Details

sample273.0ms

Algorithm

intervals

Results

140.0ms	1308×	body	80	nan
63.0ms	418×	body	80	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	720	17
3	5001	17

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 25.3b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.1b	(pow (/ d h) (/ 1.0 2.0))
11.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite658.0ms

Algorithm

rewrite-expression-head

Rules

3136×	`add-sqr-sqrt`
1958×	`associate-l`
1713×	`associate-r`
1669×	`times-frac`
1392×	`prod-diff`
1350×	`unpow-prod-down`
1190×	`*-un-lft-identity`
1183×	`add-cube-cbrt`
963×	`unswap-sqr`
698×	`distribute-rgt-in` `distribute-lft-in`
205×	`add-exp-log`
184×	`*-commutative`
107×	`prod-exp`
99×	`associate-*l/`
81×	`frac-times`
73×	`sqr-pow`
61×	`associate-/l*`
60×	`associate-/r*`
55×	`div-exp`
40×	`pow-exp`
31×	`difference-of-squares`
30×	`add-cbrt-cube`
27×	`div-inv`
26×	`pow-unpow`
21×	`clear-num`
20×	`frac-2neg`
16×	`pow1`
14×	`pow-to-exp`
13×	`cbrt-unprod`
11×	`associate-*r/`
6×	`pow-prod-down`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out--`
2×	`sub-neg` `pow-pow` `un-div-inv`
1×	`flip3--` `flip--`

Counts

4 → 1994

Calls

4 calls:

266.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
113.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
7.0ms	(pow (/ d h) (/ 1.0 2.0))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

639.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
753.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
67.0ms	(pow (/ d h) (/ 1.0 2.0))
75.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify977.0ms

Algorithm

egg-herbie

Counts

2006 → 2006

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5001	106777

prune11.3s

Filtered

2006 candidates to 1764 candidates (12.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	1981	25	2006
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1982	25	2007

Merged error: 6.0b

Counts

2007 → 25

localize46.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
5.0b	(* (* (pow (/ d (cbrt h)) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite688.0ms

Algorithm

rewrite-expression-head

Rules

3286×	`add-sqr-sqrt`
2058×	`associate-l`
1814×	`times-frac`
1791×	`associate-r`
1392×	`prod-diff`
1358×	`unpow-prod-down`
1260×	`*-un-lft-identity`
1253×	`add-cube-cbrt`
1001×	`unswap-sqr`
698×	`distribute-rgt-in` `distribute-lft-in`
214×	`add-exp-log`
210×	`*-commutative`
111×	`prod-exp`
99×	`associate-*l/`
81×	`frac-times`
74×	`sqr-pow`
73×	`associate-/l*`
72×	`associate-/r*`
58×	`div-exp`
42×	`add-cbrt-cube`
38×	`pow-exp`
31×	`difference-of-squares`
26×	`div-inv`
22×	`clear-num`
21×	`frac-2neg`
17×	`cbrt-prod` `cbrt-unprod`
15×	`pow1`
13×	`pow-to-exp` `pow-unpow`
11×	`associate-*r/`
9×	`cbrt-undiv`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-out--`
2×	`sub-neg` `un-div-inv`
1×	`flip3--` `pow-pow` `flip--`

Counts

4 → 2159

Calls

4 calls:

12.0ms	(/ (* M D) (* 2.0 d))
275.0ms	(* (* (pow (/ d (cbrt h)) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
117.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (* (pow (/ d (cbrt h)) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
759.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
74.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify1.0s

Algorithm

egg-herbie

Counts

2171 → 2171

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5001	111265

prune14.5s

Filtered

2171 candidates to 1903 candidates (12.3%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	2162	9	2171
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	2167	29	2196

Merged error: 5.1b

Counts

2196 → 29

localize61.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
11.5b	(pow (/ d l) (/ 1.0 2.0))
14.4b	(sqrt (/ h l))
14.4b	(sqrt (/ h l))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
172×	`add-sqr-sqrt`
114×	`add-cube-cbrt` `*-un-lft-identity`
78×	`associate-r` `associate-l`
26×	`sqrt-prod` `*-commutative` `unswap-sqr`
19×	`add-exp-log`
18×	`sqrt-div` `associate-/r` `associate-/l`
16×	`add-cbrt-cube`
13×	`unpow-prod-down` `pow-unpow`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`sqrt-pow1` `pow1/2` `pow-exp`
1×	`pow-to-exp` `pow-pow` `sqr-pow`

Counts

4 → 298

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(pow (/ d l) (/ 1.0 2.0))
4.0ms	(sqrt (/ h l))
4.0ms	(sqrt (/ h l))

series237.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (* M D) (* 2.0 d))
78.0ms	(pow (/ d l) (/ 1.0 2.0))
52.0ms	(sqrt (/ h l))
69.0ms	(sqrt (/ h l))

simplify65.0ms

Algorithm

egg-herbie

Counts

310 → 310

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1227	1946
1	5001	1879

prune2.4s

Filtered

310 candidates to 228 candidates (26.5%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	305	5	310
Fresh	4	24	28
Picked	1	0	1
Done	0	0	0
Total	310	29	339

Merged error: 5.1b

Counts

339 → 29

localize70.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
4.5b	(/ (* M D) (* 2.0 d))
14.4b	(sqrt (/ h l))
14.4b	(sqrt (/ h l))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

308×	`times-frac`
288×	`add-sqr-sqrt`
178×	`add-cube-cbrt` `*-un-lft-identity`
156×	`associate-r` `associate-l`
52×	`*-commutative` `unswap-sqr`
30×	`associate-/r` `associate-/l`
28×	`add-exp-log` `add-cbrt-cube`
26×	`sqrt-prod`
18×	`sqrt-div`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`

Counts

4 → 446

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(/ (* M D) (* 2.0 d))
8.0ms	(sqrt (/ h l))
5.0ms	(sqrt (/ h l))

series205.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* M D) (* 2.0 d))
40.0ms	(/ (* M D) (* 2.0 d))
55.0ms	(sqrt (/ h l))
79.0ms	(sqrt (/ h l))

simplify186.0ms

Algorithm

egg-herbie

Counts

458 → 458

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	985	2996
1	4813	2900
2	5002	2896

prune3.7s

Filtered

458 candidates to 326 candidates (28.8%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	455	3	458
Fresh	4	24	28
Picked	1	0	1
Done	0	0	0
Total	460	27	487

Merged error: 5.1b

Counts

487 → 27

regimes1.3s

Accuracy

-4.6% (7.3b remaining)

Error of 14.7b against oracle of 7.4b and baseline of 14.4b

bsearch216.0ms

Steps

Iters	Range		Point
7	3.1421519422282683e+262	3.3641440571041635e+264	3.3116082153282765e+264

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	66
1	76	66

end0.0ms

sample8.5s

Algorithm

intervals

Results

4.6s	38727×	body	80	nan
2.0s	12927×	body	80	valid