Details

sample36.0ms

Algorithm

intervals

Results

11.0ms	53×	body	1280	valid
6.0ms	47×	body	640	valid
5.0ms	126×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	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: 30.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
3.7b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite94.0ms

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:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
88.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series582.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(cbrt (+ x 1.0))
278.0ms	(cbrt x)
189.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify2.7s

Counts

53 → 53

Iterations

Useful iterations: done (2.7s)

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

prune212.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.7b	(cbrt x)
3.7b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite111.0ms

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:

8.0ms	(cbrt (+ 1.0 x))
2.0ms	(cbrt x)
99.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series681.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(cbrt (+ 1.0 x))
286.0ms	(cbrt x)
266.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify2.9s

Counts

53 → 53

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	131	649
1	312	597
2	938	573
3	3752	539
done	5001	513

prune191.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.7b	(cbrt (- x))
3.7b	(- (cbrt (+ 1.0 x)) (* (cbrt -1) (cbrt (- x))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
2×	`cbrt-div` `pow1/3`
1×	`neg-mul-1` `sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 44

Calls

3 calls:

4.0ms	(cbrt (+ 1.0 x))
2.0ms	(cbrt (- x))
59.0ms	(- (cbrt (+ 1.0 x)) (* (cbrt -1) (cbrt (- x))))

series609.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(cbrt (+ 1.0 x))
255.0ms	(cbrt (- x))
222.0ms	(- (cbrt (+ 1.0 x)) (* (cbrt -1) (cbrt (- x))))

simplify704.0ms

Counts

53 → 53

Iterations

Useful iterations: done (701.0ms)

Iter	Nodes	Cost
0	139	711
1	316	663
2	1142	612
done	5001	579

prune215.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt (- x))
4.8b	(/ (cbrt x) (* x x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log`
7×	`pow1/3` `add-cbrt-cube`
6×	`times-frac` `associate-/l*`
4×	`add-log-exp` `pow-div`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`cbrt-undiv` `div-exp`
1×	`pow2` `neg-mul-1` `frac-2neg` `pow-plus` `prod-exp` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `cbrt-unprod` `div-inv`

Counts

4 → 71

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
2.0ms	(cbrt (- x))
16.0ms	(/ (cbrt x) (* x x))

series1.6s

Counts

4 → 12

Calls

4 calls:

658.0ms	(cbrt x)
338.0ms	(cbrt x)
313.0ms	(cbrt (- x))
330.0ms	(/ (cbrt x) (* x x))

simplify1.2s

Counts

83 → 83

Iterations

Useful iterations: 3 (492.0ms)

Iter	Nodes	Cost
0	95	533
1	186	501
2	477	450
3	2045	423
done	5002	423

prune361.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes43.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 29.9b

bsearch152.0ms

Steps

Iters	Range		Point
9	28918.939680702064	6498875204.17883	65393.48371123324
10	-2676750800.736259	-2.9526231381329305e-09	-70055.06240145699

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	36	84
1	46	60
done	46	60

end0.0ms

sample1.2s

Algorithm

intervals

Results

431.0ms	1751×	body	1280	valid
240.0ms	4076×	body	80	valid
197.0ms	1244×	body	640	valid
109.0ms	634×	body	320	valid
23.0ms	295×	body	160	valid