Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	43×	body	640	valid
3.0ms	126×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 30.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.4b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite25.0ms

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:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
21.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series422.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify889.0ms

Counts

53 → 53

Iterations

Useful iterations: 3 (271.0ms)

Iter	Nodes	Cost
0	131	649
1	291	597
2	698	573
3	1804	521
done	5001	521

prune138.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
22.0b	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`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`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 45

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
22.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
185.0ms	(cbrt x)
180.0ms	(cbrt x)
150.0ms	(- (cbrt (+ x 1.0)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify967.0ms

Counts

57 → 57

Iterations

Useful iterations: 3 (305.0ms)

Iter	Nodes	Cost
0	100	645
1	240	607
2	644	399
3	1906	351
done	5000	351

prune157.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (+ x 1.0))
0.4b	(cbrt (+ x 1.0))
0.7b	(cbrt x)
10.5b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite26.0ms

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:

2.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
20.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series513.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ x 1.0))
90.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
153.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify909.0ms

Counts

63 → 63

Iterations

Useful iterations: 3 (295.0ms)

Iter	Nodes	Cost
0	126	993
1	292	945
2	734	866
3	1942	740
done	5001	740

prune210.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
17.1b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite37.0ms

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:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
35.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(cbrt x)
195.0ms	(cbrt x)
186.0ms	(cbrt x)
160.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify1.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (344.0ms)

Iter	Nodes	Cost
0	109	899
1	271	860
2	730	624
3	2142	529
done	5001	529

prune192.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.8b

regimes43.0ms

Accuracy

98.3% (0.4b remaining)

Error of 9.1b against oracle of 8.7b and baseline of 30.4b

bsearch90.0ms

Steps

Iters	Range		Point
9	0.00016167321766412214	1766.3470775505596	0.0021387086194756175
10	-3752817.331716861	-5.670122129476186e-07	-4234.572456934552

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	72
1	59	72
done	59	72

end0.0ms

sample515.0ms

Algorithm

intervals

Results

172.0ms	1703×	body	1280	valid
97.0ms	1280×	body	640	valid
91.0ms	4031×	body	80	valid
39.0ms	633×	body	320	valid
14.0ms	353×	body	160	valid