Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	51×	body	1280	valid
7.0ms	41×	body	640	valid
7.0ms	123×	body	80	valid
4.0ms	30×	body	320	valid
1.0ms	11×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.6b	(cbrt x)
3.4b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite71.0ms

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-cbrt-cube` `add-exp-log` `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:

3.0ms	(cbrt (+ 1.0 x))
1.0ms	(cbrt x)
65.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series560.0ms

Counts

3 → 9

Calls

3 calls:

112.0ms	(cbrt (+ 1.0 x))
239.0ms	(cbrt x)
209.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify2.1s

Counts

53 → 53

Iterations

Iter	Nodes
done	5003
3	3717
2	948
1	313
0	131

prune317.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (cbrt x))
22.4b	(- (cbrt (+ 1.0 x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt (cbrt x))
2.0ms	(cbrt (cbrt x))
2.0ms	(cbrt (cbrt x))
55.0ms	(- (cbrt (+ 1.0 x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.7s

Counts

4 → 12

Calls

4 calls:

387.0ms	(cbrt (cbrt x))
376.0ms	(cbrt (cbrt x))
333.0ms	(cbrt (cbrt x))
558.0ms	(- (cbrt (+ 1.0 x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify1.8s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3413
2	789
1	261
0	112

prune356.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cbrt x) x)
0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
6×	`add-exp-log` `associate-/l*`
5×	`pow1` `add-cbrt-cube`
4×	`pow1/3` `add-log-exp`
3×	`distribute-lft-neg-in` `associate-/r*` `distribute-rgt-neg-in`
1×	`cbrt-undiv` `clear-num` `neg-mul-1` `frac-2neg` `div-exp` `div-inv` `pow-div`

Counts

4 → 80

Calls

4 calls:

7.0ms	(/ (cbrt x) x)
1.0ms	(cbrt (- x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

279.0ms	(/ (cbrt x) x)
297.0ms	(cbrt (- x))
313.0ms	(cbrt x)
240.0ms	(cbrt x)

simplify1.9s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	3663
2	658
1	185
0	104

prune598.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt x) (/ 1 x))
0.6b	(cbrt (- x))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`times-frac` `associate-r` `add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`associate-l` `unswap-sqr`
5×	`pow1/3`
4×	`prod-exp` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`div-exp` `pow-prod-up` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `neg-mul-1` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 84

Calls

4 calls:

29.0ms	(* (cbrt x) (/ 1 x))
3.0ms	(cbrt (- x))
1.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.1s

Counts

4 → 12

Calls

4 calls:

272.0ms	(* (cbrt x) (/ 1 x))
283.0ms	(cbrt (- x))
281.0ms	(cbrt x)
310.0ms	(cbrt x)

simplify2.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	2283
1	282
0	122

prune509.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes151.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 31.9b

bsearch118.0ms

Steps

Iters	Range		Point
9	0.030359728269424062	9645967.64350026	58824.0950936069
11	-14746478108.679678	-8.433739504313006e-14	-78626.83968822402

simplify4.0ms

Iterations

Iter	Nodes
done	42
1	42
0	34

end0.0ms

sample1.6s

Algorithm

intervals

Results

611.0ms	4080×	body	80	valid
456.0ms	1701×	body	1280	valid
197.0ms	1239×	body	640	valid
71.0ms	641×	body	320	valid
25.0ms	339×	body	160	valid