Details

sample4.1s

Algorithm

intervals

sampling

Space saved by range analysis: 37.31102%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

61.0ms	114×	body	1280	valid
30.0ms	29×	body	1280	nan
27.0ms	34×	body	640	nan
23.0ms	54×	body	640	valid
15.0ms	87×	body	80	overflowed
7.0ms	16×	body	320	nan
7.0ms	5×	body	1280	invalid
5.0ms	60×	body	80	valid
5.0ms	18×	body	320	valid
2.0ms	6×	body	320	invalid
2.0ms	10×	body	160	valid
2.0ms	3×	body	640	invalid
1.0ms	16×	body	80	nan
1.0ms	3×	body	160	nan
1.0ms	5×	body	80	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: 30.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
3.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 51

Calls

2 calls:

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

series57.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	520
1	1648	503
2	5001	478

prune129.0ms

Filtered

47 candidates to 57 candidates (-21.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 19.5b

Counts

58 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(cbrt (pow (pow x (/ 1.0 n)) 3))
0.0b	(pow (pow x (/ 1.0 n)) 3)
3.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
53×	`unpow-prod-down`
44×	`cbrt-prod`
27×	`difference-of-squares`
25×	`sqr-pow`
24×	`*-un-lft-identity`
23×	`cube-prod`
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`
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 → 129

Calls

4 calls:

3.0ms	(pow x (/ 1.0 n))
4.0ms	(cbrt (pow (pow x (/ 1.0 n)) 3))
4.0ms	(pow (pow x (/ 1.0 n)) 3)
15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series84.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow x (/ 1.0 n))
12.0ms	(cbrt (pow (pow x (/ 1.0 n)) 3))
22.0ms	(pow (pow x (/ 1.0 n)) 3)
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify74.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	716	1309
1	2705	1262
2	5001	1230

prune232.0ms

Filtered

85 candidates to 141 candidates (-65.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	140	1	141
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	141	4	145

Merged error: 19.5b

Counts

145 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (log (/ 1 x)) (* x (pow n 2)))
2.5b	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
8.4b	(* x (pow n 2))
9.1b	(/ (/ 0.5 n) (pow x 2))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

191×	`times-frac`
106×	`add-sqr-sqrt`
100×	`add-cube-cbrt` `*-un-lft-identity`
46×	`unpow-prod-down`
32×	`add-exp-log`
19×	`associate-/l*`
16×	`add-cbrt-cube` `unpow2` `sqr-pow`
13×	`div-exp`
11×	`div-inv`
9×	`associate-/r*`
8×	`pow1` `associate-r`
6×	`associate-+r+` `prod-exp` `log-pow` `add-log-exp`
5×	`cbrt-undiv`
4×	`pow-to-exp` `pow-exp` `unswap-sqr`
3×	`distribute-rgt-in` `log-div` `distribute-lft-in` `div-sub` `associate-l`
2×	`sub-neg` `pow-flip` `frac-2neg` `sub0-neg` `associate-*r/` `frac-add` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod` `inv-pow` `associate--r-`
1×	`+-commutative` `flip3--` `flip3-+` `distribute-frac-neg` `unsub-neg` `log-rec` `sum-log` `*-commutative` `flip--` `flip-+` `associate-/l/`

Counts

4 → 223

Calls

4 calls:

7.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
14.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
5.0ms	(* x (pow n 2))
8.0ms	(/ (/ 0.5 n) (pow x 2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
13.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
6.0ms	(* x (pow n 2))
6.0ms	(/ (/ 0.5 n) (pow x 2))

simplify154.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	1037	1834
1	4830	1606
2	5001	1605

prune476.0ms

Filtered

147 candidates to 235 candidates (-59.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	228	7	235
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	229	10	239

Merged error: 19.4b

Counts

239 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 0.5 (pow (cbrt x) 4))
2.5b	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
2.8b	(* (/ 0.5 (pow (cbrt x) 4)) (/ (/ 1 n) (pow (cbrt x) 2)))
8.4b	(* x (pow n 2))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

