Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	9	12
1	14	11
2	24	10
3	31	10
done	31	10

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize10.0ms

Local error

Found 1 expressions with local error:

33.9b

(sqrt (fma z z (fma x x (* y y))))

rewrite2.0ms

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:

2.0ms

(sqrt (fma z z (fma x x (* y y))))

series147.0ms

Counts

1 → 3

Calls

1 calls:

147.0ms

(sqrt (fma z z (fma x x (* y y))))

simplify1.5s

Counts

18 → 18

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	26	207
1	38	180
2	52	172
3	85	172
4	144	172
5	239	172
6	312	172
7	490	172
8	1166	172
done	5000	172

prune89.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (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))))))
33.9b	(sqrt (fma z z (fma x x (* y y))))
33.9b	(sqrt (fma z z (fma x x (* y y))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
31×	`pow1`
20×	`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` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 128

Calls

4 calls:

4.0ms	(sqrt (sqrt (fma z z (fma x x (* y y)))))
45.0ms	(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
2.0ms	(sqrt (fma z z (fma x x (* y y))))
2.0ms	(sqrt (fma z z (fma x x (* y y))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(sqrt (sqrt (fma z z (fma x x (* y y)))))
158.0ms	(* (sqrt (sqrt (fma z z (fma x x (* y y))))) (sqrt (sqrt (fma z z (fma x x (* y y))))))
175.0ms	(sqrt (fma z z (fma x x (* y y))))
173.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify1.5s

Counts

140 → 140

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	103	2980
1	213	1821
2	1017	1681
done	5001	1644

prune435.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (fma z z (fma x x (* y y)))))
33.9b	(sqrt (fma z z (fma x x (* y y))))
33.9b	(sqrt (fma z z (fma x x (* y y))))
33.9b	(sqrt (fma z z (fma x x (* y y))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

2.0ms	(cbrt (sqrt (fma z z (fma x x (* y y)))))
2.0ms	(sqrt (fma z z (fma x x (* y y))))
2.0ms	(sqrt (fma z z (fma x x (* y y))))
2.0ms	(sqrt (fma z z (fma x x (* y y))))

series835.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(cbrt (sqrt (fma z z (fma x x (* y y)))))
212.0ms	(sqrt (fma z z (fma x x (* y y))))
223.0ms	(sqrt (fma z z (fma x x (* y y))))
197.0ms	(sqrt (fma z z (fma x x (* y y))))

simplify2.9s

Counts

73 → 73

Iterations

Useful iterations: 3 (188.0ms)

Iter	Nodes	Cost
0	60	952
1	109	852
2	260	801
3	936	794
4	4608	794
done	5000	794

prune491.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 17.5b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 17.5b

regimes208.0ms

Accuracy

62.3% (7.2b remaining)

Error of 25.3b against oracle of 18.1b and baseline of 37.2b

bsearch212.0ms

Steps

Iters	Range		Point
9	1.6747155146343206e+129	1.862783601279989e+135	1.516560416068031e+132
10	5.094640188406999e-256	1.1587112490597079e-238	7.775344849217465e-254
10	-4.6757947485079374e-293	-2.144586095365254e-308	-2.1998898291643586e-308
10	-1.9376722428958284e+123	-1.3239447562306907e+112	-3.0345443282093877e+120

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	40
done	20	40

end0.0ms

sample1.1s

Algorithm

intervals

Results

666.0ms

8000×

body

valid