Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	46×	body	640	valid
3.0ms	122×	body	80	valid
1.0ms	27×	body	320	valid
0.0ms	4×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.3b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 44

Calls

3 calls:

2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
22.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series422.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
155.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.7s

Counts

53 → 53

Iterations

Useful iterations: 3 (492.0ms)

Iter	Nodes	Cost
0	131	649
1	291	597
2	857	573
3	4009	521
done	5001	521

prune141.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (+ (cbrt (+ x 1.0)) (cbrt x)))
0.6b	(cbrt x)
3.4b	(pow x 2/3)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`cbrt-prod`
15×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
8×	`cbrt-div`
7×	`pow1` `add-exp-log` `flip3-+` `associate-l` `flip-+`
6×	`associate-r` `distribute-lft-out`
5×	`add-cbrt-cube`
4×	`frac-times` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
2×	`pow1/3` `associate-r/` `associate-l/` `unswap-sqr`
1×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

2.0ms	(cbrt (+ x 1.0))
60.0ms	(* (cbrt (+ x 1.0)) (+ (cbrt (+ x 1.0)) (cbrt x)))
0.0ms	(cbrt x)
1.0ms	(pow x 2/3)

series687.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ x 1.0))
243.0ms	(* (cbrt (+ x 1.0)) (+ (cbrt (+ x 1.0)) (cbrt x)))
181.0ms	(cbrt x)
173.0ms	(pow x 2/3)

simplify719.0ms

Counts

90 → 90

Iterations

Useful iterations: 2 (239.0ms)

Iter	Nodes	Cost
0	231	1296
1	628	1182
2	2202	1117
done	5001	1117

prune281.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (fabs (cbrt x)) (fabs (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3` `swap-sqr` `associate-r` `associate-l`
1×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

3.0ms	(* (fabs (cbrt x)) (fabs (cbrt x)))
0.0ms	(cbrt x)
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series585.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (fabs (cbrt x)) (fabs (cbrt x)))
182.0ms	(cbrt x)
184.0ms	(cbrt x)
189.0ms	(cbrt x)

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (216.0ms)

Iter	Nodes	Cost
0	55	469
1	99	380
2	285	330
3	1205	308
done	5001	308

prune225.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.7b	(pow (sqrt (fabs (cbrt x))) 3)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
6×	`pow1` `unpow-prod-down` `cube-prod` `sqrt-prod`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `pow-pow` `pow1/3`
1×	`cube-mult` `pow-to-exp` `sqrt-pow1` `pow1/2` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
2.0ms	(pow (sqrt (fabs (cbrt x))) 3)

series803.0ms

Counts

4 → 12

Calls

4 calls:

374.0ms	(cbrt x)
188.0ms	(cbrt x)
183.0ms	(cbrt x)
58.0ms	(pow (sqrt (fabs (cbrt x))) 3)

simplify1.8s

Counts

77 → 77

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	73	548
1	159	436
2	468	413
3	2797	404
done	5000	401

prune233.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.2b

regimes87.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: done (1.0ms)

Iter	Nodes	Cost
0	13	24
1	18	24
done	18	22

end0.0ms

sample498.0ms

Algorithm

intervals

Results

176.0ms	1743×	body	1280	valid
101.0ms	1264×	body	640	valid
81.0ms	4075×	body	80	valid
34.0ms	618×	body	320	valid
11.0ms	300×	body	160	valid