Details

sample198.0ms

Algorithm

intervals

Results

64.0ms	133×	body	1280	valid
34.0ms	60×	body	1280	nan
19.0ms	50×	body	640	nan
17.0ms	51×	body	640	valid
13.0ms	28×	body	10240	exit
11.0ms	187×	body	80	nan
7.0ms	30×	body	320	nan
6.0ms	24×	body	320	valid
4.0ms	93×	body	80	valid
2.0ms	14×	body	160	nan
2.0ms	13×	body	160	valid

simplify152.0ms

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	4996	6
6	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: 32.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `flip--` `div-inv` `difference-of-squares`

Counts

2 → 8

Calls

2 calls:

2.0ms	(pow x (/ 1.0 n))
4.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series331.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(pow x (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify97.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	248	158
1	788	157
2	3833	145
3	5001	145

prune50.0ms

Filtered

14 candidates to 12 candidates (85.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	11	3	14
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	12	3	15

Merged error: 21.6b

Counts

15 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b

(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

0.0b

(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

1.9b

(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`frac-times` `flip3--` `flip3-+` `flip--` `flip-+` `sqr-pow`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `associate-r` `*-commutative`

Counts

3 → 22

Calls

3 calls:

4.0ms

(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

9.0ms

(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

5.0ms

(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series966.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms

(+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

496.0ms

(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

270.0ms

(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify43.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	324	654
1	1183	637
2	5002	626

prune116.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Merged error: 21.6b

Counts

34 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
4.0b	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
7.5b	(* x (pow n 2))
9.4b	(* (pow x 2) n)

rewrite384.0ms

Algorithm

rewrite-expression-head

Rules

3192×	`frac-add`
2032×	`associate-*r/`
1680×	`associate-/r*`
1624×	`distribute-neg-frac`
884×	`frac-2neg` `clear-num`
816×	`frac-times`
696×	`associate-/l/`
450×	`associate-l`
441×	`flip3-+` `flip-+`
428×	`associate-/l*`
423×	`*-commutative`
422×	`unpow2` `sqr-pow`
394×	`associate-r`
232×	`div-inv`
196×	`log-pow` `inv-pow`
12×	`distribute-rgt-in` `associate-+l+` `distribute-neg-in` `distribute-lft-in`
9×	`+-commutative`
2×	`associate-*l/`
1×	`neg-sub0` `associate-+l-`

Counts

4 → 1659

Calls

4 calls:

103.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
31.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
3.0ms	(* x (pow n 2))
4.0ms	(* (pow x 2) n)

series518.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
82.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
36.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify729.0ms

Algorithm

egg-herbie

Counts

1671 → 1671

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5001	78331

prune10.0s

Filtered

1671 candidates to 1497 candidates (89.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1665	6	1671
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	1665	10	1675

Merged error: 21.5b

Counts

1675 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2))))) (* 0.25 (/ 1 (* (pow x 2) n)))))
4.0b	(+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2)))))
7.5b	(* x (pow n 2))
9.4b	(* (pow x 2) n)

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

4244×	`associate-*r/`
1937×	`associate-/r*`
1571×	`frac-add`
1566×	`frac-sub`
1188×	`clear-num`
1050×	`frac-times`
992×	`un-div-inv`
600×	`*-commutative`
594×	`frac-2neg`
554×	`flip3-+` `flip-+`
397×	`associate-r`
378×	`unpow2`
372×	`sqr-pow`
353×	`associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
3×	`+-commutative` `flip3--` `flip--` `sub-div`
2×	`sub-neg` `associate-*l/`

Counts

4 → 1651

Calls

4 calls:

133.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2))))) (* 0.25 (/ 1 (* (pow x 2) n)))))
11.0ms	(+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2)))))
3.0ms	(* x (pow n 2))
3.0ms	(* (pow x 2) n)

series566.0ms

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2))))) (* 0.25 (/ 1 (* (pow x 2) n)))))
148.0ms	(+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2)))))
29.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify732.0ms

Algorithm

egg-herbie

Counts

1663 → 1663

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5001	74215

prune3.9s

Filtered

1663 candidates to 575 candidates (34.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	1659	4	1663
Fresh	2	5	7
Picked	0	1	1
Done	1	1	2
Total	1662	11	1673

Merged error: 21.4b

Counts

1673 → 11

regimes276.0ms

Accuracy

83.8% (1.7b remaining)

Error of 23.3b against oracle of 21.6b and baseline of 32.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	47
1	47	47

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.8s	3926×	body	1280	valid
1.3s	2181×	body	1280	nan
743.0ms	1410×	body	10240	exit
708.0ms	1799×	body	640	nan
595.0ms	1762×	body	640	valid
263.0ms	6260×	body	80	nan
215.0ms	868×	body	320	nan
193.0ms	861×	body	320	valid
155.0ms	3228×	body	80	valid
65.0ms	462×	body	160	valid
61.0ms	430×	body	160	nan