Details

sample30.0ms

Algorithm

intervals

Results

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

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 22.1b

localize7.0ms

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)))

rewrite18.0ms

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:

10.0ms	(* c0 (sqrt (/ A (* V l))))
3.0ms	(/ A (* V l))
3.0ms	(sqrt (/ A (* V l)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* c0 (sqrt (/ A (* V l))))
20.0ms	(/ A (* V l))
35.0ms	(sqrt (/ A (* V l)))

simplify70.0ms

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

prune219.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.6b

localize14.0ms

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)))

rewrite82.0ms

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)
43.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
22.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
13.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt A)
72.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
47.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
51.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify64.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	518	1059
1	2563	904
2	5001	844

prune370.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.6b

localize8.0ms

Local error

Found 3 expressions with local error:

2.0b	(* c0 (sqrt (* (/ A V) (/ 1 l))))
3.1b	(* (/ A V) (/ 1 l))
14.9b	(sqrt (* (/ A V) (/ 1 l)))

rewrite42.0ms

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×	`sqrt-div` `div-exp`
7×	`associate-*r/` `unswap-sqr`
5×	`cbrt-unprod`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-*l/` `un-div-inv` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `sqrt-pow1` `1-exp` `sqrt-prod` `*-commutative` `div-inv`
1×	`pow1/2`

Counts

3 → 101

Calls

3 calls:

20.0ms	(* c0 (sqrt (* (/ A V) (/ 1 l))))
14.0ms	(* (/ A V) (/ 1 l))
5.0ms	(sqrt (* (/ A V) (/ 1 l)))

series101.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* c0 (sqrt (* (/ A V) (/ 1 l))))
20.0ms	(* (/ A V) (/ 1 l))
31.0ms	(sqrt (* (/ A V) (/ 1 l)))

simplify46.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	440	542
1	1884	482
2	5001	443

prune265.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (/ A V) (/ 1 l))
3.1b	(* (/ A V) (/ 1 l))
14.9b	(sqrt (* (/ A V) (/ 1 l)))
14.9b	(sqrt (* (/ A V) (/ 1 l)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
50×	`times-frac`
48×	`add-exp-log`
36×	`*-un-lft-identity`
32×	`add-cube-cbrt`
28×	`add-cbrt-cube`
26×	`associate-r` `associate-l`
16×	`div-exp` `prod-exp`
14×	`pow1`
12×	`unswap-sqr`
8×	`cbrt-undiv` `sqrt-div` `cbrt-unprod`
4×	`expm1-log1p-u` `frac-times` `rec-exp` `sqrt-pow1` `1-exp` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`pow1/2` `sqrt-prod` `*-commutative`

Counts

4 → 152

Calls

4 calls:

13.0ms	(* (/ A V) (/ 1 l))
13.0ms	(* (/ A V) (/ 1 l))
5.0ms	(sqrt (* (/ A V) (/ 1 l)))
5.0ms	(sqrt (* (/ A V) (/ 1 l)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (/ A V) (/ 1 l))
20.0ms	(* (/ A V) (/ 1 l))
30.0ms	(sqrt (* (/ A V) (/ 1 l)))
35.0ms	(sqrt (* (/ A V) (/ 1 l)))

simplify43.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	362	764
1	1532	666
2	5001	588

prune470.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 5.6b

regimes667.0ms

Accuracy

38% (8.2b remaining)

Error of 12.5b against oracle of 4.3b and baseline of 17.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	39
1	56	39

end0.0ms

sample905.0ms

Algorithm

intervals

Results

239.0ms	8937×	body	80	nan
238.0ms	8907×	body	80	valid