Details

sample766.0ms

Algorithm

intervals

Results

575.0ms	1141×	body	80	nan
79.0ms	411×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	35
1	54	35
2	174	35
3	717	35
4	4580	35
done	5000	35

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize68.0ms

Local error

Found 4 expressions with local error:

5.1b	(* (* (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))))
10.5b	(pow (/ d h) (/ 1.0 2.0))
11.2b	(pow (/ d l) (/ 1.0 2.0))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite249.0ms

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:

104.0ms	(* (* (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))))
17.0ms	(pow (/ d h) (/ 1.0 2.0))
10.0ms	(pow (/ d l) (/ 1.0 2.0))
98.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(* (* (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))))
102.0ms	(pow (/ d h) (/ 1.0 2.0))
110.0ms	(pow (/ d l) (/ 1.0 2.0))
1.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.7s

Counts

202 → 202

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	463	5058
1	1140	4644
2	3978	4180
done	5001	4172

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

localize68.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (* M D) (* 2.0 d))
5.1b	(* (* (* (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))))
11.2b	(pow (/ d l) (/ 1.0 2.0))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite732.0ms

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:

27.0ms	(/ (* M D) (* 2.0 d))
573.0ms	(* (* (* (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))))
9.0ms	(pow (/ d l) (/ 1.0 2.0))
73.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.2s

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (* (* (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))))
107.0ms	(pow (/ d l) (/ 1.0 2.0))
1.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify794.0ms

Counts

286 → 286

Iterations

Useful iterations: done (775.0ms)

Iter	Nodes	Cost
0	574	11962
1	1333	10811
done	5000	9346

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.1b

localize81.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (* M D) (* 2.0 d))
3.7b	(pow (/ d (cbrt l)) (/ 1.0 2.0))
5.1b	(* (* (* (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))))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.2s

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:

28.0ms	(/ (* M D) (* 2.0 d))
19.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
771.0ms	(* (* (* (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))))
70.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series3.0s

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (* M D) (* 2.0 d))
250.0ms	(pow (/ d (cbrt l)) (/ 1.0 2.0))
1.6s	(* (* (* (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))))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify2.0s

Counts

1255 → 1255

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	1520	84703
1	2502	70377
done	5000	62008

prune1.7s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.9b

localize137.0ms

Local error

Found 4 expressions with local error:

1.3b	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
3.3b	(/ (* M D) (* 2.0 d))
5.1b	(* (* (* (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 (/ 1 (cbrt (* (cbrt l) (cbrt l)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt l))) (/ 1.0 2.0))))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
12.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite4.9s

Algorithm

rewrite-expression-head

Rules

48183×	`add-exp-log`
38099×	`prod-exp`
20092×	`pow-exp`
11805×	`div-exp`
5826×	`pow-to-exp`
2494×	`rec-exp` `1-exp`
66×	`add-cbrt-cube`
36×	`cbrt-unprod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
16×	`associate-r`
13×	`pow-unpow`
12×	`pow1`
9×	`cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `unpow-prod-down` `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 → 6712

Calls

4 calls:

20.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
19.0ms	(/ (* M D) (* 2.0 d))
2.7s	(* (* (* (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 (/ 1 (cbrt (* (cbrt l) (cbrt l)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt l))) (/ 1.0 2.0))))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
95.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.8s

Counts

4 → 12

Calls

4 calls:

166.0ms	(pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0))
41.0ms	(/ (* M D) (* 2.0 d))
1.5s	(* (* (* (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 (/ 1 (cbrt (* (cbrt l) (cbrt l)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt l))) (/ 1.0 2.0))))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify4.4s

Counts

6724 → 6724

Iterations

Useful iterations: 0 (1.4s)

Iter	Nodes	Cost
0	5556	583415
done	5556	583415

prune52.5s

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 7.6b

regimes2.4s

Accuracy

0% (5.4b remaining)

Error of 15.4b against oracle of 10.0b and baseline of 15.4b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	41	89
1	53	89
done	53	89

end0.0ms

sample14.1s

Algorithm

intervals

Results

7.7s	38596×	body	80	nan
3.3s	12785×	body	80	valid