Details

sample265.0ms

Algorithm

intervals

Results

139.0ms	1275×	body	80	nan
60.0ms	402×	body	80	valid

simplify31.0ms

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:

6.6b	(* (* (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))))
8.7b	(pow (/ d h) (/ 1.0 2.0))
12.4b	(pow (/ d l) (/ 1.0 2.0))
13.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

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))))
6.0ms	(pow (/ d h) (/ 1.0 2.0))
9.0ms	(pow (/ d l) (/ 1.0 2.0))
13.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

628.0ms	(* (* (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))))
59.0ms	(pow (/ d h) (/ 1.0 2.0))
66.0ms	(pow (/ d l) (/ 1.0 2.0))
735.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify51.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1287	2382
1	5002	2125

prune753.0ms

Filtered

202 candidates to 119 candidates (58.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	182	20	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	20	203

Merged error: 12.1b

Counts

203 → 20

localize41.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (* M D) (* 2.0 d))
6.6b	(* (* (* (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))))
12.4b	(pow (/ d l) (/ 1.0 2.0))
13.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite76.0ms

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))
32.0ms	(* (* (* (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))))
6.0ms	(pow (/ d l) (/ 1.0 2.0))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (* M D) (* 2.0 d))
625.0ms	(* (* (* (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))))
65.0ms	(pow (/ d l) (/ 1.0 2.0))
741.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify78.0ms

Algorithm

egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1710	6060
1	5001	5717

prune800.0ms

Filtered

286 candidates to 104 candidates (36.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	279	7	286
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	282	24	306

Merged error: 12.0b

Counts

306 → 24

localize53.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (* M D) (* 2.0 d))
3.5b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.6b	(* (* (* (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))))
13.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite311.0ms

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:

13.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
74.0ms	(* (* (* (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))))
12.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.0s

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (* M D) (* 2.0 d))
174.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.1s	(* (* (* (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))))
737.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify380.0ms

Algorithm

egg-herbie

Counts

1255 → 1255

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	45180

prune1.3s

Filtered

1255 candidates to 144 candidates (11.5%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	1245	10	1255
Fresh	5	18	23
Picked	1	0	1
Done	0	0	0
Total	1251	28	1279

Merged error: 10.2b

Counts

1279 → 28

localize57.0ms

Local error

Found 4 expressions with local error:

3.5b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
6.6b	(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
6.6b	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
6.9b	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

6927×	`add-exp-log`
5233×	`prod-exp`
2609×	`pow-exp`
1607×	`div-exp`
788×	`pow-to-exp`
232×	`rec-exp` `1-exp`
48×	`add-cbrt-cube`
44×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
34×	`times-frac`
30×	`prod-diff`
25×	`cbrt-unprod`
22×	`unpow-prod-down`
17×	`distribute-rgt-in` `distribute-lft-in`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-prod` `div-inv`
8×	`associate-r`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `associate-r/` `associate-l` `-commutative`
1×	`flip3--` `pow-pow` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 1246

Calls

4 calls:

7.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
81.0ms	(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
7.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
10.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

series2.7s

Counts

4 → 12

Calls

4 calls:

185.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
979.0ms	(* (* (* (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 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))))
777.0ms	(* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h)
726.0ms	(/ (* (* 1.0 (pow (/ (* M D) (* 2.0 d)) 2.0)) h) (* 2.0 l))

simplify407.0ms

Algorithm

egg-herbie

Counts

1258 → 1258

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5001	47598

prune1.3s

Filtered

1258 candidates to 152 candidates (12.1%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	1252	6	1258
Fresh	2	25	27
Picked	1	0	1
Done	0	0	0
Total	1255	31	1286

Merged error: 9.1b

Counts

1286 → 31

regimes1.7s

Accuracy

6.7% (5.1b remaining)

Error of 14.4b against oracle of 9.3b and baseline of 14.8b

bsearch177.0ms

Steps

Iters	Range		Point
5	2.781170429713808e-51	9.007150340338912e-51	8.59510320435005e-51

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	82
1	68	82

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.1s	38070×	body	80	nan
1.8s	12689×	body	80	valid