Details

sample128.0ms

Algorithm

intervals

Results

49.0ms	107×	body	1280	valid
15.0ms	45×	body	640	valid
10.0ms	19×	body	1280	nan
8.0ms	29×	body	10240	exit
7.0ms	131×	body	80	valid
7.0ms	24×	body	640	nan
6.0ms	29×	body	320	valid
5.0ms	152×	body	80	nan
2.0ms	11×	body	320	nan
2.0ms	15×	body	160	valid
0.0ms	3×	body	160	nan

simplify36.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite64.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series480.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune339.0ms

Filtered

158 candidates to 95 candidates (60.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 300

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series991.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (+ x 1.0) (/ 1.0 n))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify94.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	542	5691
1	1694	4129
2	5001	4126

prune779.0ms

Filtered

312 candidates to 158 candidates (50.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 300

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
55.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

149.0ms	(pow (+ x 1.0) (/ 1.0 n))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
477.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify122.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	867	6070
1	2705	4345
2	5001	4341

prune1.0s

Filtered

312 candidates to 158 candidates (50.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

localize25.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.0b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

260×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
87×	`sqr-pow`
61×	`log-prod`
58×	`exp-sum`
36×	`difference-of-squares`
35×	`distribute-lft-out`
24×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 358

Calls

4 calls:

50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
103.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
52.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
277.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify125.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	917	7670
1	2478	5419
2	5001	4815

prune1.2s

Filtered

370 candidates to 172 candidates (46.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.8b

regimes263.0ms

Accuracy

82.1% (1.5b remaining)

Error of 22.8b against oracle of 21.4b and baseline of 29.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	54
1	60	54

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	3200×	body	1280	valid
525.0ms	1546×	body	640	valid
441.0ms	1113×	body	10240	exit
283.0ms	595×	body	1280	nan
247.0ms	4679×	body	80	valid
206.0ms	926×	body	320	valid
192.0ms	601×	body	640	nan
180.0ms	5039×	body	80	nan
73.0ms	385×	body	320	nan
57.0ms	429×	body	160	valid
20.0ms	188×	body	160	nan