Details

sample132.0ms

Algorithm

intervals

Results

49.0ms	107×	body	1280	valid
16.0ms	45×	body	640	valid
10.0ms	19×	body	1280	nan
10.0ms	131×	body	80	valid
8.0ms	29×	body	10240	exit
7.0ms	24×	body	640	nan
7.0ms	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

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: 31.3b

localize8.0ms

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)))

rewrite54.0ms

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))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series477.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune237.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
3.9b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
34×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 96

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
58.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series724.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
281.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify39.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	332	872
1	1120	760
2	5002	718

prune361.0ms

Filtered

108 candidates to 85 candidates (78.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
3.9b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
3.9b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
3.9b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
57.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
56.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
58.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series991.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
281.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
279.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
280.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	332	1272
1	1120	984
2	5002	874

prune346.0ms

Filtered

76 candidates to 63 candidates (82.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
2.4b	(log (* (exp (- (pow x (/ 1.0 n)))) (exp (pow (+ x 1.0) (/ 1.0 n)))))
3.9b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
3.9b	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`pow-unpow`
12×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
8×	`pow1` `unpow-prod-down` `exp-prod` `add-log-exp`
6×	`add-exp-log` `log-pow`
4×	`pow-prod-up` `add-cbrt-cube`
3×	`distribute-rgt-neg-in`
2×	`sub-neg` `log-div` `flip3--` `diff-log` `rem-log-exp` `associate-*l/` `flip--` `distribute-lft-out`
1×	`neg-sub0` `exp-neg` `pow-to-exp` `log-prod` `pow-pow` `exp-diff` `pow-prod-down` `pow-exp` `prod-exp` `div-inv` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
75.0ms	(log (* (exp (- (pow x (/ 1.0 n)))) (exp (pow (+ x 1.0) (/ 1.0 n)))))
57.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
59.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series1.2s

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
497.0ms	(log (* (exp (- (pow x (/ 1.0 n)))) (exp (pow (+ x 1.0) (/ 1.0 n)))))
290.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))
285.0ms	(- (* (* (cbrt (pow (+ x 1.0) (/ 1.0 n))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	391	1078
1	1349	684
2	5001	633

prune383.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.6b

regimes174.0ms

Accuracy

82.6% (1.5b remaining)

Error of 22.5b against oracle of 21.0b and baseline of 29.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	70
1	41	70

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	3200×	body	1280	valid
525.0ms	1546×	body	640	valid
443.0ms	1113×	body	10240	exit
288.0ms	595×	body	1280	nan
249.0ms	4679×	body	80	valid
207.0ms	926×	body	320	valid
192.0ms	601×	body	640	nan
191.0ms	5039×	body	80	nan
78.0ms	385×	body	320	nan
58.0ms	429×	body	160	valid
21.0ms	188×	body	160	nan