Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	277×	body	80	valid
7.0ms	257×	body	80	nan

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	12	8
2	14	8
done	14	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.1b

localize9.0ms

Local error

Found 3 expressions with local error:

2.0b	(* c0 (sqrt (/ A (* V l))))
7.2b	(/ A (* V l))
14.9b	(sqrt (/ A (* V l)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
6×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative`

Counts

3 → 72

Calls

3 calls:

12.0ms	(* c0 (sqrt (/ A (* V l))))
3.0ms	(/ A (* V l))
3.0ms	(sqrt (/ A (* V l)))

series116.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* c0 (sqrt (/ A (* V l))))
24.0ms	(/ A (* V l))
40.0ms	(sqrt (/ A (* V l)))

simplify1.2s

Counts

81 → 81

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	109	705
1	219	657
2	805	605
3	2762	605
done	5000	605

prune229.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
2.0b	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
2.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
14.9b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
28×	`times-frac`
27×	`add-exp-log`
26×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
14×	`cbrt-prod`
11×	`pow1`
10×	`associate-l`
9×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`sqrt-div` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-prod-down` `associate-*l/`
2×	`sqrt-pow1` `sqrt-prod` `*-commutative` `div-inv`
1×	`pow1/2` `pow1/3`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt A)
42.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
23.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
13.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt A)
86.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
53.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
54.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify899.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (207.0ms)

Iter	Nodes	Cost
0	193	1812
1	528	1718
2	2309	1223
done	5001	1223

prune459.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.6b

localize7.0ms

Local error

Found 3 expressions with local error:

2.0b	(* c0 (sqrt (/ (/ A V) l)))
3.1b	(/ (/ A V) l)
14.9b	(sqrt (/ (/ A V) l))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
134×	`add-sqr-sqrt`
117×	`add-cube-cbrt` `*-un-lft-identity`
89×	`sqrt-prod`
46×	`associate-r`
13×	`div-inv` `associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`unswap-sqr`
3×	`cbrt-undiv` `expm1-log1p-u` `rem-sqrt-square` `div-exp` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div`
1×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `associate-/l/`

Counts

3 → 197

Calls

3 calls:

29.0ms	(* c0 (sqrt (/ (/ A V) l)))
6.0ms	(/ (/ A V) l)
7.0ms	(sqrt (/ (/ A V) l))

series109.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* c0 (sqrt (/ (/ A V) l)))
21.0ms	(/ (/ A V) l)
32.0ms	(sqrt (/ (/ A V) l))

simplify940.0ms

Counts

206 → 206

Iterations

Useful iterations: 2 (195.0ms)

Iter	Nodes	Cost
0	316	2554
1	592	2368
2	2138	2266
done	5000	2266

prune799.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 1.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
0.6b	(cbrt A)
2.0b	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (/ (cbrt A) (cbrt V)) l))))
5.3b	(sqrt (/ (/ (cbrt A) (cbrt V)) l))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

237×	`times-frac`
138×	`add-sqr-sqrt`
124×	`sqrt-prod`
123×	`add-cube-cbrt` `*-un-lft-identity`
118×	`cbrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
6×	`rem-sqrt-square`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 189

Calls

4 calls:

1.0ms	(cbrt A)
1.0ms	(cbrt A)
69.0ms	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (/ (cbrt A) (cbrt V)) l))))
27.0ms	(sqrt (/ (/ (cbrt A) (cbrt V)) l))

series981.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt A)
397.0ms	(cbrt A)
195.0ms	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (/ (cbrt A) (cbrt V)) l))))
207.0ms	(sqrt (/ (/ (cbrt A) (cbrt V)) l))

simplify1.1s

Counts

201 → 201

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	554	3728
1	1038	3489
2	3130	3284
done	5001	3283

prune722.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 1.0b

regimes513.0ms

Accuracy

0% (1.5b remaining)

Error of 2.1b against oracle of 0.6b and baseline of 2.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	35
1	28	35
done	28	35

end0.0ms

sample1.1s

Algorithm

intervals

Results

284.0ms	8937×	body	80	nan
277.0ms	8907×	body	80	valid