Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample223.0ms

Algorithm

intervals

Results

63.0ms	109×	body	1280	valid
47.0ms	41×	body	1280	nan
26.0ms	57×	body	640	valid
18.0ms	25×	body	640	nan
14.0ms	80×	body	80	overflowed
11.0ms	34×	body	320	valid
7.0ms	16×	body	320	nan
7.0ms	9×	body	640	invalid
5.0ms	4×	body	1280	invalid
4.0ms	48×	body	80	valid
2.0ms	8×	body	160	valid
1.0ms	5×	body	160	nan
1.0ms	17×	body	80	nan
1.0ms	6×	body	80	invalid
1.0ms	3×	body	160	invalid
1.0ms	2×	body	320	invalid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4852	13
1	4852	13

prune4.0ms

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: 33.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite23.0ms

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 → 78

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series70.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow x (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify61.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4964	1240
1	4964	1240

prune190.0ms

Filtered

69 candidates to 87 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 22.8b

Counts

88 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite11.0ms

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 → 44

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
21.0ms	(cbrt x)
22.0ms	(cbrt x)
84.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify45.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4986	748
1	4986	748

prune149.0ms

Filtered

43 candidates to 56 candidates (-30.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	54	6	60

Merged error: 22.6b

Counts

60 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (exp (log (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
4.3b	(exp (log (cbrt x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod` `exp-sum` `add-log-exp`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`log-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (exp (log (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
3.0ms	(exp (log (cbrt x)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt x)
22.0ms	(cbrt x)
84.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (exp (log (cbrt x)))) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))
21.0ms	(exp (log (cbrt x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4978	789
1	4978	789

prune157.0ms

Filtered

49 candidates to 64 candidates (-30.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	64	6	70

Merged error: 22.6b

Counts

70 → 6

localize22.0ms

Local error

Found 3 expressions with local error:

0.5b	(/ 1.0 (* x n))
6.2b	(/ (pow (log 1) 2) (* n n))
6.2b	(/ (log 1) (* n n))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
18×	`add-cbrt-cube`
16×	`times-frac` `associate-/l*`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`div-exp`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv`
5×	`prod-exp`
4×	`log-pow`
3×	`frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

3 → 81

Calls

3 calls:

4.0ms	(/ 1.0 (* x n))
6.0ms	(/ (pow (log 1) 2) (* n n))
5.0ms	(/ (log 1) (* n n))

series29.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/ 1.0 (* x n))
14.0ms	(/ (pow (log 1) 2) (* n n))
12.0ms	(/ (log 1) (* n n))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4952	657
1	4952	657

prune168.0ms

Filtered

56 candidates to 90 candidates (-60.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	86	4	90
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	86	10	96

Merged error: 22.3b

Counts

96 → 10

regimes332.0ms

Accuracy

84.7% (1.7b remaining)

Error of 23.6b against oracle of 21.9b and baseline of 33.0b

bsearch78.0ms

Steps

Iters	Range		Point
4	2.357510937174305e+17	3.361581068865142e+17	2.3813994208623306e+17
7	-93.8314579326654	-3.6435235945322955	-92.67036924943247

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	181	106
1	181	106

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.1s	3816×	body	1280	valid
1.2s	1130×	body	1280	nan
668.0ms	1486×	body	640	valid
630.0ms	880×	body	640	nan
500.0ms	2788×	body	80	overflowed
243.0ms	760×	body	320	valid
202.0ms	447×	body	320	nan
181.0ms	254×	body	640	invalid
146.0ms	1546×	body	80	valid
139.0ms	112×	body	1280	invalid
87.0ms	194×	body	320	invalid
79.0ms	392×	body	160	valid
47.0ms	206×	body	160	nan
31.0ms	237×	body	80	invalid
30.0ms	504×	body	80	nan
25.0ms	85×	body	160	invalid

Details

analyze1.1s

sample223.0ms

simplify54.0ms

prune4.0ms

localize8.0ms

rewrite23.0ms

series70.0ms

simplify61.0ms

prune190.0ms

localize16.0ms

rewrite11.0ms

series149.0ms

simplify45.0ms

prune149.0ms

localize19.0ms

rewrite15.0ms

series149.0ms

simplify45.0ms

prune157.0ms

localize22.0ms

rewrite18.0ms

series29.0ms

simplify58.0ms

prune168.0ms

regimes332.0ms

bsearch78.0ms

simplify3.0ms

end0.0ms

sample6.7s

Profiling