Details

sample240.0ms

Algorithm

intervals

Results

73.0ms	135×	body	1280	valid
42.0ms	38×	body	1280	nan
22.0ms	147×	body	80	overflowed
21.0ms	45×	body	640	valid
19.0ms	27×	body	640	nan
17.0ms	112×	body	80	valid
9.0ms	28×	body	320	valid
9.0ms	189×	body	80	nan
3.0ms	6×	body	320	nan
3.0ms	15×	body	160	valid
2.0ms	11×	body	160	nan

simplify35.0ms

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: 29.8b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

9.0ms

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

series281.0ms

Counts

1 → 3

Calls

1 calls:

280.0ms

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

simplify77.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	222	326
1	594	313
2	2745	307
3	5003	307

prune73.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	3	28

Merged error: 20.0b

Counts

28 → 3

localize15.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`unpow-prod-down`
18×	`*-un-lft-identity` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
12×	`sqr-pow`
6×	`distribute-lft-out--`
5×	`log-prod`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1`
2×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

2 → 54

Calls

2 calls:

9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series559.0ms

Counts

2 → 6

Calls

2 calls:

279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	290	609
1	797	574
2	3273	562
3	5001	562

prune148.0ms

Filtered

60 candidates to 48 candidates (80.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	58	5	63

Merged error: 20.0b

Counts

63 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.1b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
40×	`unpow-prod-down`
38×	`*-un-lft-identity`
36×	`log-pow` `difference-of-squares`
32×	`sqrt-pow1`
30×	`exp-prod`
24×	`sqr-pow`
16×	`log-prod`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt` `sqrt-prod`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 118

Calls

4 calls:

9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
12.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
465.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
465.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	349	1482
1	940	1394
2	4101	1370
3	5001	1370

prune479.0ms

Filtered

130 candidates to 102 candidates (78.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	129	6	135

Merged error: 20.0b

Counts

135 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) 2) (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.1b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.1b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
114×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`difference-of-squares`
73×	`associate-l`
70×	`times-frac`
57×	`sqrt-prod`
44×	`sqr-pow`
35×	`add-cube-cbrt`
22×	`distribute-lft-out--`
18×	`log-pow`
16×	`sqrt-pow1`
15×	`exp-prod`
11×	`distribute-lft-out`
10×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1` `log-prod` `add-log-exp`
7×	`associate-r`
3×	`sub-neg`
2×	`frac-times` `flip3--` `flip3-+` `diff-log` `associate-*r/` `exp-sum` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `log-div` `distribute-lft-in` `pow1/2` `exp-diff` `sqrt-div` `div-exp` `rem-log-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 193

Calls

4 calls:

42.0ms	(* (/ (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) 2) (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series3.3s

Counts

4 → 12

Calls

4 calls:

1.6s	(* (/ (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))) 2) (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
433.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
480.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
742.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify118.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	1131	3520
1	3804	3213
2	5001	3195

prune775.0ms

Filtered

205 candidates to 141 candidates (68.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	0	4	4
Picked	1	0	1
Done	1	0	1
Total	205	6	211

Merged error: 20.0b

Counts

211 → 6

regimes222.0ms

Accuracy

78.8% (2.2b remaining)

Error of 24.4b against oracle of 22.1b and baseline of 32.7b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	73
1	57	73

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.1s	3831×	body	1280	valid
1.3s	1148×	body	1280	nan
835.0ms	1800×	body	640	valid
691.0ms	4271×	body	80	overflowed
650.0ms	903×	body	640	nan
337.0ms	3248×	body	80	valid
314.0ms	6376×	body	80	nan
287.0ms	918×	body	320	valid
195.0ms	454×	body	320	nan
89.0ms	453×	body	160	valid
54.0ms	242×	body	160	nan

Details

sample240.0ms

simplify35.0ms

prune2.0ms

localize9.0ms

rewrite10.0ms

series281.0ms

simplify77.0ms

prune73.0ms

localize15.0ms

rewrite22.0ms

series559.0ms

simplify90.0ms

prune148.0ms

localize14.0ms

rewrite47.0ms

series1.5s

simplify122.0ms

prune479.0ms

localize26.0ms

rewrite88.0ms

series3.3s

simplify118.0ms

prune775.0ms

regimes222.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling