Details

analyze2.0s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	81.1%	18.9%	7
0%	68.6%	31.4%	8
0%	59.2%	40.8%	9
0%	59.2%	40.8%	10
0%	59.2%	40.8%	11
0.4%	49.5%	50.1%	12
0.8%	44.4%	54.8%	13
1.4%	39.9%	58.7%	14

sample136.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
36.0ms	233×	body	80	nan
25.0ms	140×	body	80	invalid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5401	35

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 23.1b

Counts

2 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

5.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.4b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
8.9b	(pow (/ d h) (/ 1.0 2.0))
13.0b	(pow (/ d l) (/ 1.0 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-exp-log`
51×	`times-frac`
43×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
41×	`prod-exp`
33×	`div-exp`
30×	`unpow-prod-down`
26×	`pow-unpow`
24×	`add-cbrt-cube`
16×	`pow-exp`
11×	`pow1`
9×	`cbrt-unprod`
6×	`sqr-pow`
5×	`cbrt-undiv` `pow-to-exp` `div-inv` `associate-/l*`
4×	`associate-*r/` `add-log-exp`
3×	`associate-l` `pow-prod-down` `associate-/r*`
2×	`pow-pow`
1×	`frac-times` `frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 153

Calls

4 calls:

11.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
8.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
5.0ms	(pow (/ d h) (/ 1.0 2.0))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series388.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
179.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
13.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4978	2434
1	4978	2434

prune543.0ms

Filtered

116 candidates to 165 candidates (-42.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	148	17	165
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	149	18	167

Merged error: 11.1b

Counts

167 → 18

localize42.0ms

Local error

Found 4 expressions with local error:

5.2b	(* M (/ D (* d 2.0)))
5.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.4b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
13.0b	(pow (/ d l) (/ 1.0 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-exp-log`
45×	`prod-exp`
36×	`times-frac`
34×	`add-sqr-sqrt` `div-exp`
33×	`add-cbrt-cube`
32×	`add-cube-cbrt` `*-un-lft-identity`
17×	`unpow-prod-down`
14×	`pow-exp`
13×	`pow-unpow` `cbrt-unprod`
12×	`pow1`
8×	`associate-r`
7×	`cbrt-undiv`
6×	`associate-l`
5×	`associate-r/` `associate-/l` `sqr-pow`
4×	`pow-to-exp` `pow-prod-down` `div-inv` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative`
1×	`frac-times` `pow-pow` `frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

7.0ms	(* M (/ D (* d 2.0)))
11.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
5.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series384.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* M (/ D (* d 2.0)))
186.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
175.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
17.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5322	2198

prune550.0ms

Filtered

103 candidates to 154 candidates (-49.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	147	7	154
Fresh	1	16	17
Picked	1	0	1
Done	0	0	0
Total	149	23	172

Merged error: 10.5b

Counts

172 → 23

localize53.0ms

Local error

Found 4 expressions with local error:

3.9b	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
5.2b	(* M (/ D (* d 2.0)))
5.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.4b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-exp-log`
49×	`prod-exp`
37×	`div-exp`
33×	`add-cbrt-cube`
27×	`add-sqr-sqrt` `times-frac`
25×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
17×	`pow-exp`
13×	`pow-unpow` `cbrt-unprod`
8×	`associate-r`
7×	`cbrt-undiv`
6×	`pow-pow` `associate-l`
5×	`unpow-prod-down` `associate-r/` `pow-prod-down` `associate-/l` `sqr-pow`
4×	`pow-to-exp` `add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`*-commutative`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-*l/` `clear-num` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

13.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
7.0ms	(* M (/ D (* d 2.0)))
11.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
7.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)

series399.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
8.0ms	(* M (/ D (* d 2.0)))
184.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
179.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)

simplify39.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5084	2273

prune575.0ms

Filtered

94 candidates to 150 candidates (-59.6%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	144	6	150
Fresh	4	18	22
Picked	1	0	1
Done	0	0	0
Total	149	24	173

Merged error: 9.1b

Counts

173 → 24

localize57.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l)
5.2b	(* M (/ D (* d 2.0)))
5.2b	(* M (/ D (* d 2.0)))
5.2b	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

628×	`add-exp-log`
373×	`prod-exp`
179×	`div-exp`
108×	`pow-exp`
53×	`add-cbrt-cube`
27×	`pow-to-exp`
25×	`add-sqr-sqrt` `cbrt-unprod`
21×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
15×	`associate-r`
13×	`pow1`
10×	`cbrt-undiv`
9×	`associate-l`
8×	`associate-*r/`
5×	`pow-prod-down` `associate-/l*`
4×	`unpow-prod-down` `add-log-exp` `sqr-pow`
3×	`associate-/r` `-commutative` `div-inv`
2×	`unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 205

Calls

4 calls:

5.0ms	(/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l)
7.0ms	(* M (/ D (* d 2.0)))
7.0ms	(* M (/ D (* d 2.0)))
19.0ms	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l)
6.0ms	(* M (/ D (* d 2.0)))
6.0ms	(* M (/ D (* d 2.0)))
190.0ms	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l))))

simplify51.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5199	3840

prune485.0ms

Filtered

96 candidates to 217 candidates (-126.0%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	0	23	23
Picked	1	0	1
Done	0	0	0
Total	215	26	241

Merged error: 9.0b

Counts

241 → 26

regimes1.9s

Accuracy

-21.7% (5.0b remaining)

Error of 13.8b against oracle of 8.8b and baseline of 12.9b

bsearch242.0ms

Steps

Iters	Range		Point
9	1.0062287987880106e-69	1.5139404774653972e-61	1.343847384176876e-64
8	-1.5006390816232757e-65	-2.6565080376779386e-70	-1.8117921193423651e-68

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	228	246
1	228	246

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8371×	body	80	nan
837.0ms	4625×	body	80	invalid

Details

analyze2.0s

sample136.0ms

simplify20.0ms

prune18.0ms

localize30.0ms

rewrite37.0ms

series388.0ms

simplify53.0ms

prune543.0ms

localize42.0ms

rewrite35.0ms

series384.0ms

simplify38.0ms

prune550.0ms

localize53.0ms

rewrite44.0ms

series399.0ms

simplify39.0ms

prune575.0ms

localize57.0ms

rewrite57.0ms

series378.0ms

simplify51.0ms

prune485.0ms

regimes1.9s

bsearch242.0ms

simplify4.0ms

end0.0ms

sample4.2s

Profiling