Details

sample472.0ms

Algorithm

intervals

Results

210.0ms	1101×	body	80	nan
88.0ms	402×	body	80	valid

simplify7.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3968
3	655
2	170
1	54
0	22

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize105.0ms

Local error

Found 4 expressions with local error:

7.5b	(* (* (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))))
12.2b	(pow (/ d h) (/ 1.0 2.0))
14.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

205×	`add-exp-log`
107×	`prod-exp`
55×	`div-exp`
45×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
40×	`pow-exp`
30×	`add-cbrt-cube`
26×	`pow-unpow` `unpow-prod-down`
16×	`associate-r`
14×	`pow-to-exp`
13×	`cbrt-unprod`
10×	`pow1`
6×	`prod-diff`
5×	`distribute-rgt-in` `cbrt-undiv` `distribute-lft-in` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `pow-pow` `associate-l` `pow-prod-down` `*-commutative` `sqr-pow`
1×	`frac-times` `flip3--` `flip--`

Counts

4 → 194

Calls

4 calls:

175.0ms	(* (* (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))))
20.0ms	(pow (/ d h) (/ 1.0 2.0))
114.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

series4.5s

Counts

4 → 12

Calls

4 calls:

2.2s	(* (* (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))))
136.0ms	(pow (/ d h) (/ 1.0 2.0))
2.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
129.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify8.0s

Counts

206 → 206

Iterations

Iter	Nodes
done	5001
2	4597
1	1396
0	464

prune3.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.9b

localize269.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (* M D) (* 2.0 d))
7.5b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (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))))
14.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
15.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite859.0ms

Algorithm

rewrite-expression-head

Rules

818×	`add-exp-log`
567×	`prod-exp`
280×	`pow-exp`
187×	`div-exp`
94×	`pow-to-exp`
46×	`add-cbrt-cube`
32×	`rec-exp` `1-exp`
28×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`cbrt-unprod`
16×	`associate-r`
13×	`pow-unpow` `unpow-prod-down`
9×	`pow1` `cbrt-undiv`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`sub-neg` `associate-l` `pow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `flip3--` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 310

Calls

4 calls:

31.0ms	(/ (* M D) (* 2.0 d))
659.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (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))))
76.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
13.0ms	(pow (/ d l) (/ 1.0 2.0))

series5.0s

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ (* M D) (* 2.0 d))
2.7s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (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))))
2.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
146.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify4.6s

Counts

322 → 322

Iterations

Iter	Nodes
done	5001
1	1732
0	633

prune3.5s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 11.0b

localize481.0ms

Local error

Found 4 expressions with local error:

2.2b	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
3.2b	(/ (* M D) (* 2.0 d))
7.5b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
14.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

6975×	`add-exp-log`
5249×	`prod-exp`
2617×	`pow-exp`
1629×	`div-exp`
789×	`pow-to-exp`
232×	`rec-exp` `1-exp`
55×	`add-cbrt-cube`
27×	`cbrt-unprod`
21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`pow1` `times-frac`
16×	`associate-r`
13×	`pow-unpow`
9×	`cbrt-undiv`
6×	`pow-pow` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l/` `associate-r/` `div-inv`
2×	`sub-neg` `associate-l` `*-commutative`
1×	`pow2` `frac-times` `clear-num` `associate-/r` `unpow-prod-down` `frac-2neg` `pow-plus` `flip3--` `pow-sqr` `pow-prod-up` `flip--` `associate-/l` `sqr-pow`

Counts

4 → 1234

Calls

4 calls:

36.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
29.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
90.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series5.2s

Counts

4 → 12

Calls

4 calls:

374.0ms	(pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0))
40.0ms	(/ (* M D) (* 2.0 d))
2.8s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
2.0s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify17.8s

Counts

1246 → 1246

Iterations

Iter	Nodes
done	5002
1	3435
0	1450

prune4.1s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.7b

localize580.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))
3.2b	(/ (/ (* M D) 2.0) d)
7.5b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))))
7.8b	(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0)))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

8136×	`add-exp-log`
5861×	`prod-exp`
2712×	`pow-exp`
2043×	`div-exp`
814×	`pow-to-exp`
232×	`rec-exp` `1-exp`
184×	`add-cbrt-cube`
157×	`cbrt-unprod`
72×	`cbrt-undiv`
69×	`times-frac`
48×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
44×	`associate-r`
36×	`cbrt-prod`
24×	`associate-*r/`
23×	`pow1`
22×	`frac-times` `associate-*l/`
12×	`pow-prod-down`
7×	`associate-/l*`
6×	`prod-diff` `div-inv`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `-commutative`
2×	`sub-neg`
1×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`

Counts

4 → 1495

Calls

4 calls:

817.0ms	(* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))
25.0ms	(/ (/ (* M D) 2.0) d)
1.0s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))))
243.0ms	(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0)))

series5.8s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))
45.0ms	(/ (/ (* M D) 2.0) d)
2.8s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0))) (/ (cbrt h) (cbrt l)))))
1.7s	(* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (* (pow (/ (/ (* M D) 2.0) d) 2.0) (/ 1.0 2.0)))

simplify15.0s

Counts

1507 → 1507

Iterations

Iter	Nodes
done	5000
1	3731
0	1762

prune5.5s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 6.4b

regimes8.0s

Accuracy

13.8% (6.0b remaining)

Error of 14.2b against oracle of 8.2b and baseline of 15.1b

bsearch13.0ms

simplify49.0ms

Iterations

Iter	Nodes
done	88
1	88
0	71

end0.0ms

sample16.9s

Algorithm

intervals

Results

10.0s	38005×	body	80	nan
3.4s	12701×	body	80	valid