Details

sample290.0ms

Algorithm

intervals

Results

81.0ms	120×	body	1280	valid
51.0ms	33×	body	1280	nan
34.0ms	55×	body	640	valid
23.0ms	26×	body	640	nan
23.0ms	118×	body	80	overflowed
13.0ms	100×	body	80	valid
12.0ms	32×	body	320	valid
11.0ms	162×	body	80	nan
8.0ms	15×	body	320	nan
4.0ms	17×	body	160	valid
3.0ms	9×	body	160	nan

simplify31.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 30.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
2.8b	(- (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)))

series71.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	552	688
1	1885	669
2	5002	641

prune177.0ms

Filtered

88 candidates to 71 candidates (19.3%)

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: 20.8b

Counts

89 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
3.3b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
26×	`pow-unpow`
24×	`*-un-lft-identity`
23×	`sqrt-prod`
22×	`add-cube-cbrt` `unpow-prod-down`
18×	`times-frac`
16×	`difference-of-squares`
12×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`rem-sqrt-square`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 102

Calls

4 calls:

4.0ms	(sqrt (pow x (/ 1.0 n)))
4.0ms	(pow x (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (pow x (/ 1.0 n)))
12.0ms	(pow x (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
74.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	572	1081
1	2007	1049
2	5002	1000

prune466.0ms

Filtered

114 candidates to 88 candidates (22.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	114	4	118

Merged error: 20.8b

Counts

118 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
0.0b	(* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n))))
3.3b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
52×	`cbrt-prod`
38×	`unpow-prod-down`
34×	`*-un-lft-identity`
32×	`add-cube-cbrt`
26×	`pow-unpow`
22×	`sqr-pow`
18×	`times-frac`
16×	`sqrt-prod` `difference-of-squares` `unswap-sqr`
13×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
8×	`add-exp-log`
6×	`pow1/3` `add-log-exp`
4×	`add-cbrt-cube`
2×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 147

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
10.0ms	(* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n))))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow x (/ 1.0 n))
13.0ms	(pow x (/ 1.0 n))
29.0ms	(* (cbrt (pow x (/ 1.0 n))) (cbrt (pow x (/ 1.0 n))))
64.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify75.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	719	1670
1	2688	1609
2	5001	1544

prune734.0ms

Filtered

159 candidates to 113 candidates (28.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	159	4	163

Merged error: 20.8b

Counts

163 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (neg 0.5) (* (pow x 2) n))
2.3b	(+ (* (/ 1.0 x) (+ (/ 1 n) 0)) (/ (* (log x) 1.0) (* x (pow n 2))))
8.5b	(* x (pow n 2))
10.3b	(* (pow x 2) n)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`add-exp-log`
16×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`associate-r` `associate-l`
10×	`times-frac` `associate-/l*`
9×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `add-log-exp`
5×	`frac-add`
4×	`pow1` `div-exp` `unpow2` `sqr-pow`
3×	`pow-to-exp` `flip3-+` `pow-exp` `cbrt-unprod` `flip-+`
2×	`cbrt-undiv` `frac-times` `neg-mul-1` `associate-+l+` `associate-r/` `-commutative`
1×	`+-commutative` `neg-sub0` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-sub` `distribute-frac-neg` `associate-l/` `clear-num` `associate-/r` `sum-log` `div-inv`

Counts

4 → 111

Calls

4 calls:

6.0ms	(/ (neg 0.5) (* (pow x 2) n))
13.0ms	(+ (* (/ 1.0 x) (+ (/ 1 n) 0)) (/ (* (log x) 1.0) (* x (pow n 2))))
5.0ms	(* x (pow n 2))
5.0ms	(* (pow x 2) n)

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ (neg 0.5) (* (pow x 2) n))
24.0ms	(+ (* (/ 1.0 x) (+ (/ 1 n) 0)) (/ (* (log x) 1.0) (* x (pow n 2))))
7.0ms	(* x (pow n 2))
4.0ms	(* (pow x 2) n)

simplify254.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (241.0ms)

Iter	Nodes	Cost
0	667	764
1	3837	668
2	5001	665

prune202.0ms

Filtered

123 candidates to 87 candidates (29.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	118	9	127

Merged error: 20.7b

Counts

127 → 9

regimes278.0ms

Accuracy

83.6% (1.7b remaining)

Error of 23.3b against oracle of 21.5b and baseline of 32.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	45
1	62	45
2	62	45

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.2s	3900×	body	1280	valid
1.2s	1064×	body	1280	nan
859.0ms	1820×	body	640	valid
636.0ms	916×	body	640	nan
593.0ms	3987×	body	80	overflowed
335.0ms	6379×	body	80	nan
321.0ms	3110×	body	80	valid
285.0ms	894×	body	320	valid
187.0ms	444×	body	320	nan
85.0ms	434×	body	160	valid
40.0ms	182×	body	160	nan

Details

sample290.0ms

simplify31.0ms

prune3.0ms

localize12.0ms

rewrite20.0ms

series71.0ms

simplify46.0ms

prune177.0ms

localize13.0ms

rewrite28.0ms

series117.0ms

simplify52.0ms

prune466.0ms

localize23.0ms

rewrite36.0ms

series117.0ms

simplify75.0ms

prune734.0ms

localize23.0ms

rewrite33.0ms

series39.0ms

simplify254.0ms

prune202.0ms

regimes278.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.3s

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