Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
7.0ms	252×	body	80	nan

simplify50.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ y z))
0.3b	(fma y z (* x (+ y z)))
20.2b	(sqrt (fma y z (* x (+ y z))))

rewrite26.0ms

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:

23.0ms	(* x (+ y z))
0.0ms	(fma y z (* x (+ y z)))
2.0ms	(sqrt (fma y z (* x (+ y z))))

series181.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(* x (+ y z))
28.0ms	(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

prune193.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.2b

localize14.0ms

Local error

Found 4 expressions with local error:

18.1b	(cbrt (* x (+ y z)))
18.1b	(cbrt (* x (+ y z)))
18.1b	(cbrt (* x (+ y z)))
20.2b	(sqrt (fma y z (* (* (cbrt (* x (+ y z))) (cbrt (* x (+ y z)))) (cbrt (* x (+ y z))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

7.0ms	(cbrt (* x (+ y z)))
7.0ms	(cbrt (* x (+ y z)))
7.0ms	(cbrt (* x (+ y z)))
2.0ms	(sqrt (fma y z (* (* (cbrt (* x (+ y z))) (cbrt (* x (+ y z)))) (cbrt (* x (+ y z))))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (* x (+ y z)))
127.0ms	(cbrt (* x (+ y z)))
131.0ms	(cbrt (* x (+ y z)))
128.0ms	(sqrt (fma y z (* (* (cbrt (* x (+ y z))) (cbrt (* x (+ y z)))) (cbrt (* x (+ y z))))))

simplify2.9s

Counts

66 → 66

Iterations

Useful iterations: 5 (2.1s)

Iter	Nodes	Cost
0	91	975
1	212	901
2	460	654
3	1068	590
4	2206	563
5	4785	546
done	5000	546

prune290.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
18.1b	(cbrt (* x (+ y z)))
18.1b	(cbrt (* x (+ y z)))
20.2b	(sqrt (fma y z (* (* (cbrt (* x (+ y z))) (* (cbrt x) (cbrt (+ y z)))) (cbrt (* x (+ y z))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `cbrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `associate-*r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`flip3-+` `flip-+`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt x)
7.0ms	(cbrt (* x (+ y z)))
11.0ms	(cbrt (* x (+ y z)))
2.0ms	(sqrt (fma y z (* (* (cbrt (* x (+ y z))) (* (cbrt x) (cbrt (+ y z)))) (cbrt (* x (+ y z))))))

series936.0ms

Counts

4 → 12

Calls

4 calls:

453.0ms	(cbrt x)
141.0ms	(cbrt (* x (+ y z)))
153.0ms	(cbrt (* x (+ y z)))
189.0ms	(sqrt (fma y z (* (* (cbrt (* x (+ y z))) (* (cbrt x) (cbrt (+ y z)))) (cbrt (* x (+ y z))))))

simplify1.5s

Counts

66 → 66

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	124	916
1	294	841
2	681	780
3	1800	756
done	5000	737

prune323.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 21.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
18.1b	(cbrt (* x (+ y z)))
20.2b	(sqrt (fma y z (* (* (* (cbrt x) (cbrt (+ y z))) (* (cbrt x) (cbrt (+ y z)))) (cbrt (* x (+ y z))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`cbrt-prod` `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`
2×	`cbrt-div` `associate-*r/`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 54

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
7.0ms	(cbrt (* x (+ y z)))
2.0ms	(sqrt (fma y z (* (* (* (cbrt x) (cbrt (+ y z))) (* (cbrt x) (cbrt (+ y z)))) (cbrt (* x (+ y z))))))

series752.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt x)
209.0ms	(cbrt x)
128.0ms	(cbrt (* x (+ y z)))
208.0ms	(sqrt (fma y z (* (* (* (cbrt x) (cbrt (+ y z))) (* (cbrt x) (cbrt (+ y z)))) (cbrt (* x (+ y z))))))

simplify1.6s

Counts

66 → 66

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	125	847
1	299	771
2	718	686
3	1980	663
done	5000	649

prune296.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 21.1b

regimes148.0ms

Accuracy

0% (0.2b remaining)

Error of 19.4b against oracle of 19.2b and baseline of 19.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample973.0ms

Algorithm

intervals

Results

257.0ms	8000×	body	80	valid
253.0ms	8187×	body	80	nan