Details

sample71.0ms

Algorithm

intervals

Results

43.0ms	248×	body	10240	exit
5.0ms	194×	body	80	valid
3.0ms	30×	body	320	valid
2.0ms	13×	body	640	valid
1.0ms	23×	body	160	valid

simplify46.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5001	8
done	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
6.3b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite535.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

10.0ms	(/ wj (+ wj 1))
10.0ms	(/ x (+ wj 1))
23.0ms	(/ (/ x (+ wj 1)) (exp wj))
483.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ wj (+ wj 1))
24.0ms	(/ x (+ wj 1))
43.0ms	(/ (/ x (+ wj 1)) (exp wj))
64.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify78.0ms

Counts

188 → 188

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	721	1524
1	3303	1471
2	5001	1469
done	5001	1469

prune412.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* wj x))
0.0b	(+ x (pow wj 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `distribute-lft-out`

Counts

2 → 30

Calls

2 calls:

15.0ms	(* 2 (* wj x))
8.0ms	(+ x (pow wj 2))

series52.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(* 2 (* wj x))
30.0ms	(+ x (pow wj 2))

simplify69.0ms

Counts

36 → 36

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	149	122
1	551	108
2	2352	107
3	5001	107
done	5001	107

prune67.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

63.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
7.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
8.0ms	(cbrt (+ x (pow wj 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
319.0ms	(cbrt (+ x (pow wj 2)))
315.0ms	(cbrt (+ x (pow wj 2)))
315.0ms	(cbrt (+ x (pow wj 2)))

simplify173.0ms

Counts

107 → 107

Iterations

Useful iterations: 3 (158.0ms)

Iter	Nodes	Cost
0	252	878
1	944	827
2	4715	760
3	5001	749
done	5001	749

prune265.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
1.0b	(pow (cbrt (cbrt (+ x (pow wj 2)))) 5)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cbrt-prod`
19×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

10.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
7.0ms	(cbrt (+ x (pow wj 2)))
17.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 5)

series1.4s

Counts

4 → 12

Calls

4 calls:

321.0ms	(cbrt (+ x (pow wj 2)))
326.0ms	(cbrt (+ x (pow wj 2)))
329.0ms	(cbrt (+ x (pow wj 2)))
456.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 5)

simplify130.0ms

Counts

79 → 79

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	273	571
1	931	533
2	3965	527
3	5002	507
done	5002	507

prune261.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes67.0ms

Accuracy

61.5% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.2b

bsearch33.0ms

Steps

Iters	Range		Point
8	2.925089333066609e-14	7.704108445868586e-11	7.575706194898737e-11

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	25
1	33	25
done	33	25

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	7758×	body	10240	exit
190.0ms	6302×	body	80	valid
81.0ms	796×	body	320	valid
65.0ms	471×	body	640	valid
31.0ms	525×	body	160	valid