Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	50×	body	1280	valid
4.0ms	49×	body	640	valid
3.0ms	127×	body	80	valid
1.0ms	22×	body	320	valid
0.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite49.0ms

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)
43.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series413.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify165.0ms

Counts

53 → 53

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	287	358
1	934	344
2	4833	322
3	5001	322
done	5001	322

prune149.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.0b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`cbrt-prod`
11×	`log-pow`
10×	`exp-prod`
8×	`add-cube-cbrt` `difference-of-squares`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-lft-out`
2×	`sub-neg` `cbrt-div` `pow1/3` `exp-sum`
1×	`log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `flip--` `flip-+`

Counts

4 → 69

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
87.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
39.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series532.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cbrt (+ x 1.0))
169.0ms	(cbrt x)
142.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
139.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify33.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	336	568
1	1025	536
2	5001	505
done	5001	505

prune239.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
2.0b	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`cbrt-prod`
9×	`add-log-exp`
8×	`difference-of-squares`
6×	`add-cube-cbrt` `distribute-lft-out--`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`log-prod` `log-pow`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
1×	`exp-prod` `exp-to-pow` `pow1/3` `rem-log-exp`

Counts

4 → 63

Calls

4 calls:

1.0ms	(cbrt x)
3.0ms	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
41.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
39.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series594.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt x)
144.0ms	(log (exp (* (sqrt (- (cbrt (+ x 1.0)) (cbrt x))) (sqrt (- (cbrt (+ x 1.0)) (cbrt x))))))
138.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
141.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify129.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	256	656
1	798	607
2	4119	572
3	5002	572
done	5002	572

prune282.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
23.3b	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod` `*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `cbrt-div` `add-cbrt-cube`
3×	`pow1/3`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 51

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
83.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series477.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (+ x 1.0))
81.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
138.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify158.0ms

Counts

63 → 63

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	288	590
1	972	483
2	4915	434
3	5001	434
done	5001	434

prune184.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.5b

regimes74.0ms

Accuracy

99.2% (0.1b remaining)

Error of 11.5b against oracle of 11.3b and baseline of 29.7b

bsearch90.0ms

Steps

Iters	Range		Point
9	1.7355052557369657e-07	0.016621422887445694	8.515663798864148e-06
9	-7.149767289149974e+63	-1.497073903866961e+55	-4.445502958773829e+61

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	40
1	76	40
2	76	40
done	76	40

end0.0ms

sample519.0ms

Algorithm

intervals

Results

162.0ms	1654×	body	1280	valid
94.0ms	1303×	body	640	valid
84.0ms	4117×	body	80	valid
33.0ms	624×	body	320	valid
17.0ms	302×	body	160	valid