Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	278×	body	80	valid
7.0ms	291×	body	80	nan

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	4
1	14	4
2	14	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.0b

localize7.0ms

Local error

Found 3 expressions with local error:

1.7b	(* c0 (sqrt (/ A (* V l))))
5.4b	(/ A (* V l))
14.2b	(sqrt (/ A (* V l)))

rewrite41.0ms

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:

25.0ms	(* c0 (sqrt (/ A (* V l))))
7.0ms	(/ A (* V l))
6.0ms	(sqrt (/ A (* V l)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* c0 (sqrt (/ A (* V l))))
21.0ms	(/ A (* V l))
32.0ms	(sqrt (/ A (* V l)))

simplify66.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	215	345
1	819	320
2	3061	317
3	5001	317

prune205.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 7.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt A)
1.7b	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
3.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
14.2b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite133.0ms

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)
69.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
38.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
21.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt A)
76.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
43.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
59.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	518	1061
1	2563	904
2	5001	844

prune348.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

3.0b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
14.2b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
14.2b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
14.2b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
22×	`associate-r`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-cbrt-cube`
15×	`pow1`
11×	`cbrt-prod`
9×	`sqrt-div`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`sqrt-pow1` `unswap-sqr`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `sqrt-prod`
2×	`div-inv`
1×	`*-commutative`

Counts

4 → 109

Calls

4 calls:

35.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
21.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
21.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
24.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
56.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
52.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))
56.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify52.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	421	1026
1	2054	918
2	5001	845

prune451.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 5.7b

localize8.0ms

Local error

Found 3 expressions with local error:

1.7b	(* c0 (sqrt (* (/ 1 V) (/ A l))))
4.3b	(* (/ 1 V) (/ A l))
14.2b	(sqrt (* (/ 1 V) (/ A l)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
27×	`add-exp-log`
25×	`times-frac`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
17×	`associate-r` `add-cbrt-cube`
16×	`associate-l`
10×	`pow1`
9×	`prod-exp`
8×	`div-exp`
7×	`unswap-sqr`
6×	`sqrt-div` `associate-*r/`
5×	`cbrt-unprod`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `sqrt-pow1` `1-exp` `sqrt-prod` `*-commutative` `div-inv`
1×	`pow1/2`

Counts

3 → 98

Calls

3 calls:

34.0ms	(* c0 (sqrt (* (/ 1 V) (/ A l))))
22.0ms	(* (/ 1 V) (/ A l))
9.0ms	(sqrt (* (/ 1 V) (/ A l)))

series131.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* c0 (sqrt (* (/ 1 V) (/ A l))))
20.0ms	(* (/ 1 V) (/ A l))
58.0ms	(sqrt (* (/ 1 V) (/ A l)))

simplify48.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	424	535
1	1846	470
2	5001	444

prune215.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 5.6b

regimes604.0ms

Accuracy

31.6% (9.3b remaining)

Error of 14.1b against oracle of 4.8b and baseline of 18.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	29
1	39	29

end0.0ms

sample1.0s

Algorithm

intervals

Results

218.0ms	8870×	body	80	valid
214.0ms	8793×	body	80	nan