Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	51×	body	1280	valid
3.0ms	41×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	9×	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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.6b

Counts

2 → 1

localize5.0ms

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))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip3-+` `flip--` `flip-+`

Counts

3 → 8

Calls

3 calls:

2.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
3.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series408.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(cbrt (+ x 1.0))
176.0ms	(cbrt x)
146.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify126.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	238	172
1	790	167
2	3656	145
3	5001	145

prune60.0ms

Filtered

17 candidates to 15 candidates (88.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	5	18

Merged error: 11.9b

Counts

18 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-commutative` `difference-of-squares`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `flip--`

Counts

4 → 11

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
9.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series708.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt x)
180.0ms	(cbrt x)
176.0ms	(cbrt x)
175.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	212	174
1	695	160
2	2405	141
3	5001	141

prune72.0ms

Filtered

23 candidates to 16 candidates (69.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	22	6	28

Merged error: 11.9b

Counts

28 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
10.4b	(- (/ (cbrt (+ (pow x 3) (pow 1.0 3))) (cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))) (cbrt x))
15.2b	(cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
19.6b	(cbrt (+ (pow x 3) (pow 1.0 3)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`cbrt-div`
3×	`pow1/3`
2×	`flip3-+` `flip-+`
1×	`cbrt-prod` `sub-neg` `flip3--` `sum-cubes` `flip--`

Counts

4 → 12

Calls

4 calls:

1.0ms	(cbrt x)
12.0ms	(- (/ (cbrt (+ (pow x 3) (pow 1.0 3))) (cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))) (cbrt x))
10.0ms	(cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
4.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))

series853.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
188.0ms	(- (/ (cbrt (+ (pow x 3) (pow 1.0 3))) (cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))) (cbrt x))
107.0ms	(cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
375.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))

simplify48.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	435	338
1	1593	331
2	5001	310

prune127.0ms

Filtered

24 candidates to 21 candidates (87.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	19	5	24
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	20	10	30

Merged error: 11.8b

Counts

30 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

15.2b	(cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
19.6b	(cbrt (+ (pow x 3) (pow 1.0 3)))
19.6b	(cbrt (+ (pow x 3) (pow 1.0 3)))
19.6b	(cbrt (+ (pow x 3) (pow 1.0 3)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-div`
4×	`flip3-+` `pow1/3` `flip-+`
3×	`cbrt-prod` `sum-cubes`

Counts

4 → 15

Calls

4 calls:

5.0ms	(cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
4.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))
4.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))
4.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))

series1.2s

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
375.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))
378.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))
376.0ms	(cbrt (+ (pow x 3) (pow 1.0 3)))

simplify36.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	302	368
1	1068	352
2	5001	349

prune173.0ms

Filtered

27 candidates to 27 candidates (100.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	8	8
Picked	1	0	1
Done	1	0	1
Total	25	12	37

Merged error: 11.8b

Counts

37 → 12

regimes86.0ms

Accuracy

99.3% (0.1b remaining)

Error of 11.8b against oracle of 11.7b and baseline of 30.6b

bsearch121.0ms

Steps

Iters	Range		Point
9	2.5653698016906928e-06	357.20278190505735	9.776879829956754e-05
10	-1.3417951029768598e+66	-5.3118556719433245e+54	-4.495023653592418e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	59
1	85	59
2	85	59

end0.0ms

sample505.0ms

Algorithm

intervals

Results

176.0ms	1750×	body	1280	valid
105.0ms	1246×	body	640	valid
82.0ms	4098×	body	80	valid
35.0ms	616×	body	320	valid
11.0ms	290×	body	160	valid