Details

sample17.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	9	12
1	14	11
2	24	10
3	30	10
done	30	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma z z (fma x x (* y y)))
33.0b	(sqrt (fma z z (fma x x (* y y))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 25

Calls

2 calls:

0.0ms	(fma z z (fma x x (* y y)))
1.0ms	(sqrt (fma z z (fma x x (* y y))))

series191.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(fma z z (fma x x (* y y)))
138.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify953.0ms

Counts

31 → 31

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	38	363
1	59	333
2	117	304
3	373	304
4	1905	304
done	5001	304

prune102.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z z (fma x x (* y y)))
0.5b	(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
33.0b	(sqrt (fma z z (fma x x (* y y))))
33.0b	(sqrt (fma z z (fma x x (* y y))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma z z (fma x x (* y y)))
12.0ms	(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
1.0ms	(sqrt (fma z z (fma x x (* y y))))
1.0ms	(sqrt (fma z z (fma x x (* y y))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma z z (fma x x (* y y)))
131.0ms	(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
130.0ms	(sqrt (fma z z (fma x x (* y y))))
139.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify1.0s

Counts

129 → 129

Iterations

Useful iterations: 3 (247.0ms)

Iter	Nodes	Cost
0	97	2809
1	156	1683
2	358	1546
3	1334	1499
done	5000	1499

prune288.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 18.9b

localize1.0ms

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

prune3.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 18.9b

localize1.0ms

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: 18.9b

regimes145.0ms

Accuracy

63% (7.0b remaining)

Error of 25.7b against oracle of 18.7b and baseline of 37.7b

bsearch79.0ms

Steps

Iters	Range		Point
8	1.6412830483463572e+100	2.8581932616512657e+104	2.8186674257036996e+104
11	-4.586395826824086e+114	-6.177616083621757e+80	-4.055402228526117e+113

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
done	14	21

end0.0ms

sample412.0ms

Algorithm

intervals

Results

244.0ms

8000×

body

valid