Details

sample207.0ms

Algorithm

intervals

Results

53.0ms	84×	body	1280	nan
50.0ms	113×	body	1280	valid
21.0ms	56×	body	640	nan
18.0ms	54×	body	640	valid
12.0ms	43×	body	10240	exit
8.0ms	194×	body	80	nan
8.0ms	34×	body	320	nan
6.0ms	125×	body	80	valid
5.0ms	24×	body	320	valid
3.0ms	21×	body	160	valid
2.0ms	17×	body	160	nan

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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 1 expressions with local error:

3.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

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:

9.0ms

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

series287.0ms

Counts

1 → 3

Calls

1 calls:

286.0ms

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

simplify74.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	326
1	594	313
2	2745	307
3	5003	307

prune74.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	4	28

Merged error: 22.2b

Counts

28 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(sqrt (pow x (/ 1.0 n)))
0.0b	(sqrt (pow x (/ 1.0 n)))
3.7b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
34×	`sqrt-prod`
20×	`unpow-prod-down`
16×	`difference-of-squares`
13×	`*-un-lft-identity`
12×	`sqr-pow`
9×	`add-cube-cbrt`
7×	`rem-sqrt-square`
6×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`sqrt-pow1` `pow1/2`
2×	`sqrt-div`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 83

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
2.0ms	(sqrt (pow x (/ 1.0 n)))
2.0ms	(sqrt (pow x (/ 1.0 n)))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
81.0ms	(sqrt (pow x (/ 1.0 n)))
81.0ms	(sqrt (pow x (/ 1.0 n)))
483.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify121.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	427	913
1	1246	878
2	4886	866
3	5001	866

prune285.0ms

Filtered

95 candidates to 74 candidates (77.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	95	4	99

Merged error: 22.2b

Counts

99 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- 0.5) (* (pow x 2) n))
0.8b	(/ (log (/ 1 x)) (pow n 2))
4.9b	(* (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))))
11.0b	(* (pow x 2) n)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
94×	`times-frac`
59×	`*-un-lft-identity`
44×	`add-cube-cbrt`
29×	`add-exp-log`
28×	`unpow-prod-down` `log-pow`
25×	`pow1` `associate-r`
21×	`associate-l`
18×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`difference-of-squares`
12×	`unpow2` `sqr-pow`
9×	`pow-flip` `associate-/r*` `inv-pow`
8×	`div-exp` `prod-exp`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `unswap-sqr`
4×	`cbrt-undiv` `div-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `add-log-exp`
3×	`distribute-rgt-in` `frac-times` `pow-to-exp` `log-div` `distribute-lft-in` `associate-*r/` `pow-exp`
2×	`neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `distribute-frac-neg` `clear-num` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`neg-sub0` `log-rec` `pow-prod-down` `associate-*l/`

Counts

4 → 207

Calls

4 calls:

7.0ms	(/ (- 0.5) (* (pow x 2) n))
11.0ms	(/ (log (/ 1 x)) (pow n 2))
44.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))))
5.0ms	(* (pow x 2) n)

series239.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- 0.5) (* (pow x 2) n))
68.0ms	(/ (log (/ 1 x)) (pow n 2))
129.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))))
18.0ms	(* (pow x 2) n)

simplify118.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	892	1593
1	4324	1425
2	5003	1420

prune554.0ms

Filtered

219 candidates to 147 candidates (67.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	211	8	219
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	212	11	223

Merged error: 22.1b

Counts

223 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- 0.5) (* (pow x 2) n))
0.8b	(/ (log (/ 1 x)) (pow n 2))
4.9b	(/ (* 1.0 (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2)))) x)
11.0b	(* (pow x 2) n)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

61×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log`
27×	`log-pow`
25×	`unpow-prod-down`
22×	`pow1`
18×	`add-cbrt-cube`
17×	`associate-/l*`
12×	`associate-/r*`
9×	`pow-flip` `div-exp` `unpow2` `inv-pow` `sqr-pow`
8×	`associate-l`
7×	`prod-exp`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`cbrt-undiv`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `frac-2neg` `associate-r/` `associate-r*` `pow-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
2×	`neg-mul-1` `div-sub` `distribute-frac-neg`
1×	`neg-sub0` `log-div` `flip3--` `log-rec` `*-commutative` `frac-sub` `flip--`

Counts

4 → 168

Calls

4 calls:

6.0ms	(/ (- 0.5) (* (pow x 2) n))
7.0ms	(/ (log (/ 1 x)) (pow n 2))
41.0ms	(/ (* 1.0 (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2)))) x)
5.0ms	(* (pow x 2) n)

series191.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- 0.5) (* (pow x 2) n))
70.0ms	(/ (log (/ 1 x)) (pow n 2))
79.0ms	(/ (* 1.0 (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2)))) x)
18.0ms	(* (pow x 2) n)

simplify88.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	633	1198
1	3048	1043
2	5002	1037

prune422.0ms

Filtered

180 candidates to 119 candidates (66.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	183	8	191

Merged error: 22.1b

Counts

191 → 8

regimes196.0ms

Accuracy

81.6% (2.0b remaining)

Error of 23.4b against oracle of 21.4b and baseline of 32.2b

bsearch208.0ms

Steps

Iters	Range		Point
10	2.731921632534707e-06	2067903636486.0269	2309.126163488031
9	-35960.30255326699	-0.0014566459989916651	-35172.91644639978

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	45
1	62	45

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3880×	body	1280	valid
1.2s	2158×	body	1280	nan
721.0ms	1829×	body	640	nan
601.0ms	1804×	body	640	valid
587.0ms	1396×	body	10240	exit
273.0ms	6186×	body	80	nan
247.0ms	961×	body	320	nan
192.0ms	895×	body	320	valid
151.0ms	3178×	body	80	valid
62.0ms	440×	body	160	nan
57.0ms	418×	body	160	valid

Details

sample207.0ms

simplify34.0ms

prune2.0ms

localize8.0ms

rewrite10.0ms

series287.0ms

simplify74.0ms

prune74.0ms

localize12.0ms

rewrite23.0ms

series676.0ms

simplify121.0ms

prune285.0ms

localize23.0ms

rewrite75.0ms

series239.0ms

simplify118.0ms

prune554.0ms

localize18.0ms

rewrite66.0ms

series191.0ms

simplify88.0ms

prune422.0ms

regimes196.0ms

bsearch208.0ms

simplify2.0ms

end0.0ms

sample6.4s

Profiling