Details

sample21.0ms

Algorithm

intervals

Results

5.0ms	49×	body	1280	valid
4.0ms	48×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	8×	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: 29.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite12.0ms

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:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
8.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series444.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(cbrt (+ x 1.0))
190.0ms	(cbrt x)
160.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify158.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	285	358
1	913	344
2	4502	322
3	5001	322

prune326.0ms

Filtered

53 candidates to 45 candidates (84.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	44	9	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	9	54

Merged error: 11.3b

Counts

54 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.3b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-sqr-sqrt`
137×	`cbrt-prod`
81×	`difference-of-squares`
72×	`unswap-sqr`
46×	`swap-sqr`
44×	`*-un-lft-identity`
18×	`*-commutative`
11×	`distribute-lft-out--`
8×	`associate-l`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 137

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
49.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt x)
186.0ms	(cbrt x)
183.0ms	(cbrt x)
193.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify160.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	1796
1	1084	1724
2	4177	1697
3	5002	1697

prune223.0ms

Filtered

149 candidates to 69 candidates (46.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	149	9	158

Merged error: 11.3b

Counts

158 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt x)
9.2b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

255×	`cbrt-prod`
232×	`add-sqr-sqrt`
88×	`unswap-sqr`
62×	`difference-of-squares`
40×	`*-un-lft-identity`
24×	`cbrt-div`
21×	`swap-sqr`
16×	`add-cube-cbrt`
11×	`associate-l`
7×	`flip3-+` `associate-r` `*-commutative` `flip-+` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `frac-times` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 154

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
11.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
1.0ms	(cbrt x)
58.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series570.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (cbrt (+ x 1.0)))
113.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
197.0ms	(cbrt x)
164.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify80.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	736	2870
1	1989	2819
2	5002	2746

prune371.0ms

Filtered

166 candidates to 103 candidates (62.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	159	7	166
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	163	12	175

Merged error: 11.3b

Counts

175 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ x 1.0)))
0.3b	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
0.6b	(cbrt x)
9.2b	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

255×	`cbrt-prod`
232×	`add-sqr-sqrt`
88×	`unswap-sqr`
62×	`difference-of-squares`
40×	`*-un-lft-identity`
24×	`cbrt-div`
21×	`swap-sqr`
16×	`add-cube-cbrt`
11×	`associate-l`
7×	`flip3-+` `associate-r` `*-commutative` `flip-+` `distribute-lft-out`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `frac-times` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow1/3`
2×	`associate-r/` `associate-l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 154

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ x 1.0)))
11.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
1.0ms	(cbrt x)
55.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

series548.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (cbrt (+ x 1.0)))
109.0ms	(cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))
182.0ms	(cbrt x)
162.0ms	(- (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0)))) (cbrt x))

simplify80.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	736	2870
1	1989	2819
2	5002	2746

prune421.0ms

Filtered

166 candidates to 105 candidates (63.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	163	15	178

Merged error: 11.3b

Counts

178 → 15

regimes87.0ms

Accuracy

99.2% (0.1b remaining)

Error of 11.4b against oracle of 11.2b and baseline of 29.1b

bsearch102.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	0.0678110794257023
9	-9.882636446590618e+66	-3.181364016106587e+61	-4.5086911354082924e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	48
1	67	48
2	67	48

end0.0ms

sample544.0ms

Algorithm

intervals

Results

186.0ms	1663×	body	1280	valid
105.0ms	1193×	body	640	valid
97.0ms	4200×	body	80	valid
42.0ms	618×	body	320	valid
14.0ms	326×	body	160	valid