Details

sample130.0ms

Algorithm

intervals

Results

39.0ms	83×	body	1280	valid
15.0ms	46×	body	640	valid
15.0ms	35×	body	10240	exit
9.0ms	28×	body	640	nan
9.0ms	178×	body	80	valid
8.0ms	17×	body	1280	nan
7.0ms	27×	body	320	valid
6.0ms	169×	body	80	nan
3.0ms	22×	body	160	valid
2.0ms	12×	body	320	nan
1.0ms	6×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite53.0ms

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:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series467.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))
267.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune241.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`unpow-prod-down`
27×	`difference-of-squares`
19×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series964.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (+ x 1.0) (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
267.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	359	1142
1	1141	1101
2	5002	1078

prune434.0ms

Filtered

112 candidates to 93 candidates (83.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
32×	`*-un-lft-identity`
24×	`sqr-pow`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(- (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)))
273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify84.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	1304
1	594	1252
2	2745	1228
3	5003	1228

prune487.0ms

Filtered

108 candidates to 92 candidates (85.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.4b

localize26.0ms

Local error

Found 4 expressions with local error:

2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.6b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
32×	`*-un-lft-identity`
24×	`sqr-pow`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

284.0ms	(- (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)))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
284.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify44.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	372	1372
1	1023	1313
2	5002	1296

prune602.0ms

Filtered

108 candidates to 92 candidates (85.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.4b

regimes272.0ms

Accuracy

82.3% (1.5b remaining)

Error of 22.1b against oracle of 20.6b and baseline of 29.1b

bsearch187.0ms

Steps

Iters	Range		Point
6	1.1214764895679895e+25	1.6500185919950112e+26	1.1509948313898308e+25
10	-967231509580097.9	-4.875215488264433	-185656871.63279188

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	76
1	59	76

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3093×	body	1280	valid
555.0ms	1622×	body	640	valid
486.0ms	1145×	body	10240	exit
297.0ms	652×	body	1280	nan
267.0ms	4852×	body	80	valid
217.0ms	672×	body	640	nan
193.0ms	5135×	body	80	nan
190.0ms	872×	body	320	valid
75.0ms	374×	body	320	nan
62.0ms	439×	body	160	valid
24.0ms	193×	body	160	nan