Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	262×	body	80	nan
12.0ms	256×	body	80	valid

simplify87.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	11	14
1	22	12
2	44	11
3	63	11
4	67	11
5	68	11
done	68	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ y z))
1.3b	(fma y z (* x (+ y z)))
19.7b	(sqrt (fma y z (* x (+ y z))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`pow1` `add-cube-cbrt`
5×	`add-exp-log` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `sqrt-prod` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

20.0ms	(* x (+ y z))
0.0ms	(fma y z (* x (+ y z)))
2.0ms	(sqrt (fma y z (* x (+ y z))))

series231.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* x (+ y z))
37.0ms	(fma y z (* x (+ y z)))
151.0ms	(sqrt (fma y z (* x (+ y z))))

simplify2.0s

Counts

59 → 59

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	91	581
1	220	532
2	621	483
3	2012	479
done	5000	478

prune317.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
1.3b	(fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))))
19.7b	(sqrt (fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
1.0ms	(fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))))
4.0ms	(sqrt (fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z)))))

series885.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt x)
324.0ms	(cbrt x)
69.0ms	(fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z))))
200.0ms	(sqrt (fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z)))))

simplify1.9s

Counts

63 → 63

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	76	727
1	154	667
2	388	505
3	1238	420
done	5000	417

prune395.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma y z (* x (+ y z)))
1.3b	(fma y z (* x (+ y z)))
19.7b	(sqrt (fma y z (* x (+ y z))))
19.7b	(sqrt (fma y z (* x (+ y z))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

0.0ms	(fma y z (* x (+ y z)))
0.0ms	(fma y z (* x (+ y z)))
2.0ms	(sqrt (fma y z (* x (+ y z))))
2.0ms	(sqrt (fma y z (* x (+ y z))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma y z (* x (+ y z)))
42.0ms	(fma y z (* x (+ y z)))
187.0ms	(sqrt (fma y z (* x (+ y z))))
173.0ms	(sqrt (fma y z (* x (+ y z))))

simplify3.0s

Counts

62 → 62

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	51	750
1	106	674
2	243	616
3	749	608
4	3241	602
done	5000	602

prune460.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ y z))
0.6b	(* (cbrt (+ y z)) (cbrt (+ y z)))
1.3b	(fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z))))
19.7b	(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`cbrt-prod`
23×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `cbrt-div`
12×	`pow1`
9×	`swap-sqr`
7×	`flip3-+` `pow1/3` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 96

Calls

4 calls:

19.0ms	(cbrt (+ y z))
64.0ms	(* (cbrt (+ y z)) (cbrt (+ y z)))
0.0ms	(fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z))))
2.0ms	(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

series839.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt (+ y z))
281.0ms	(* (cbrt (+ y z)) (cbrt (+ y z)))
71.0ms	(fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z))))
219.0ms	(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

simplify2.6s

Counts

108 → 108

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	166	1679
1	356	1511
2	884	1207
3	2356	1063
done	5000	1052

prune517.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 20.6b

regimes336.0ms

Accuracy

0% (0.3b remaining)

Error of 20.1b against oracle of 19.8b and baseline of 20.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11
done	12	11

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
686.0ms	8029×	body	80	nan