Details

sample441.0ms

Algorithm

intervals

Results

320.0ms	1158×	body	80	nan
60.0ms	400×	body	80	valid

simplify30.0ms

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

prune4.0ms

Filtered

1 candidates to 0 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: 24.9b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

7.2b	(* (* (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))))
11.4b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b	(pow (/ d l) (/ 1.0 2.0))
11.9b	(pow (/ d h) (/ 1.0 2.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`unpow-prod-down` `pow-unpow`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 190

Calls

4 calls:

14.0ms	(* (* (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))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d l) (/ 1.0 2.0))
6.0ms	(pow (/ d h) (/ 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))))
733.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
66.0ms	(pow (/ d l) (/ 1.0 2.0))
63.0ms	(pow (/ d h) (/ 1.0 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5001	2125

prune772.0ms

Filtered

202 candidates to 119 candidates (58.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	181	21	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	21	203

Merged error: 11.1b

Counts

203 → 21

localize49.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
7.2b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
11.4b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.6b	(pow (/ d l) (/ 1.0 2.0))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

738×	`add-exp-log`
487×	`prod-exp`
216×	`pow-exp`
171×	`div-exp`
78×	`pow-to-exp`
46×	`add-cbrt-cube`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`unpow-prod-down` `pow-unpow`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 274

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
29.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
6.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
640.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt 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))))
747.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
65.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717

prune854.0ms

Filtered

286 candidates to 104 candidates (36.4%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	276	10	286
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	280	27	307

Merged error: 9.9b

Counts

307 → 27

localize59.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
4.8b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
7.2b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
11.4b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite323.0ms

Algorithm

rewrite-expression-head

Rules

6965×	`add-exp-log`
5245×	`prod-exp`
2614×	`pow-exp`
1626×	`div-exp`
789×	`pow-to-exp`
232×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
37×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-unprod`
22×	`unpow-prod-down`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv` `cbrt-prod`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`frac-times` `flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1243

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
79.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.9s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
184.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
986.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
747.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify379.0ms

Algorithm

egg-herbie

Counts

1255 → 1255

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5001	45180

prune1.4s

Filtered

1255 candidates to 144 candidates (11.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	1246	9	1255
Fresh	5	21	26
Picked	1	0	1
Done	0	0	0
Total	1252	30	1282

Merged error: 8.6b

Counts

1282 → 30

localize59.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* M D) (* 2.0 d))
4.8b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.6b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
7.2b	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

6885×	`add-exp-log`
5208×	`prod-exp`
2604×	`pow-exp`
1596×	`div-exp`
787×	`pow-to-exp`
232×	`rec-exp` `1-exp`
43×	`add-cbrt-cube`
28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
22×	`unpow-prod-down` `cbrt-unprod`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-prod`
6×	`associate-r` `prod-diff`
5×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`sub-neg` `associate-r/` `associate-l` `associate-l/` `*-commutative`
1×	`flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1213

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
10.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
78.0ms	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))

series2.1s

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* M D) (* 2.0 d))
176.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
742.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
1.2s	(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (/ 1 l))))

simplify358.0ms

Algorithm

egg-herbie

Counts

1225 → 1225

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5001	44973

prune1.1s

Filtered

1225 candidates to 114 candidates (9.3%)

Pruning

33 alts after pruning (33 fresh and 0 done)

	Pruned	Kept	Total
New	1215	10	1225
Fresh	6	23	29
Picked	1	0	1
Done	0	0	0
Total	1222	33	1255

Merged error: 7.8b

Counts

1255 → 33

regimes1.7s

Accuracy

0% (5.9b remaining)

Error of 14.8b against oracle of 9.0b and baseline of 14.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	48
1	53	48

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.0s	38777×	body	80	nan
1.8s	12765×	body	80	valid