Details

sample27.0ms

Algorithm

intervals

Results

7.0ms	50×	body	1280	valid
6.0ms	51×	body	640	valid
3.0ms	119×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 32.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite115.0ms

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:

7.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt x)
104.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series719.0ms

Counts

3 → 9

Calls

3 calls:

142.0ms	(cbrt (+ x 1.0))
302.0ms	(cbrt x)
275.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify4.3s

Counts

53 → 53

Iterations

Useful iterations: 4 (2.4s)

Iter	Nodes	Cost
0	131	649
1	290	597
2	672	573
3	1717	521
4	4878	501
done	5000	501

prune266.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b	(cbrt x)
9.6b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

31×	`cbrt-prod`
30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
47.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
39.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series839.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (+ x 1.0))
142.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
313.0ms	(cbrt x)
248.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify2.9s

Counts

102 → 102

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	188	1594
1	421	1459
2	1061	1351
3	3177	1200
done	5001	1034

prune480.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))
3.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`cbrt-prod`
26×	`*-un-lft-identity`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`pow1/3`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt x)
79.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
82.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
88.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series885.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt x)
196.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
233.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
190.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify3.6s

Counts

80 → 80

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	108	1154
1	237	1083
2	548	1024
3	1389	937
4	4123	904
done	5000	904

prune414.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
20.1b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`pow3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 46

Calls

4 calls:

2.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt x)
109.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

301.0ms	(cbrt x)
298.0ms	(cbrt x)
310.0ms	(cbrt x)
186.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	109	899
1	271	860
2	710	624
3	2054	523
done	5000	511

prune341.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes76.0ms

Accuracy

99% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 32.2b

bsearch3.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	49
1	32	49
done	32	49

end0.0ms

sample1.2s

Algorithm

intervals

Results

433.0ms	1697×	body	1280	valid
256.0ms	4118×	body	80	valid
204.0ms	1274×	body	640	valid
107.0ms	600×	body	320	valid
23.0ms	311×	body	160	valid