Details

analyze1.9s

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
42.0ms	272×	body	80	nan
20.0ms	113×	body	80	invalid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5401	35

prune17.0ms

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: 21.9b

Counts

2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
8.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
9.9b	(pow (/ d h) (/ 1.0 2.0))
10.2b	(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:

5.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
14.0ms	(* h (* (/ 1.0 2.0) (/ (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))

series377.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
182.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
12.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4978	2434
1	4978	2434

prune536.0ms

Filtered

116 candidates to 165 candidates (-42.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	145	20	165
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	146	21	167

Merged error: 8.1b

Counts

167 → 21

localize40.0ms

Local error

Found 4 expressions with local error:

3.7b	(* M (/ D (* d 2.0)))
5.4b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
8.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
10.2b	(pow (/ d l) (/ 1.0 2.0))

rewrite36.0ms

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

series378.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* M (/ D (* d 2.0)))
177.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
182.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5322	2198

prune534.0ms

Filtered

103 candidates to 154 candidates (-49.5%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	143	11	154
Fresh	4	16	20
Picked	1	0	1
Done	0	0	0
Total	148	27	175

Merged error: 7.7b

Counts

175 → 27

localize53.0ms

Local error

Found 4 expressions with local error:

2.9b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
3.7b	(* M (/ D (* d 2.0)))
5.4b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
8.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-exp-log`
45×	`times-frac` `prod-exp`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
34×	`div-exp`
33×	`add-cbrt-cube`
26×	`unpow-prod-down`
14×	`pow-exp`
13×	`pow-unpow` `cbrt-unprod`
12×	`pow1`
9×	`cbrt-prod`
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 → 151

Calls

4 calls:

9.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
7.0ms	(* M (/ D (* d 2.0)))
5.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
11.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.0ms	(* M (/ D (* d 2.0)))
175.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
184.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))

simplify40.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5502	2451

prune719.0ms

Filtered

116 candidates to 163 candidates (-40.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	6	20	26
Picked	1	0	1
Done	0	0	0
Total	162	28	190

Merged error: 6.9b

Counts

190 → 28

localize54.0ms

Local error

Found 4 expressions with local error:

3.7b	(* M (/ D (* 2.0 d)))
3.7b	(* M (/ D (* 2.0 d)))
4.3b	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
8.2b	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (/ (pow (* M (/ D (* 2.0 d))) (/ 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:

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

series373.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* M (/ D (* 2.0 d)))
8.0ms	(* M (/ D (* 2.0 d)))
173.0ms	(/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l)
186.0ms	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) (/ (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)) l))))

simplify58.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5203	3840

prune458.0ms

Filtered

90 candidates to 217 candidates (-141.1%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	212	5	217
Fresh	2	25	27
Picked	1	0	1
Done	0	0	0
Total	215	30	245

Merged error: 6.8b

Counts

245 → 30

regimes1.9s

Accuracy

0% (4.1b remaining)

Error of 13.1b against oracle of 9.0b and baseline of 13.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	165	82
1	165	82

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8463×	body	80	nan
872.0ms	4875×	body	80	invalid

Details

analyze1.9s

sample136.0ms

simplify21.0ms

prune17.0ms

localize29.0ms

rewrite37.0ms

series377.0ms

simplify51.0ms

prune536.0ms

localize40.0ms

rewrite36.0ms

series378.0ms

simplify41.0ms

prune534.0ms

localize53.0ms

rewrite39.0ms

series401.0ms

simplify40.0ms

prune719.0ms

localize54.0ms

rewrite57.0ms

series373.0ms

simplify58.0ms

prune458.0ms

regimes1.9s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample4.2s

Profiling