Details

analyze1.2s

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

sample207.0ms

Algorithm

intervals

Results

59.0ms	109×	body	1280	valid
41.0ms	37×	body	1280	nan
32.0ms	65×	body	640	valid
16.0ms	97×	body	80	overflowed
15.0ms	24×	body	640	nan
8.0ms	26×	body	320	valid
5.0ms	12×	body	320	nan
5.0ms	3×	body	1280	invalid
4.0ms	51×	body	80	valid
4.0ms	5×	body	640	invalid
1.0ms	4×	body	320	invalid
1.0ms	17×	body	80	nan
1.0ms	5×	body	160	valid
1.0ms	6×	body	80	invalid
0.0ms	2×	body	160	invalid
0.0ms	2×	body	160	nan

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5058	13

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: 33.9b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.1b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

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))
8.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series70.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(pow x (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify38.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4992	1200
1	4992	1200

prune184.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 25.4b

Counts

88 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.6b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
40×	`sqrt-prod`
38×	`unpow-prod-down`
34×	`*-un-lft-identity`
32×	`difference-of-squares`
26×	`pow-unpow`
24×	`add-cube-cbrt`
20×	`associate-r`
18×	`times-frac` `sqr-pow`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `associate-l` `flip--`
3×	`sub-neg` `flip3-+` `flip-+` `distribute-lft-out`
2×	`pow-to-exp` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv` `distribute-lft-out--`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 142

Calls

4 calls:

29.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series240.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))))
29.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
31.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
55.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify41.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5523	3539

prune542.0ms

Filtered

110 candidates to 154 candidates (-40.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	149	5	154
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	151	9	160

Merged error: 25.4b

Counts

160 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))) 3))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.1b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
2.6b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt`
70×	`unpow-prod-down`
56×	`sqrt-prod`
48×	`difference-of-squares`
46×	`cbrt-prod`
35×	`*-un-lft-identity`
27×	`sqr-pow`
26×	`pow-unpow`
25×	`add-cube-cbrt`
20×	`cube-prod`
18×	`times-frac`
8×	`pow1`
6×	`add-exp-log` `pow-pow` `add-log-exp`
4×	`add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-pow2` `flip--` `div-inv` `distribute-lft-out`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 153

Calls

4 calls:

15.0ms	(cbrt (pow (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))) 3))
8.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series176.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (pow (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))) 3))
29.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
29.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
58.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify41.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5160	3690

prune489.0ms

Filtered

98 candidates to 165 candidates (-68.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	166	8	174

Merged error: 25.4b

Counts

174 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fabs (cbrt (+ x 1.0))) (/ 1.0 n))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
2.6b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
16×	`sqrt-prod` `difference-of-squares`
15×	`unpow-prod-down`
14×	`add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac` `sqr-pow`
8×	`cbrt-prod`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `add-cbrt-cube`
2×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 83

Calls

4 calls:

3.0ms	(pow (fabs (cbrt (+ x 1.0))) (/ 1.0 n))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series83.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (fabs (cbrt (+ x 1.0))) (/ 1.0 n))
6.0ms	(cbrt (+ x 1.0))
6.0ms	(cbrt (+ x 1.0))
58.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify42.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4936	1692
1	4936	1692

prune404.0ms

Filtered

72 candidates to 95 candidates (-31.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Merged error: 25.4b

Counts

103 → 8

regimes395.0ms

Accuracy

86.5% (1.4b remaining)

Error of 23.9b against oracle of 22.5b and baseline of 33.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	115
1	48	115

end0.0ms

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

sample6.5s

Algorithm

intervals

Results

2.1s	3814×	body	1280	valid
1.2s	1100×	body	1280	nan
694.0ms	1563×	body	640	valid
596.0ms	868×	body	640	nan
482.0ms	2737×	body	80	overflowed
228.0ms	756×	body	320	valid
187.0ms	447×	body	320	nan
153.0ms	222×	body	640	invalid
142.0ms	1522×	body	80	valid
115.0ms	87×	body	1280	invalid
73.0ms	345×	body	160	valid
67.0ms	169×	body	320	invalid
47.0ms	213×	body	160	nan
32.0ms	522×	body	80	nan
29.0ms	236×	body	80	invalid
23.0ms	81×	body	160	invalid

Details

analyze1.2s

sample207.0ms

simplify40.0ms

prune3.0ms

localize8.0ms

rewrite19.0ms

series70.0ms

simplify38.0ms

prune184.0ms

localize13.0ms

rewrite57.0ms

series240.0ms

simplify41.0ms

prune542.0ms

localize16.0ms

rewrite47.0ms

series176.0ms

simplify41.0ms

prune489.0ms

localize23.0ms

rewrite24.0ms

series83.0ms

simplify42.0ms

prune404.0ms

regimes395.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

analyze1.1s

sample6.5s

Profiling