Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
11.0ms	249×	body	80	nan

simplify65.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ y z))
0.5b	(fma y z (* x (+ y z)))
16.6b	(sqrt (fma y z (* x (+ y z))))

rewrite33.0ms

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:

29.0ms	(* x (+ y z))
0.0ms	(fma y z (* x (+ y z)))
2.0ms	(sqrt (fma y z (* x (+ y z))))

series300.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* x (+ y z))
52.0ms	(fma y z (* x (+ y z)))
211.0ms	(sqrt (fma y z (* x (+ y z))))

simplify1.9s

Counts

59 → 59

Iterations

Useful iterations: done (1.9s)

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

prune237.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* y (+ z x))
0.0b	(fma x z (* y (+ z x)))
16.6b	(sqrt (fma x z (* y (+ z x))))

rewrite39.0ms

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:

34.0ms	(* y (+ z x))
1.0ms	(fma x z (* y (+ z x)))
3.0ms	(sqrt (fma x z (* y (+ z x))))

series290.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* y (+ z x))
49.0ms	(fma x z (* y (+ z x)))
194.0ms	(sqrt (fma x z (* y (+ z x))))

simplify2.3s

Counts

59 → 59

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	89	581
1	214	532
2	635	483
3	2272	479
done	5000	476

prune272.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
16.6b	(sqrt (fma x z (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

rewrite6.0ms

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

series1.2s

Counts

4 → 12

Calls

4 calls:

354.0ms	(cbrt y)
310.0ms	(cbrt y)
348.0ms	(cbrt y)
221.0ms	(sqrt (fma x z (* (* (cbrt y) (cbrt y)) (* (cbrt y) (+ z x)))))

simplify3.4s

Counts

66 → 66

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	65	570
1	133	515
2	325	417
3	922	359
4	3132	356
done	5000	356

prune350.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ y z))
0.5b	(cbrt (+ y z))
0.5b	(cbrt (+ y z))
16.6b	(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `sqrt-prod` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 63

Calls

4 calls:

4.0ms	(cbrt (+ y z))
4.0ms	(cbrt (+ y z))
5.0ms	(cbrt (+ y z))
2.0ms	(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

series952.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt (+ y z))
237.0ms	(cbrt (+ y z))
240.0ms	(cbrt (+ y z))
226.0ms	(sqrt (fma y z (* (* x (* (cbrt (+ y z)) (cbrt (+ y z)))) (cbrt (+ y z)))))

simplify3.9s

Counts

75 → 75

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	95	942
1	213	858
2	467	690
3	1091	629
4	2732	620
done	5001	618

prune388.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 17.3b

regimes232.0ms

Accuracy

0% (0.2b remaining)

Error of 19.7b against oracle of 19.6b and baseline of 19.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.2s

Algorithm

intervals

Results

755.0ms	8000×	body	80	valid
644.0ms	7973×	body	80	nan