491×	`times-frac`
451×	`add-sqr-sqrt`
192×	`*-un-lft-identity`
188×	`add-exp-log`
186×	`unpow-prod-down`
167×	`add-cube-cbrt`
155×	`associate-r`
114×	`div-exp`
91×	`cbrt-prod`
84×	`unswap-sqr`
55×	`prod-exp`
53×	`sqr-pow`
37×	`associate-l`
31×	`pow-to-exp` `pow-exp`
30×	`unpow2`
29×	`add-cbrt-cube`
14×	`div-inv`
12×	`rec-exp` `1-exp`
10×	`cbrt-undiv` `associate-/r*`
7×	`cbrt-unprod`
6×	`pow1` `associate-+r+` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-/l`
2×	`sub-neg` `log-div` `sub0-neg` `div-sub` `frac-add` `*-commutative` `distribute-rgt-neg-out` `associate--r-`
1×	`+-commutative` `frac-times` `flip3--` `frac-2neg` `flip3-+` `unsub-neg` `pow-prod-down` `associate-*l/` `clear-num` `sum-log` `flip--` `flip-+`

Counts

4 → 436

Calls

4 calls:

5.0ms	(/ 0.5 (pow (cbrt x) 4))
13.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
88.0ms	(* (/ 0.5 (pow (cbrt x) 4)) (/ (/ 1 n) (pow (cbrt x) 2)))
5.0ms	(* x (pow n 2))

series65.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 0.5 (pow (cbrt x) 4))
13.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
8.0ms	(* (/ 0.5 (pow (cbrt x) 4)) (/ (/ 1 n) (pow (cbrt x) 2)))
7.0ms	(* x (pow n 2))

simplify88.0ms

Algorithm

egg-herbie

Counts

448 → 448

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2388	5251
1	5001	4797

prune1.3s

Filtered

269 candidates to 448 candidates (-66.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	446	2	448
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	448	10	458

Merged error: 19.4b

Counts

458 → 10

regimes326.0ms

Accuracy

81.7% (2.0b remaining)

Error of 23.9b against oracle of 21.9b and baseline of 33.0b

bsearch121.0ms

Steps

Iters	Range		Point
7	12.915300556607248	382.23319458364557	377.3545087368791
7	-3751055200892.781	-39483352177.47715	-43883455996.70513

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	34
1	56	34
2	59	34
3	59	34

end0.0ms

sample10.7s

Algorithm

intervals

sampling

Space saved by range analysis: 37.31102%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

2.1s	3845×	body	1280	valid
1.2s	1096×	body	1280	nan
719.0ms	1601×	body	640	valid
639.0ms	908×	body	640	nan
481.0ms	2704×	body	80	overflowed
242.0ms	507×	body	80	nan
205.0ms	668×	body	320	valid
186.0ms	441×	body	320	nan
172.0ms	242×	body	640	invalid
150.0ms	115×	body	1280	invalid
142.0ms	1539×	body	80	valid
81.0ms	179×	body	320	invalid
68.0ms	347×	body	160	valid
45.0ms	187×	body	160	nan
17.0ms	132×	body	80	invalid
13.0ms	54×	body	160	invalid

Details

sample4.1s

simplify33.0ms

prune3.0ms

localize8.0ms

rewrite14.0ms

series57.0ms

simplify43.0ms

prune129.0ms

localize13.0ms

rewrite30.0ms

series84.0ms

simplify74.0ms

prune232.0ms

localize22.0ms

rewrite44.0ms

series42.0ms

simplify154.0ms

prune476.0ms

localize26.0ms

rewrite146.0ms

series65.0ms

simplify88.0ms

prune1.3s

regimes326.0ms

bsearch121.0ms

simplify2.0ms

end0.0ms

sample10.7s

Profiling