Details

sample860.0ms

Algorithm

intervals

Results

641.0ms	1175×	body	80	nan
84.0ms	388×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	35
1	54	35
2	174	35
3	720	35
done	5000	35

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize79.0ms

Local error

Found 4 expressions with local error:

6.3b	(* (* (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))))
11.1b	(pow (/ d h) (/ 1.0 2.0))
11.9b	(pow (/ d l) (/ 1.0 2.0))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite202.0ms

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:

91.0ms	(* (* (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))))
10.0ms	(pow (/ d h) (/ 1.0 2.0))
12.0ms	(pow (/ d l) (/ 1.0 2.0))
69.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (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))))
86.0ms	(pow (/ d h) (/ 1.0 2.0))
100.0ms	(pow (/ d l) (/ 1.0 2.0))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify853.0ms

Counts

202 → 202

Iterations

Useful iterations: done (838.0ms)

Iter	Nodes	Cost
0	463	5058
1	1476	4743
done	5000	4206

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.6b

localize96.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* M D) (* 2.0 d))
6.3b	(* (* (* (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))))
11.9b	(pow (/ d l) (/ 1.0 2.0))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite585.0ms

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` `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 → 306

Calls

4 calls:

22.0ms	(/ (* M D) (* 2.0 d))
411.0ms	(* (* (* (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))))
9.0ms	(pow (/ d l) (/ 1.0 2.0))
103.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.6s

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (* M D) (* 2.0 d))
1.3s	(* (* (* (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))))
102.0ms	(pow (/ d l) (/ 1.0 2.0))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.4s

Counts

318 → 318

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	630	12762
1	2039	11647
done	5000	10207

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.3b

localize128.0ms

Local error

Found 4 expressions with local error:

2.0b	(pow (/ d (cbrt h)) (/ 1.0 2.0))
3.6b	(/ (* M D) (* 2.0 d))
6.3b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (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))))
14.1b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

rewrite1.5s

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:

12.0ms	(pow (/ d (cbrt h)) (/ 1.0 2.0))
29.0ms	(/ (* M D) (* 2.0 d))
977.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (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))))
121.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

series2.8s

Counts

4 → 12

Calls

4 calls:

293.0ms	(pow (/ d (cbrt h)) (/ 1.0 2.0))
65.0ms	(/ (* M D) (* 2.0 d))
1.3s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (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))))
1.1s	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))

simplify1.1s

Counts

1255 → 1255

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	1519	84720
done	5000	73197

prune1.9s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.5b

localize85.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
3.6b	(/ (* M D) (* 2.0 d))
6.3b	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
9.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

8382×	`add-exp-log`
6058×	`prod-exp`
2742×	`pow-exp`
2061×	`div-exp`
814×	`pow-to-exp`
232×	`rec-exp` `1-exp`
187×	`add-cbrt-cube`
160×	`cbrt-unprod`
71×	`cbrt-undiv`
48×	`associate-r`
38×	`times-frac`
36×	`cbrt-prod`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`pow1`
12×	`associate-*l/`
7×	`pow-prod-down`
6×	`frac-times` `associate-*r/` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative` `div-inv`
2×	`sub-neg`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r` `flip--` `associate-/l`

Counts

4 → 1484

Calls

4 calls:

446.0ms	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
18.0ms	(/ (* M D) (* 2.0 d))
729.0ms	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
101.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

series3.2s

Counts

4 → 12

Calls

4 calls:

922.0ms	(* (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))
35.0ms	(/ (* M D) (* 2.0 d))
1.3s	(* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
890.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))))

simplify1.2s

Counts

1496 → 1496

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	1744	112581
done	5001	99711

prune2.7s

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 9.0b

regimes1.7s

Accuracy

0% (5.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	80
1	48	80
done	48	80

end0.0ms

sample15.7s

Algorithm

intervals

Results

9.2s	38480×	body	80	nan
3.0s	12757×	body	80	valid