Details

sample15.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
2.0ms	90×	body	80	nan

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 20.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) y)
19.3b	(sqrt (+ (* x x) y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

3.0ms	(+ (* x x) y)
4.0ms	(sqrt (+ (* x x) y))

series64.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(+ (* x x) y)
40.0ms	(sqrt (+ (* x x) y))

simplify3.8s

Counts

32 → 32

Iterations

Useful iterations: 4 (864.0ms)

Iter	Nodes	Cost
0	59	319
1	141	294
2	450	258
3	1310	255
4	4666	254
done	5000	254

prune75.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* x x) y)))
0.5b	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
19.3b	(sqrt (+ (* x x) y))
19.3b	(sqrt (+ (* x x) y))

rewrite47.0ms

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:

5.0ms	(sqrt (sqrt (+ (* x x) y)))
28.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
4.0ms	(sqrt (+ (* x x) y))
4.0ms	(sqrt (+ (* x x) y))

series198.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (sqrt (+ (* x x) y)))
45.0ms	(* (sqrt (sqrt (+ (* x x) y))) (sqrt (sqrt (+ (* x x) y))))
39.0ms	(sqrt (+ (* x x) y))
45.0ms	(sqrt (+ (* x x) y))

simplify742.0ms

Counts

146 → 146

Iterations

Useful iterations: done (738.0ms)

Iter	Nodes	Cost
0	138	2475
1	267	1584
2	1023	1419
done	5000	1410

prune253.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fabs (cbrt (+ (* x x) y)))) (sqrt (sqrt (+ (* x x) y))))
19.3b	(sqrt (+ (* x x) y))
20.0b	(cbrt (+ (* x x) y))
20.0b	(cbrt (+ (* x x) y))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `associate-r`
6×	`add-exp-log` `cbrt-prod` `sqrt-div` `associate-l` `add-cbrt-cube` `unswap-sqr`
4×	`cbrt-div` `flip3-+` `flip-+` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`pow1/3` `associate-*r/`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 78

Calls

4 calls:

16.0ms	(* (sqrt (fabs (cbrt (+ (* x x) y)))) (sqrt (sqrt (+ (* x x) y))))
4.0ms	(sqrt (+ (* x x) y))
2.0ms	(cbrt (+ (* x x) y))
3.0ms	(cbrt (+ (* x x) y))

series297.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (sqrt (fabs (cbrt (+ (* x x) y)))) (sqrt (sqrt (+ (* x x) y))))
45.0ms	(sqrt (+ (* x x) y))
80.0ms	(cbrt (+ (* x x) y))
77.0ms	(cbrt (+ (* x x) y))

simplify1.9s

Counts

90 → 90

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	136	1441
1	282	1336
2	897	1227
3	3172	1209
done	5000	1208

prune308.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes167.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.3b

bsearch54.0ms

Steps

Iters	Range		Point
9	4.342265995353652e+77	8.721286125398812e+82	1.2922566123944575e+80
9	-1.1045029026290381e+161	-1.4102566258715918e+152	-1.3778733035656446e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample362.0ms

Algorithm

intervals

Results

149.0ms	8000×	body	80	valid
46.0ms	2570×	body	80	nan