Details

sample138.0ms

Algorithm

intervals

Results

54.0ms	113×	body	1280	valid
16.0ms	51×	body	640	valid
10.0ms	24×	body	1280	nan
10.0ms	35×	body	10240	exit
7.0ms	131×	body	80	valid
6.0ms	19×	body	640	nan
6.0ms	153×	body	80	nan
5.0ms	23×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

simplify35.0ms

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: 30.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (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)))

series448.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(pow x (/ 1.0 n))
139.0ms	(pow (+ x 1.0) (/ 1.0 n))
258.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify71.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

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

prune331.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
169.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series699.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow x (/ 1.0 n))
137.0ms	(pow (+ x 1.0) (/ 1.0 n))
257.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
253.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify89.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune520.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ (/ 1.0 n) 2))
1.0b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.0b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.1b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite140.0ms

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))
90.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series589.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow x (/ (/ 1.0 n) 2))
142.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
133.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
262.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify104.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 2 (66.0ms)

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

prune904.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.7b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.1b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
2.1b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
2.1b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

207×	`*-un-lft-identity`
202×	`unpow-prod-down`
172×	`add-sqr-sqrt`
168×	`prod-diff`
136×	`add-cube-cbrt`
67×	`sqr-pow`
66×	`times-frac`
43×	`pow-unpow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
10×	`add-log-exp`
9×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp`

Counts

4 → 330

Calls

4 calls:

14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
87.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
88.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
90.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
263.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
266.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
268.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify118.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	784	7290
1	2796	5302
2	5001	5296

prune944.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.7b

regimes238.0ms

Accuracy

84% (1.4b remaining)

Error of 22.4b against oracle of 21.0b and baseline of 29.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	70
1	53	70

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	3138×	body	1280	valid
562.0ms	1627×	body	640	valid
453.0ms	1100×	body	10240	exit
294.0ms	645×	body	1280	nan
251.0ms	4707×	body	80	valid
208.0ms	643×	body	640	nan
200.0ms	853×	body	320	valid
184.0ms	4912×	body	80	nan
71.0ms	340×	body	320	nan
63.0ms	455×	body	160	valid
22.0ms	198×	body	160	nan