Details

sample125.0ms

Algorithm

intervals

Results

52.0ms	112×	body	1280	valid
13.0ms	38×	body	640	valid
8.0ms	9×	body	1280	nan
7.0ms	143×	body	80	valid
6.0ms	26×	body	320	valid
6.0ms	159×	body	80	nan
4.0ms	9×	body	640	nan
4.0ms	75×	body	80	overflowed
2.0ms	9×	body	320	nan
2.0ms	14×	body	160	valid
0.0ms	2×	body	160	nan

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize8.0ms

Local error

Found 3 expressions with local error:

1.2b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite98.0ms

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 → 79

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
79.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series441.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(pow x (/ 1.0 n))
131.0ms	(pow (+ x 1.0) (/ 1.0 n))
255.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune247.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.8b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ (/ 1.0 n) 2))
1.5b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.5b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.3b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
129×	`pow-unpow`
124×	`add-sqr-sqrt`
123×	`*-un-lft-identity`
112×	`add-cube-cbrt`
21×	`unpow-prod-down`
12×	`div-inv`
9×	`difference-of-squares` `sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 197

Calls

4 calls:

8.0ms	(pow x (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
79.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow x (/ (/ 1.0 n) 2))
138.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
134.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
258.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify72.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	807	1617
1	2937	1584
2	5001	1584

prune779.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ (/ 1.0 n) 2))
1.5b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.5b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.3b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
129×	`pow-unpow`
124×	`add-sqr-sqrt`
123×	`*-un-lft-identity`
112×	`add-cube-cbrt`
21×	`unpow-prod-down`
12×	`div-inv`
9×	`difference-of-squares` `sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 197

Calls

4 calls:

8.0ms	(pow x (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
15.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
80.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series592.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow x (/ (/ 1.0 n) 2))
134.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
140.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
259.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify67.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	807	1617
1	2937	1584
2	5001	1584

prune921.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt x) (cbrt x))
1.2b	(pow (cbrt x) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
3.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
26×	`pow-unpow`
19×	`cbrt-prod`
18×	`times-frac`
13×	`pow1`
10×	`unpow-prod-down`
8×	`add-exp-log`
7×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`add-cbrt-cube` `unswap-sqr`
3×	`pow-pow`
2×	`pow-to-exp` `pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv` `sqr-pow`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 111

Calls

4 calls:

11.0ms	(* (cbrt x) (cbrt x))
5.0ms	(pow (cbrt x) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series831.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(* (cbrt x) (cbrt x))
92.0ms	(pow (cbrt x) (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))
404.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify75.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	685	945
1	2778	881
2	5002	861

prune405.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.6b

regimes237.0ms

Accuracy

83.7% (1.5b remaining)

Error of 21.8b against oracle of 20.4b and baseline of 29.4b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	3140×	body	1280	valid
533.0ms	1581×	body	640	valid
241.0ms	4755×	body	80	valid
183.0ms	5110×	body	80	nan
182.0ms	840×	body	320	valid
151.0ms	164×	body	1280	nan
138.0ms	275×	body	640	nan
132.0ms	2367×	body	80	overflowed
61.0ms	451×	body	160	valid
35.0ms	153×	body	320	nan
11.0ms	86×	body	160	nan