Details

sample14.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
1.0ms	90×	body	80	nan

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	7	5
done	7	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize4.0ms

Local error

Found 1 expressions with local error:

19.3b

(sqrt (fma x x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `sqrt-prod`
2×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
1×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt (fma x x y))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(sqrt (fma x x y))

simplify1.2s

Counts

18 → 18

Iterations

Useful iterations: 4 (283.0ms)

Iter	Nodes	Cost
0	37	145
1	75	127
2	188	120
3	552	118
4	1890	104
done	5000	104

prune44.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(hypot (sqrt y) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `hypot-udef` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(hypot (sqrt y) x)

series204.0ms

Counts

1 → 3

Calls

1 calls:

204.0ms

(hypot (sqrt y) x)

simplify12.1s

Counts

13 → 13

Iterations

Useful iterations: 5 (1.4s)

Iter	Nodes	Cost
0	29	104
1	57	97
2	132	80
3	457	79
4	1482	78
5	3177	75
6	4512	75
done	5000	75

prune34.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt y) x)
0.0b	(sqrt (hypot (sqrt y) x))
0.0b	(sqrt (hypot (sqrt y) x))
0.3b	(* (sqrt (hypot (sqrt y) x)) (sqrt (hypot (sqrt y) x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `hypot-udef` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

0.0ms	(hypot (sqrt y) x)
1.0ms	(sqrt (hypot (sqrt y) x))
1.0ms	(sqrt (hypot (sqrt y) x))
6.0ms	(* (sqrt (hypot (sqrt y) x)) (sqrt (hypot (sqrt y) x)))

series940.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(hypot (sqrt y) x)
266.0ms	(sqrt (hypot (sqrt y) x))
271.0ms	(sqrt (hypot (sqrt y) x))
204.0ms	(* (sqrt (hypot (sqrt y) x)) (sqrt (hypot (sqrt y) x)))

simplify490.0ms

Counts

103 → 103

Iterations

Useful iterations: done (488.0ms)

Iter	Nodes	Cost
0	114	1240
1	249	847
2	903	754
done	5000	738

prune193.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize2.0ms

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

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes63.0ms

Accuracy

98.1% (0.4b remaining)

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

bsearch48.0ms

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: 1 (1.0ms)

Iter	Nodes	Cost
0	16	23
1	19	21
2	21	21
done	21	21

end0.0ms

sample344.0ms

Algorithm

intervals

Results

138.0ms	8000×	body	80	valid
46.0ms	2570×	body	80	nan