sqrt (+ (* a1 a1) (pow a2 2)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
31×	`add-cbrt-cube`
27×	`add-sqr-sqrt`
26×	`times-frac`
19×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
18×	`cbrt-prod`
16×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r`
10×	`associate-l`
9×	`associate-/r*`
8×	`pow1`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`flip3-+` `associate-*l/` `flip-+` `div-inv` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `associate-/l*`

Counts

4 → 121

Calls

4 calls:

28.0ms	(/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0)))
115.0ms	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0))))
15.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
31.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))

series924.0ms

Counts

4 → 12

Calls

4 calls:

567.0ms	(/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0)))
265.0ms	(* (/ (sqrt (+ (* a1 a1) (pow a2 2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (* (sqrt (+ (* a1 a1) (pow a2 2))) (cos th)) (cbrt (sqrt 2.0))))
47.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))
45.0ms	(sqrt (+ (* a1 a1) (pow a2 2)))

simplify1.7s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	3670
1	564
0	194

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes569.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	14

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.6s	2617×	body	1280	valid
1.5s	8062×	body	80	valid
1.2s	2014×	body	640	valid
418.0ms	1043×	body	320	valid
110.0ms	547×	body	160	valid