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

sample236.0ms

Algorithm

intervals

Results

41.0ms

256×

body

valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

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: 22.2b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
4.8b	(* M (/ D (* d 2.0)))
9.5b	(pow (/ d h) (/ 1.0 2.0))
13.3b	(pow (/ d l) (/ 1.0 2.0))

rewrite28.0ms

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))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series220.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (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))
16.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4971	1922
1	4971	1922

prune526.0ms

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: 7.7b

Counts

157 → 21

localize43.0ms

Local error

Found 4 expressions with local error:

3.8b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
4.7b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
4.8b	(* M (/ D (* d 2.0)))
9.5b	(pow (/ d h) (/ 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:

13.0ms	(* 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 h) (/ 1.0 2.0))

series396.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
186.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms	(* M (/ D (* d 2.0)))
14.0ms	(pow (/ d h) (/ 1.0 2.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5283	2198

prune530.0ms

Filtered

101 candidates to 154 candidates (-52.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	144	10	154
Fresh	7	13	20
Picked	1	0	1
Done	0	0	0
Total	152	23	175

Merged error: 7.0b

Counts

175 → 23

localize60.0ms

Local error

Found 4 expressions with local error:

3.2b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
3.8b	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
4.7b	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
4.8b	(* M (/ D (* d 2.0)))

rewrite41.0ms

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

series426.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
198.0ms	(* h (* (/ 1.0 2.0) (/ (pow (* M (/ D (* d 2.0))) 2.0) l)))
185.0ms	(/ (pow (* M (/ D (* d 2.0))) 2.0) l)
6.0ms	(* M (/ D (* d 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5502	2451

prune660.0ms

Filtered

112 candidates to 163 candidates (-45.5%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	3	19	22
Picked	0	1	1
Done	0	0	0
Total	161	25	186

Merged error: 6.5b

Counts

186 → 25

localize62.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
3.8b	(* h (* (/ 1.0 2.0) (* (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (cbrt l)))))
4.8b	(* M (/ D (* d 2.0)))
4.8b	(* M (/ D (* d 2.0)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

1568×	`add-exp-log`
873×	`prod-exp`
544×	`div-exp`
224×	`pow-exp`
92×	`add-cbrt-cube`
56×	`pow-to-exp`
54×	`cbrt-unprod`
27×	`cbrt-undiv`
17×	`pow1` `add-sqr-sqrt`
15×	`associate-r`
14×	`associate-*r/`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac`
9×	`associate-l`
8×	`pow-prod-down`
5×	`frac-times` `associate-/l*`
4×	`add-log-exp`
3×	`associate-l/` `-commutative` `div-inv`
2×	`unpow-prod-down` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r*`

Counts

4 → 311

Calls

4 calls:

8.0ms	(/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
29.0ms	(* h (* (/ 1.0 2.0) (* (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (cbrt l)))))
7.0ms	(* M (/ D (* d 2.0)))
7.0ms	(* M (/ D (* d 2.0)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (* (cbrt l) (cbrt l)))
204.0ms	(* h (* (/ 1.0 2.0) (* (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* M (/ D (* d 2.0))) (/ 2.0 2)) (cbrt l)))))
6.0ms	(* M (/ D (* d 2.0)))
6.0ms	(* M (/ D (* d 2.0)))

simplify128.0ms

Algorithm

egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4932	6200
1	4932	6200

prune430.0ms

Filtered

84 candidates to 323 candidates (-284.5%)

Pruning

26 alts after pruning (25 fresh and 1 done)

	Pruned	Kept	Total
New	321	2	323
Fresh	0	23	23
Picked	0	1	1
Done	1	0	1
Total	322	26	348

Merged error: 6.5b

Counts

348 → 26

regimes1.7s

Accuracy

0% (4.7b remaining)

Error of 13.2b against oracle of 8.6b and baseline of 13.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	119	87
1	119	87

end0.0ms

sample7.4s

Algorithm

intervals

Results

1.3s

8000×

body

valid

Details

analyze1.9s

sample236.0ms

simplify23.0ms

prune17.0ms

localize32.0ms

rewrite28.0ms

series220.0ms

simplify59.0ms

prune526.0ms

localize43.0ms

rewrite36.0ms

series396.0ms

simplify39.0ms

prune530.0ms

localize60.0ms

rewrite41.0ms

series426.0ms

simplify43.0ms

prune660.0ms

localize62.0ms

rewrite95.0ms

series363.0ms

simplify128.0ms

prune430.0ms

regimes1.7s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample7.4s

Profiling