Details

sample228.0ms

Algorithm

intervals

Results

66.0ms	118×	body	1280	valid
32.0ms	32×	body	1280	nan
25.0ms	60×	body	640	valid
21.0ms	142×	body	80	overflowed
21.0ms	30×	body	640	nan
15.0ms	102×	body	80	valid
10.0ms	207×	body	80	nan
8.0ms	17×	body	320	nan
7.0ms	24×	body	320	valid
3.0ms	17×	body	160	valid
2.0ms	9×	body	160	nan

simplify34.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.1b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

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:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts

3 → 9

Calls

3 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(pow x (/ 1.0 n))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune196.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 21.7b

Counts

89 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

11.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series756.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
63.0ms	(pow x (/ 1.0 n))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify67.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	686	1271
1	2625	1268
2	5001	1266

prune309.0ms

Filtered

138 candidates to 95 candidates (68.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	135	7	142

Merged error: 21.7b

Counts

142 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

12.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series771.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(pow x (/ 1.0 n))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	686	1271
1	2625	1268
2	5001	1266

prune380.0ms

Filtered

138 candidates to 95 candidates (68.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	138	7	145

Merged error: 21.7b

Counts

145 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

16.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))
63.0ms	(pow x (/ 1.0 n))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify75.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	686	1271
1	2625	1268
2	5001	1266

prune420.0ms

Filtered

138 candidates to 96 candidates (69.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	138	7	145

Merged error: 21.7b

Counts

145 → 7

regimes211.0ms

Accuracy

84% (1.7b remaining)

Error of 24.5b against oracle of 22.8b and baseline of 33.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	28
1	42	28

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.1s	3877×	body	1280	valid
1.2s	1108×	body	1280	nan
797.0ms	1813×	body	640	valid
636.0ms	908×	body	640	nan
607.0ms	4106×	body	80	overflowed
311.0ms	3121×	body	80	valid
311.0ms	6361×	body	80	nan
292.0ms	931×	body	320	valid
174.0ms	410×	body	320	nan
84.0ms	447×	body	160	valid
48.0ms	220×	body	160	nan