Details

analyze1.9s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0%	98.1%	1.9%	13
0%	98.1%	1.9%	14

sample317.0ms

Algorithm

intervals

Results

39.0ms	69×	body	5120	valid
26.0ms	55×	body	2560	valid
16.0ms	25×	body	5120	exit
9.0ms	24×	body	1280	valid
6.0ms	14×	body	640	valid
5.0ms	61×	body	80	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	2560	invalid
0.0ms	3×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5515	42

prune21.0ms

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: 61.1b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

16.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.8b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
41.2b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 143

Calls

4 calls:

12.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
13.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
47.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series194.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
31.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
33.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
100.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify65.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4954	2695
1	4954	2695

prune144.0ms

Filtered

54 candidates to 155 candidates (-187.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	150	5	155
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	5	157

Merged error: 31.5b

Counts

157 → 5

localize6.0ms

Local error

Found 1 expressions with local error:

10.6b

(* (/ c0 (* 2.0 w)) 0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
3×	`pow1` `times-frac` `associate-r`
2×	`cbrt-undiv` `div-exp`
1×	`pow-prod-down` `associate-l/` `-commutative` `mul0-rgt` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 28

Calls

1 calls:

6.0ms

(* (/ c0 (* 2.0 w)) 0)

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

(* (/ c0 (* 2.0 w)) 0)

simplify41.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5176	78

prune61.0ms

Filtered

21 candidates to 31 candidates (-47.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	31	5	36

Merged error: 24.7b

Counts

36 → 5

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune24.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Merged error: 24.7b

Counts

5 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

12.8b	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
15.5b	(* (/ c0 (* 2.0 w)) (/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M))))))
17.8b	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
20.1b	(/ (* (pow d 4) c0) (* (pow D 4) (* w h)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

212×	`add-exp-log`
135×	`add-cbrt-cube`
105×	`prod-exp`
64×	`div-exp`
57×	`cbrt-unprod`
42×	`cbrt-undiv`
32×	`associate-/r/`
28×	`sqrt-div` `frac-sub`
26×	`frac-times` `associate-*r/`
24×	`associate-r`
17×	`add-sqr-sqrt`
16×	`flip3--` `associate-*l/` `flip--`
15×	`pow-to-exp` `pow-exp`
14×	`times-frac` `associate-l`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
5×	`div-inv`
4×	`pow-prod-down` `associate-/r*` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `-commutative` `associate-/l`

Counts

4 → 202

Calls

4 calls:

12.0ms	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
40.0ms	(* (/ c0 (* 2.0 w)) (/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M))))))
35.0ms	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
10.0ms	(/ (* (pow d 4) c0) (* (pow D 4) (* w h)))

series549.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
283.0ms	(* (/ c0 (* 2.0 w)) (/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M))))))
201.0ms	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
26.0ms	(/ (* (pow d 4) c0) (* (pow D 4) (* w h)))

simplify78.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5112	7212

prune352.0ms

Filtered

106 candidates to 214 candidates (-101.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	206	8	214
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	207	12	219

Merged error: 18.7b

Counts

219 → 12

regimes968.0ms

Accuracy

-0.8% (8.5b remaining)

Error of 31.5b against oracle of 23.0b and baseline of 31.4b

bsearch495.0ms

Steps

Iters	Range		Point
11	4.4732764793571553e-215	2.997577127719712e-190	1.5861563218221685e-202
9	-8.958916786771457e-205	-1.4881792747704425e-211	-5.0948708970042e-209

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	31
1	31	31

end0.0ms

sample10.1s

Algorithm

intervals

Results

1.4s	2259×	body	5120	valid
772.0ms	1583×	body	2560	valid
325.0ms	513×	body	5120	exit
309.0ms	772×	body	1280	valid
175.0ms	2241×	body	80	valid
110.0ms	363×	body	640	valid
44.0ms	185×	body	320	valid
13.0ms	84×	body	160	valid

Details

analyze1.9s

sample317.0ms

simplify36.0ms

prune21.0ms

localize24.0ms

rewrite95.0ms

series194.0ms

simplify65.0ms

prune144.0ms

localize6.0ms

rewrite7.0ms

series1.0ms

simplify41.0ms

prune61.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune24.0ms

localize35.0ms

rewrite114.0ms

series549.0ms

simplify78.0ms

prune352.0ms

regimes968.0ms

bsearch495.0ms

simplify1.0ms

end0.0ms

sample10.1s

Profiling