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

sample141.0ms

Algorithm

intervals

Results

48.0ms	256×	body	80	valid
35.0ms	249×	body	80	nan
26.0ms	145×	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: 24.1b

Counts

2 → 2

localize34.0ms

Local error

Found 4 expressions with local error:

6.7b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
7.6b	(* M (/ D (* d 2.0)))
11.1b	(pow (/ d h) (/ 1.0 2.0))
12.6b	(pow (/ d l) (/ 1.0 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`add-sqr-sqrt`
45×	`add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log`
30×	`unpow-prod-down`
26×	`pow-unpow`
15×	`add-cbrt-cube`
12×	`div-exp`
8×	`pow1` `pow-exp` `prod-exp`
7×	`associate-r`
6×	`div-inv` `sqr-pow`
5×	`associate-/l*`
4×	`cbrt-unprod` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `associate-l` `associate-/r*`
2×	`pow-pow`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `unswap-sqr`

Counts

4 → 143

Calls

4 calls:

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

series205.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms	(* M (/ D (* d 2.0)))
13.0ms	(pow (/ d h) (/ 1.0 2.0))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	1922
1	4971	1922

prune538.0ms

Filtered

116 candidates to 155 candidates (-33.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	135	20	155
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	21	157

Merged error: 11.4b

Counts

157 → 21

localize42.0ms

Local error

Found 4 expressions with local error:

5.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.7b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
7.6b	(* M (/ D (* d 2.0)))
12.6b	(pow (/ d l) (/ 1.0 2.0))

rewrite33.0ms

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:

10.0ms	(* 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)
7.0ms	(* M (/ D (* d 2.0)))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series371.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
172.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms	(* M (/ D (* d 2.0)))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5322	2198

prune530.0ms

Filtered

103 candidates to 154 candidates (-49.5%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	149	26	175

Merged error: 10.2b

Counts

175 → 26

localize43.0ms

Local error

Found 4 expressions with local error:

4.8b	(pow (/ (cbrt d) l) (/ 1.0 2.0))
5.2b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
6.7b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
7.6b	(* M (/ D (* d 2.0)))

rewrite37.0ms

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:

7.0ms	(pow (/ (cbrt d) l) (/ 1.0 2.0))
10.0ms	(* 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)
8.0ms	(* M (/ D (* d 2.0)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (/ (cbrt d) l) (/ 1.0 2.0))
178.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
173.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms	(* M (/ D (* d 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5443	2454

prune649.0ms

Filtered

112 candidates to 163 candidates (-45.5%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	3	22	25
Picked	1	0	1
Done	0	0	0
Total	162	27	189

Merged error: 9.7b

Counts

189 → 27

localize49.0ms

Local error

Found 4 expressions with local error:

4.8b	(pow (/ (cbrt d) l) (/ 1.0 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))))
7.6b	(* M (/ D (* d 2.0)))
7.6b	(* M (/ D (* d 2.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

614×	`add-exp-log`
369×	`prod-exp`
172×	`div-exp`
106×	`pow-exp`
51×	`add-cbrt-cube`
35×	`add-sqr-sqrt`
33×	`times-frac`
31×	`add-cube-cbrt` `*-un-lft-identity`
27×	`pow-to-exp`
25×	`cbrt-unprod`
22×	`unpow-prod-down`
15×	`associate-r`
14×	`pow1`
13×	`pow-unpow`
9×	`cbrt-undiv` `cbrt-prod` `associate-l`
8×	`associate-*r/`
5×	`pow-prod-down`
4×	`div-inv` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`frac-times` `pow-pow` `associate-*l/` `sqr-pow`

Counts

4 → 212

Calls

4 calls:

7.0ms	(pow (/ (cbrt d) l) (/ 1.0 2.0))
18.0ms	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l))))
7.0ms	(* M (/ D (* d 2.0)))
7.0ms	(* M (/ D (* d 2.0)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(pow (/ (cbrt d) l) (/ 1.0 2.0))
178.0ms	(* h (* (/ 1.0 2.0) (* (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) l))))
6.0ms	(* M (/ D (* d 2.0)))
6.0ms	(* M (/ D (* d 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4976	3698
1	4976	3698

prune478.0ms

Filtered

98 candidates to 224 candidates (-128.6%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	2	24	26
Picked	0	1	1
Done	0	0	0
Total	223	28	251

Merged error: 9.5b

Counts

251 → 28

regimes1.7s

Accuracy

19.8% (3.6b remaining)

Error of 12.3b against oracle of 8.7b and baseline of 13.2b

bsearch3.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	211	244
1	211	244

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
1.2s	8552×	body	80	nan
880.0ms	4789×	body	80	invalid

Details

analyze2.0s

sample141.0ms

simplify21.0ms

prune17.0ms

localize34.0ms

rewrite27.0ms

series205.0ms

simplify56.0ms

prune538.0ms

localize42.0ms

rewrite33.0ms

series371.0ms

simplify40.0ms

prune530.0ms

localize43.0ms

rewrite37.0ms

series393.0ms

simplify42.0ms

prune649.0ms

localize49.0ms

rewrite61.0ms

series226.0ms

simplify82.0ms

prune478.0ms

regimes1.7s

bsearch3.0ms

simplify4.0ms

end0.0ms

sample4.3s

Profiling