Details

sample33.0ms

Algorithm

intervals

Results

10.0ms	51×	body	1280	valid
6.0ms	44×	body	640	valid
5.0ms	134×	body	80	valid
2.0ms	21×	body	320	valid
0.0ms	6×	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: 29.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite65.0ms

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)
53.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series587.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(cbrt (+ x 1.0))
243.0ms	(cbrt x)
219.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.5s

Counts

53 → 53

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	131	649
1	312	597
2	928	573
3	3661	539
done	5003	513

prune266.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))
1.8b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite228.0ms

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:

1.0ms	(cbrt x)
81.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
61.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
83.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series985.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(cbrt x)
244.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
197.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
256.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify1.7s

Counts

80 → 80

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	108	1154
1	255	1083
2	726	1024
3	2715	964
done	5000	922

prune387.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
18.6b	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (cbrt x))
3.0ms	(cbrt (cbrt x))
70.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.3s

Counts

4 → 12

Calls

4 calls:

377.0ms	(cbrt (cbrt x))
373.0ms	(cbrt (cbrt x))
353.0ms	(cbrt (cbrt x))
240.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	112	774
1	262	733
2	769	510
3	3298	480
done	5001	466

prune278.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 8.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (cbrt (+ x 1.0)))
0.6b	(cbrt x)
10.3b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`cbrt-div`
15×	`add-cube-cbrt`
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 → 93

Calls

4 calls:

79.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
6.0ms	(cbrt (cbrt (+ x 1.0)))
1.0ms	(cbrt x)
61.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series782.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
124.0ms	(cbrt (cbrt (+ x 1.0)))
275.0ms	(cbrt x)
209.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	233	1653
1	560	1521
2	1963	1407
done	5000	1353

prune352.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.7b

regimes183.0ms

Accuracy

98.3% (0.4b remaining)

Error of 8.9b against oracle of 8.5b and baseline of 29.6b

bsearch133.0ms

Steps

Iters	Range		Point
8	5.523051691372288e-07	0.022891638200552334	0.0024730145507638147
10	-911936.9907706906	-4.3470241882695893e-07	-4454.769258694104

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	42	68
1	53	68
done	53	68

end0.0ms

sample1.6s

Algorithm

intervals

Results

817.0ms	1721×	body	1280	valid
279.0ms	4127×	body	80	valid
222.0ms	1227×	body	640	valid
72.0ms	614×	body	320	valid
23.0ms	311×	body	160	valid