Details

sample56.0ms

Algorithm

intervals

Results

15.0ms	229×	body	80	nan
14.0ms	256×	body	80	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ y z))
0.3b	(fma y z (* x (+ y z)))
19.5b	(sqrt (fma y z (* x (+ y z))))

rewrite22.0ms

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:

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

series192.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* x (+ y z))
30.0ms	(fma y z (* x (+ y z)))
124.0ms	(sqrt (fma y z (* x (+ y z))))

simplify1.3s

Counts

59 → 59

Iterations

Useful iterations: done (1.3s)

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

prune165.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma y z (* x (+ y z)))
0.5b	(* (sqrt (sqrt (fma y z (* x (+ y z))))) (sqrt (sqrt (fma y z (* x (+ y z))))))
19.5b	(sqrt (fma y z (* x (+ y z))))
19.5b	(sqrt (fma y z (* x (+ y z))))

rewrite30.0ms

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 y z (* x (+ y z)))
22.0ms	(* (sqrt (sqrt (fma y z (* x (+ y z))))) (sqrt (sqrt (fma y z (* x (+ y z))))))
1.0ms	(sqrt (fma y z (* x (+ y z))))
2.0ms	(sqrt (fma y z (* x (+ y z))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma y z (* x (+ y z)))
112.0ms	(* (sqrt (sqrt (fma y z (* x (+ y z))))) (sqrt (sqrt (fma y z (* x (+ y z))))))
112.0ms	(sqrt (fma y z (* x (+ y z))))
114.0ms	(sqrt (fma y z (* x (+ y z))))

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	110	2711
1	202	1644
2	486	1506
3	1583	1452
done	5000	1407

prune285.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
19.5b	(sqrt (fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z)))))

rewrite5.0ms

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:

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

series702.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt x)
193.0ms	(cbrt x)
185.0ms	(cbrt x)
131.0ms	(sqrt (fma y z (* (* (cbrt x) (cbrt x)) (* (cbrt x) (+ y z)))))

simplify2.2s

Counts

66 → 66

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	65	570
1	134	515
2	325	417
3	924	359
4	3121	356
done	5000	354

prune225.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 20.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(fma x (+ y z) (* y z))
0.8b	(fma x (+ y z) (* y z))
20.1b	(cbrt (fma x (+ y z) (* y z)))
20.1b	(cbrt (fma x (+ y z) (* y z)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

0.0ms	(fma x (+ y z) (* y z))
0.0ms	(fma x (+ y z) (* y z))
1.0ms	(cbrt (fma x (+ y z) (* y z)))
1.0ms	(cbrt (fma x (+ y z) (* y z)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(fma x (+ y z) (* y z))
26.0ms	(fma x (+ y z) (* y z))
247.0ms	(cbrt (fma x (+ y z) (* y z)))
251.0ms	(cbrt (fma x (+ y z) (* y z)))

simplify1.4s

Counts

58 → 58

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	55	718
1	112	694
2	230	624
3	653	614
4	2669	598
done	5001	594

prune211.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 20.5b

regimes108.0ms

Accuracy

0% (0.1b remaining)

Error of 19.9b against oracle of 19.8b and baseline of 19.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample954.0ms

Algorithm

intervals

Results

260.0ms	8000×	body	80	valid
242.0ms	7931×	body	80	nan