Details

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.359131%

Guaranteed chance to sample good point: 62.745571%

Results

68.0ms	123×	body	1280	valid
30.0ms	28×	body	1280	nan
21.0ms	48×	body	640	valid
19.0ms	24×	body	640	nan
8.0ms	26×	body	320	valid
5.0ms	12×	body	320	nan
5.0ms	7×	body	640	invalid
5.0ms	50×	body	80	valid
3.0ms	2×	body	1280	invalid
2.0ms	9×	body	160	valid
2.0ms	4×	body	320	invalid
1.0ms	6×	body	80	invalid
1.0ms	3×	body	160	nan
0.0ms	6×	body	80	nan
0.0ms	2×	body	80	overflowed
0.0ms	1×	body	160	invalid

simplify33.0ms

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: 32.8b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

12.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify95.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	280	352
1	785	337
2	3548	329
3	5001	329

prune84.0ms

Filtered

23 candidates to 27 candidates (-17.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Merged error: 22.1b

Counts

28 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
0.0b	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
56×	`unpow-prod-down`
45×	`*-un-lft-identity`
36×	`sqrt-prod`
32×	`difference-of-squares`
23×	`associate-r`
16×	`sqr-pow`
13×	`distribute-lft-out`
8×	`distribute-lft-out--` `add-log-exp`
7×	`pow1` `add-cube-cbrt` `associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`frac-times` `flip3--` `flip--`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `associate-r/` `associate-l/`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
14.0ms	(+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
29.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
65.0ms	(+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
198.0ms	(* (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
107.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify86.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	690	2178
1	3001	2029
2	5001	2017

prune392.0ms

Filtered

92 candidates to 129 candidates (-40.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	128	6	134

Merged error: 22.1b

Counts

134 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
88×	`unpow-prod-down`
64×	`difference-of-squares`
48×	`sqrt-prod`
41×	`*-un-lft-identity`
32×	`sqr-pow`
23×	`cbrt-prod`
16×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 129

Calls

4 calls:

12.0ms	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series779.0ms

Counts

4 → 12

Calls

4 calls:

456.0ms	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
106.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
106.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
111.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	554	2652
1	2016	2567
2	5001	2524

prune832.0ms

Filtered

96 candidates to 141 candidates (-46.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	141	6	147

Merged error: 22.1b

Counts

147 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
2.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
88×	`unpow-prod-down`
64×	`difference-of-squares`
48×	`sqrt-prod`
40×	`*-un-lft-identity`
32×	`sqr-pow`
16×	`distribute-lft-out--`
12×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 128

Calls

4 calls:

14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
103.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
105.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify157.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	280	2376
1	961	2296
2	4702	2264
3	5003	2264

prune1.2s

Filtered

96 candidates to 140 candidates (-45.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	140	6	146

Merged error: 22.1b

Counts

146 → 6

regimes400.0ms

Accuracy

83% (1.8b remaining)

Error of 24.2b against oracle of 22.3b and baseline of 33.2b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	72
1	69	72
2	72	72
3	72	72

end0.0ms

sample8.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 49.359131%

Guaranteed chance to sample good point: 62.745571%

Results

2.1s	3785×	body	1280	valid
1.1s	1039×	body	1280	nan
730.0ms	1569×	body	640	valid
638.0ms	881×	body	640	nan
230.0ms	729×	body	320	valid
196.0ms	453×	body	320	nan
171.0ms	242×	body	640	invalid
147.0ms	1577×	body	80	valid
146.0ms	109×	body	1280	invalid
73.0ms	168×	body	320	invalid
71.0ms	340×	body	160	valid
58.0ms	221×	body	160	nan
16.0ms	259×	body	80	nan
14.0ms	111×	body	80	invalid
13.0ms	52×	body	160	invalid
10.0ms	62×	body	80	overflowed

Details

sample2.5s

simplify33.0ms

prune3.0ms

localize8.0ms

rewrite13.0ms

series41.0ms

simplify95.0ms

prune84.0ms

localize12.0ms

rewrite64.0ms

series374.0ms

simplify86.0ms

prune392.0ms

localize17.0ms

rewrite58.0ms

series779.0ms

simplify66.0ms

prune832.0ms

localize21.0ms

rewrite58.0ms

series417.0ms

simplify157.0ms

prune1.2s

regimes400.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

sample8.6s

Profiling