Details

analyze1.1s

Algorithm: search

sample209.0ms

Algorithm

intervals

Results

61.0ms	110×	body	1280	valid
43.0ms	38×	body	1280	nan
23.0ms	54×	body	640	valid
22.0ms	33×	body	640	nan
13.0ms	80×	body	80	overflowed
8.0ms	25×	body	320	valid
5.0ms	8×	body	640	invalid
5.0ms	53×	body	80	valid
4.0ms	10×	body	320	nan
3.0ms	14×	body	160	valid
2.0ms	2×	body	1280	invalid
2.0ms	26×	body	80	nan
1.0ms	9×	body	80	invalid
1.0ms	5×	body	160	nan
0.0ms	2×	body	160	invalid
0.0ms	1×	body	320	invalid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune3.0ms

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: 33.3b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series75.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow x (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
45.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune189.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 22.5b

Counts

89 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite10.0ms

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:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series147.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
23.0ms	(cbrt x)
21.0ms	(cbrt x)
82.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	370	561
1	1262	511
2	5002	465

prune138.0ms

Filtered

46 candidates to 57 candidates (-23.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Merged error: 22.1b

Counts

63 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
0.0b	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
1.8b	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

60×	`unpow-prod-down`
58×	`add-sqr-sqrt`
46×	`cbrt-prod`
34×	`*-un-lft-identity`
27×	`difference-of-squares`
25×	`cube-prod` `sqr-pow`
22×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1` `pow-exp` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `rem-cbrt-cube` `div-inv` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 134

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
6.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
17.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
17.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
38.0ms	(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
40.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify68.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	620	1351
1	2217	1298
2	5001	1287

prune245.0ms

Filtered

85 candidates to 146 candidates (-71.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	144	10	154

Merged error: 22.1b

Counts

154 → 10

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ 1 (* x n))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`pow1` `div-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `prod-exp` `associate-/l`
2×	`cbrt-undiv` `rec-exp` `pow-flip` `1-exp`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `inv-pow` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

5.0ms

(/ 1 (* x n))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ 1 (* x n))

simplify53.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	109	91
1	417	76
2	1585	70
3	3452	70
4	5001	70

prune26.0ms

Filtered

13 candidates to 31 candidates (-138.5%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	25	6	31
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	26	15	41

Merged error: 22.1b

Counts

41 → 15

regimes372.0ms

Accuracy

85.8% (1.6b remaining)

Error of 23.3b against oracle of 21.7b and baseline of 33.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

analyze1.1s

Algorithm: search

sample6.4s

Algorithm

intervals

Results

2.1s	3855×	body	1280	valid
1.2s	1072×	body	1280	nan
661.0ms	1512×	body	640	valid
617.0ms	878×	body	640	nan
456.0ms	2655×	body	80	overflowed
224.0ms	731×	body	320	valid
187.0ms	445×	body	320	nan
146.0ms	210×	body	640	invalid
142.0ms	1528×	body	80	valid
123.0ms	101×	body	1280	invalid
71.0ms	374×	body	160	valid
67.0ms	159×	body	320	invalid
47.0ms	214×	body	160	nan
35.0ms	517×	body	80	nan
26.0ms	214×	body	80	invalid
18.0ms	76×	body	160	invalid

Details

analyze1.1s

sample209.0ms

simplify34.0ms

prune3.0ms

localize8.0ms

rewrite20.0ms

series75.0ms

simplify53.0ms

prune189.0ms

localize13.0ms

rewrite10.0ms

series147.0ms

simplify36.0ms

prune138.0ms

localize10.0ms

rewrite38.0ms

series113.0ms

simplify68.0ms

prune245.0ms

localize9.0ms

rewrite6.0ms

series3.0ms

simplify53.0ms

prune26.0ms

regimes372.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

analyze1.1s

sample6.4s

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