Details

sample49.0ms

Algorithm

intervals

Results

27.0ms

256×

body

valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	29
3	29
2	24
1	14
0	9

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize25.0ms

Local error

Found 1 expressions with local error:

35.6b

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

rewrite5.0ms

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:

5.0ms

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

series282.0ms

Counts

1 → 3

Calls

1 calls:

282.0ms

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

simplify10.3s

Counts

18 → 18

Iterations

Iter	Nodes
done	5025
10	4124
9	1149
8	452
7	281
6	226
5	197
4	138
3	81
2	51
1	38
0	26

prune222.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.8b

localize36.0ms

Local error

Found 3 expressions with local error:

0.5b	(* (sqrt (sqrt (fma y y (fma z z (* x x))))) (sqrt (sqrt (fma y y (fma z z (* x x))))))
35.6b	(sqrt (fma y y (fma z z (* x x))))
35.6b	(sqrt (fma y y (fma z z (* x x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
49×	`add-sqr-sqrt`
34×	`sqrt-pow1`
28×	`pow1`
18×	`pow1/2`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`swap-sqr`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
5×	`add-exp-log` `pow-prod-down` `pow-sqr` `add-cbrt-cube`
3×	`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`

Counts

3 → 107

Calls

3 calls:

47.0ms	(* (sqrt (sqrt (fma y y (fma z z (* x x))))) (sqrt (sqrt (fma y y (fma z z (* x x))))))
3.0ms	(sqrt (fma y y (fma z z (* x x))))
3.0ms	(sqrt (fma y y (fma z z (* x x))))

series854.0ms

Counts

3 → 9

Calls

3 calls:

298.0ms	(* (sqrt (sqrt (fma y y (fma z z (* x x))))) (sqrt (sqrt (fma y y (fma z z (* x x))))))
284.0ms	(sqrt (fma y y (fma z z (* x x))))
272.0ms	(sqrt (fma y y (fma z z (* x x))))

simplify5.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5002
4	2356
3	647
2	279
1	155
0	86

prune665.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.8b

localize98.0ms

Local error

Found 4 expressions with local error:

35.6b	(sqrt (fma y y (fma z z (* x x))))
36.9b	(cbrt (fma y y (fma z z (* x x))))
36.9b	(cbrt (fma y y (fma z z (* x x))))
36.9b	(cbrt (fma y y (fma z z (* x x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(sqrt (fma y y (fma z z (* x x))))
2.0ms	(cbrt (fma y y (fma z z (* x x))))
2.0ms	(cbrt (fma y y (fma z z (* x x))))
2.0ms	(cbrt (fma y y (fma z z (* x x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

310.0ms	(sqrt (fma y y (fma z z (* x x))))
276.0ms	(cbrt (fma y y (fma z z (* x x))))
285.0ms	(cbrt (fma y y (fma z z (* x x))))
300.0ms	(cbrt (fma y y (fma z z (* x x))))

simplify4.4s

Counts

66 → 66

Iterations

Iter	Nodes
done	5099
4	3136
3	861
2	262
1	104
0	55

prune947.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.8b

localize104.0ms

Local error

Found 4 expressions with local error:

35.6b	(sqrt (fma y y (fma z z (* x x))))
36.9b	(cbrt (fma y y (fma z z (* x x))))
36.9b	(cbrt (fma y y (fma z z (* x x))))
36.9b	(cbrt (fma y y (fma z z (* x x))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(sqrt (fma y y (fma z z (* x x))))
2.0ms	(cbrt (fma y y (fma z z (* x x))))
2.0ms	(cbrt (fma y y (fma z z (* x x))))
2.0ms	(cbrt (fma y y (fma z z (* x x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

276.0ms	(sqrt (fma y y (fma z z (* x x))))
287.0ms	(cbrt (fma y y (fma z z (* x x))))
308.0ms	(cbrt (fma y y (fma z z (* x x))))
294.0ms	(cbrt (fma y y (fma z z (* x x))))

simplify4.5s

Counts

66 → 66

Iterations

Iter	Nodes
done	5099
4	3136
3	861
2	262
1	104
0	55

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 20.8b

regimes688.0ms

Accuracy

58.9% (8.1b remaining)

Error of 26.1b against oracle of 18.1b and baseline of 37.7b

bsearch269.0ms

Steps

Iters	Range		Point
10	3.858611127710002e+126	1.6100917271418707e+137	1.5619765056270288e+137
6	4.0479140857407816e-272	3.4117062808087914e-271	5.255127935317791e-272
8	-3.698686403717241e-255	-1.3491470958722732e-258	-8.594175512162318e-256
6	-1.175192332246113e+148	-2.921356713214837e+147	-6.210791644306185e+147

simplify5.0ms

Iterations

Iter	Nodes
done	20
0	20

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.5s

8000×

body

valid