Details

sample516.0ms

Algorithm

intervals

Results

179.0ms	124×	body	1280	valid
81.0ms	57×	body	1280	nan
63.0ms	62×	body	640	valid
58.0ms	62×	body	640	nan
41.0ms	39×	body	10240	exit
20.0ms	39×	body	320	nan
19.0ms	25×	body	320	valid
13.0ms	210×	body	80	nan
11.0ms	105×	body	80	valid
7.0ms	19×	body	160	valid
5.0ms	15×	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: 33.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite55.0ms

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))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series486.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(pow x (/ 1.0 n))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (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

prune238.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 24.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
0.6b	(cbrt n)
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
17×	`unpow-prod-down`
15×	`difference-of-squares`
11×	`sqr-pow`
9×	`cbrt-prod` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 61

Calls

4 calls:

0.0ms	(cbrt n)
0.0ms	(cbrt n)
1.0ms	(cbrt n)
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

series1.2s

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt n)
175.0ms	(cbrt n)
175.0ms	(cbrt n)
695.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

simplify97.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	315	1017
1	824	975
2	3586	963
3	5001	963

prune299.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
0.6b	(cbrt n)
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
17×	`unpow-prod-down`
15×	`difference-of-squares`
11×	`sqr-pow`
9×	`cbrt-prod` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 61

Calls

4 calls:

0.0ms	(cbrt n)
0.0ms	(cbrt n)
1.0ms	(cbrt n)
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt n)
180.0ms	(cbrt n)
183.0ms	(cbrt n)
568.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

simplify106.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	315	1017
1	824	975
2	3586	963
3	5001	963

prune361.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
2.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
51×	`unpow-prod-down`
45×	`difference-of-squares`
33×	`sqr-pow`
11×	`*-un-lft-identity`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-prod` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
1×	`pow1/3`

Counts

4 → 95

Calls

4 calls:

1.0ms	(cbrt n)
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

series1.9s

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt n)
579.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
585.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
583.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

simplify111.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	315	2739
1	824	2637
2	3586	2617
3	5001	2617

prune683.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.4b

regimes198.0ms

Accuracy

84% (1.7b remaining)

Error of 23.9b against oracle of 22.2b and baseline of 33.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	85
1	44	85

end0.0ms

sample16.1s

Algorithm

intervals

Results

5.6s	3894×	body	1280	valid
3.1s	2160×	body	1280	nan
1.8s	1768×	body	640	valid
1.7s	1761×	body	640	nan
1.4s	1367×	body	10240	exit
530.0ms	858×	body	320	valid
442.0ms	867×	body	320	nan
390.0ms	6179×	body	80	nan
336.0ms	3098×	body	80	valid
168.0ms	444×	body	160	valid
138.0ms	445×	body	160	nan