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

sample180.0ms

Algorithm

intervals

Results

40.0ms	67×	body	5120	valid
29.0ms	378×	body	80	nan
29.0ms	63×	body	2560	valid
13.0ms	16×	body	5120	exit
11.0ms	149×	body	80	invalid
11.0ms	29×	body	1280	valid
6.0ms	81×	body	80	valid
2.0ms	7×	body	640	valid
2.0ms	4×	body	1280	invalid
1.0ms	4×	body	320	valid
1.0ms	5×	body	160	valid
0.0ms	1×	body	2560	invalid
0.0ms	1×	body	320	invalid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

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: 59.0b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

18.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
18.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
25.6b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite94.0ms

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)))
44.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series188.0ms

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)))
96.0ms	(+ (/ (* 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 (48.0ms)

Iter	Nodes	Cost
0	4954	2695
1	4954	2695

prune182.0ms

Filtered

54 candidates to 155 candidates (-187.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	9	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	146	11	157

Merged error: 33.7b

Counts

157 → 11

localize5.0ms

Local error

Found 1 expressions with local error:

6.2b	(* (/ 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

prune86.0ms

Filtered

21 candidates to 31 candidates (-47.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	31	11	42

Merged error: 31.5b

Counts

42 → 11

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

prune51.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	1	1
Total	11	11

Merged error: 31.5b

Counts

11 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

13.7b	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
17.1b	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
18.1b	(sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))
21.5b	(/ (* (pow d 4) c0) (* (pow D 4) (* w h)))

rewrite81.0ms

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:

12.0ms	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
34.0ms	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
16.0ms	(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)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ c0 (* w h)) (* (/ d D) (/ d D)))
204.0ms	(/ (* M M) (- (* (/ c0 (* w h)) (* (/ d D) (/ d D))) (sqrt (- (* (/ c0 (* w h)) (/ (* (pow d 4) c0) (* (pow D 4) (* w h)))) (* M M)))))
142.0ms	(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)))

simplify71.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5044	4037

prune220.0ms

Filtered

79 candidates to 167 candidates (-111.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	160	7	167
Fresh	4	4	8
Picked	1	0	1
Done	0	2	2
Total	165	13	178

Merged error: 25.4b

Counts

178 → 13

regimes1.4s

Accuracy

-17.9% (10.6b remaining)

Error of 35.6b against oracle of 25.0b and baseline of 34.0b

bsearch243.0ms

Steps

Iters	Range		Point
6	1.583312385938121e+66	2.286361789371756e+67	1.6586793484181144e+66
7	2.2342370237793464e+45	6.353341867197057e+46	6.267249107531437e+46
3	-1.1129883041398436e+145	-8.696198321183997e+144	-1.0977777746385034e+145
6	-3.956029392381567e+231	-4.3059777986539765e+230	-4.401938303607714e+230

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	40
1	53	40

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.3s	2238×	body	5120	valid
973.0ms	12505×	body	80	nan
808.0ms	1726×	body	2560	valid
341.0ms	4302×	body	80	invalid
334.0ms	544×	body	5120	exit
324.0ms	860×	body	1280	valid
200.0ms	2527×	body	80	valid
110.0ms	371×	body	640	valid
41.0ms	188×	body	320	valid
25.0ms	68×	body	1280	invalid
18.0ms	37×	body	2560	invalid
14.0ms	48×	body	640	invalid
13.0ms	90×	body	160	valid
6.0ms	26×	body	320	invalid
3.0ms	20×	body	160	invalid
2.0ms	3×	body	5120	invalid

Details

analyze1.9s

sample180.0ms

simplify36.0ms

prune16.0ms

localize20.0ms

rewrite94.0ms

series188.0ms

simplify65.0ms

prune182.0ms

localize5.0ms

rewrite7.0ms

series1.0ms

simplify41.0ms

prune86.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune51.0ms

localize26.0ms

rewrite81.0ms

series411.0ms

simplify71.0ms

prune220.0ms

regimes1.4s

bsearch243.0ms

simplify2.0ms

end0.0ms

sample5.4s

Profiling