Details

sample124.0ms

Algorithm

intervals

Results

53.0ms	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	14×	body	160	valid
2.0ms	9×	body	320	nan
0.0ms	2×	body	160	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize9.0ms

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)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
91.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series442.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(pow x (/ 1.0 n))
138.0ms	(pow (+ x 1.0) (/ 1.0 n))
251.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify70.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune329.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.6b

localize12.0ms

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)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

7.0ms	(pow x (/ (/ 1.0 n) 2))
13.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
13.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
92.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series575.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow x (/ (/ 1.0 n) 2))
137.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
131.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
256.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify98.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	985	3525
1	3500	2856
2	5001	2853

prune869.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.7b

localize15.0ms

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)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

7.0ms	(pow x (/ (/ 1.0 n) 2))
15.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
13.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
92.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow x (/ (/ 1.0 n) 2))
142.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
134.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
257.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify99.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	985	3525
1	3500	2856
2	5001	2853

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.7b

localize19.0ms

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))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`add-cube-cbrt`
26×	`pow-unpow`
19×	`cbrt-prod`
18×	`unpow-prod-down` `times-frac`
13×	`pow1`
8×	`add-exp-log` `fma-neg` `prod-diff`
7×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unswap-sqr` `sqr-pow`
3×	`pow-pow` `distribute-lft-out`
2×	`pow-to-exp` `pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 135

Calls

4 calls:

12.0ms	(* (cbrt x) (cbrt x))
5.0ms	(pow (cbrt x) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
84.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

series829.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt x) (cbrt x))
91.0ms	(pow (cbrt x) (/ 1.0 n))
133.0ms	(pow (+ x 1.0) (/ 1.0 n))
406.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (pow (cbrt x) (/ 1.0 n))))

simplify79.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	744	1352
1	3019	1236
2	5001	1214

prune483.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.6b

regimes243.0ms

Accuracy

83.6% (1.5b remaining)

Error of 21.8b against oracle of 20.3b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	43
1	50	43

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	3140×	body	1280	valid
544.0ms	1581×	body	640	valid
252.0ms	4755×	body	80	valid
194.0ms	5110×	body	80	nan
184.0ms	840×	body	320	valid
152.0ms	164×	body	1280	nan
137.0ms	2367×	body	80	overflowed
133.0ms	275×	body	640	nan
62.0ms	451×	body	160	valid
36.0ms	153×	body	320	nan
11.0ms	86×	body	160	nan