Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
2.0ms	90×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	6	6
done	6	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize5.0ms

Local error

Found 1 expressions with local error:

21.8b

(sqrt (+ (* x x) y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
1×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

10.0ms

(sqrt (+ (* x x) y))

series54.0ms

Counts

1 → 3

Calls

1 calls:

54.0ms

(sqrt (+ (* x x) y))

simplify3.7s

Counts

18 → 18

Iterations

Useful iterations: 4 (337.0ms)

Iter	Nodes	Cost
0	51	195
1	116	173
2	251	157
3	484	154
4	858	153
5	1588	153
6	3836	153
done	5001	153

prune61.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ (* x x) y)))
0.5b	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
21.8b	(sqrt (+ (* x x) y))
21.8b	(sqrt (+ (* x x) y))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ (* x x) y)))
64.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
15.0ms	(sqrt (+ (* x x) y))
11.0ms	(sqrt (+ (* x x) y))

series218.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (sqrt (+ (* x x) y)))
46.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
42.0ms	(sqrt (+ (* x x) y))
51.0ms	(sqrt (+ (* x x) y))

simplify4.1s

Counts

146 → 146

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	138	2475
1	262	1570
2	631	1419
3	1554	1383
4	4280	1351
done	5001	1337

prune323.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (/ y x) -1/2)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-l`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

18.0ms

(* (/ y x) -1/2)

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(* (/ y x) -1/2)

simplify6.2s

Counts

35 → 35

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	67	261
1	153	244
2	404	224
3	1033	224
4	2565	224
done	5001	224

prune91.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 1/2 (/ y x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 32

Calls

1 calls:

25.0ms

(* 1/2 (/ y x))

series28.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(* 1/2 (/ y x))

simplify6.2s

Counts

35 → 35

Iterations

Useful iterations: 3 (354.0ms)

Iter	Nodes	Cost
0	68	277
1	162	250
2	426	230
3	1067	229
4	2498	229
done	5000	229

prune117.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes248.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 21.1b

bsearch79.0ms

Steps

Iters	Range		Point
6	1.3691772692280127e+122	1.865416815092154e+123	1.4388934535207275e+123
10	-4.750953680063193e+156	-7.066707918776839e+146	-1.3349869326014939e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	28
1	22	28
done	22	28

end0.0ms

sample782.0ms

Algorithm

intervals

Results

349.0ms	8000×	body	80	valid
94.0ms	2684×	body	80	nan