Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	129×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	10×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize5.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite24.0ms

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))
0.0ms	(cbrt x)
21.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series411.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
175.0ms	(cbrt x)
148.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify163.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (27.0ms)

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

prune144.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.7b	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite78.0ms

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:

2.0ms	(cbrt (+ x 1.0))
0.0ms	(cbrt x)
49.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
25.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series565.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
150.0ms	(log (exp (- (cbrt (+ x 1.0)) (cbrt x))))
151.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify36.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (29.0ms)

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

prune247.0ms

Filtered

81 candidates to 66 candidates (81.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite69.0ms

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)
24.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
21.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
21.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series621.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
150.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
145.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
150.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify135.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	234	664
1	748	628
2	3971	589
3	5002	589

prune280.0ms

Filtered

80 candidates to 66 candidates (82.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 13.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
22.4b	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite49.0ms

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

series682.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ x 1.0))
272.0ms	(cbrt (+ x 1.0))
174.0ms	(cbrt x)
149.0ms	(- (* (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify161.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (29.0ms)

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

prune183.0ms

Filtered

63 candidates to 52 candidates (82.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 13.3b

regimes130.0ms

Accuracy

99.2% (0.1b remaining)

Error of 11.8b against oracle of 11.7b and baseline of 29.5b

bsearch88.0ms

Steps

Iters	Range		Point
9	7.206039552426127e-07	5.540917366542361	0.0020701410194009636
11	-6.361978161628334e+80	-1.3656651874097087e+58	-4.510541549900266e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	35
1	61	35
2	61	35

end0.0ms

sample492.0ms

Algorithm

intervals

Results

164.0ms	1671×	body	1280	valid
97.0ms	1242×	body	640	valid
92.0ms	4146×	body	80	valid
36.0ms	643×	body	320	valid
11.0ms	298×	body	160	valid