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

sample192.0ms

Algorithm

intervals

Results

55.0ms	84×	body	5120	valid
30.0ms	382×	body	80	nan
28.0ms	58×	body	2560	valid
12.0ms	18×	body	5120	exit
9.0ms	23×	body	1280	valid
9.0ms	110×	body	80	invalid
6.0ms	73×	body	80	valid
3.0ms	11×	body	640	valid
2.0ms	4×	body	1280	invalid
1.0ms	5×	body	320	valid
1.0ms	2×	body	2560	invalid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5515	42

prune16.0ms

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: 60.0b

Counts

2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

19.1b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.1b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
19.1b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
31.0b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite92.0ms

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)))
12.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
12.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
43.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
30.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
30.0ms	(/ (* 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))))

simplify64.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4954	2695
1	4954	2695

prune168.0ms

Filtered

54 candidates to 155 candidates (-187.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	148	7	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	148	9	157

Merged error: 30.6b

Counts

157 → 9

localize5.0ms

Local error

Found 1 expressions with local error:

7.2b	(* (/ 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

prune73.0ms

Filtered

21 candidates to 31 candidates (-47.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	31	9	40

Merged error: 28.2b

Counts

40 → 9

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune38.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	1	1
Total	9	9

Merged error: 28.2b

Counts

9 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

13.1b	(sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))
13.1b	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
17.4b	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
24.7b	(/ (* (pow d 4) c0) (* (pow D 4) (* w h)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
99×	`add-cbrt-cube`
90×	`prod-exp`
52×	`div-exp`
42×	`cbrt-unprod`
30×	`cbrt-undiv`
16×	`sqrt-div` `associate-/r/`
15×	`frac-times` `pow-to-exp` `associate-*r/` `pow-exp`
14×	`frac-sub`
11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cube-cbrt` `flip3--` `-un-lft-identity` `associate-l/` `flip--`
7×	`times-frac` `associate-l`
4×	`associate-/r*` `add-log-exp`
3×	`pow-prod-down` `sqrt-prod` `div-inv`
2×	`frac-2neg` `clear-num` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

16.0ms	(sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))
13.0ms	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
36.0ms	(/ (* 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)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))
37.0ms	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
205.0ms	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
31.0ms	(/ (* (pow d 4) c0) (* (pow D 4) (* w h)))

simplify70.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5044	4037

prune221.0ms

Filtered

79 candidates to 167 candidates (-111.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	166	10	176

Merged error: 22.5b

Counts

176 → 10

regimes1.1s

Accuracy

8.3% (8.0b remaining)

Error of 32.1b against oracle of 24.1b and baseline of 32.8b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	77
1	58	77

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.4s	2364×	body	5120	valid
1.0s	12553×	body	80	nan
842.0ms	1709×	body	2560	valid
361.0ms	559×	body	5120	exit
359.0ms	4316×	body	80	invalid
357.0ms	879×	body	1280	valid
199.0ms	2404×	body	80	valid
120.0ms	377×	body	640	valid
44.0ms	186×	body	320	valid
29.0ms	71×	body	1280	invalid
17.0ms	36×	body	2560	invalid
13.0ms	42×	body	640	invalid
13.0ms	81×	body	160	valid
7.0ms	29×	body	320	invalid
2.0ms	12×	body	160	invalid
2.0ms	3×	body	5120	invalid

Details

analyze1.9s

sample192.0ms

simplify37.0ms

prune16.0ms

localize23.0ms

rewrite92.0ms

series192.0ms

simplify64.0ms

prune168.0ms

localize5.0ms

rewrite7.0ms

series1.0ms

simplify41.0ms

prune73.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune38.0ms

localize26.0ms

rewrite84.0ms

series414.0ms

simplify70.0ms

prune221.0ms

regimes1.1s

bsearch3.0ms

simplify2.0ms

end0.0ms

sample5.7s

Profiling