Details

analyze3.9s

Algorithm

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 37.31102%

Guaranteed chance to sample good point: 50.637098%

sample236.0ms

Algorithm

intervals

Results

73.0ms	126×	body	1280	valid
47.0ms	40×	body	1280	nan
25.0ms	57×	body	640	valid
24.0ms	33×	body	640	nan
15.0ms	87×	body	80	overflowed
9.0ms	13×	body	640	invalid
9.0ms	28×	body	320	valid
5.0ms	12×	body	320	nan
3.0ms	38×	body	80	valid
3.0ms	2×	body	1280	invalid
2.0ms	6×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	17×	body	80	nan
1.0ms	4×	body	160	nan
1.0ms	6×	body	80	invalid
0.0ms	1×	body	160	invalid

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

prune3.0ms

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: 35.3b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

2.0b	(- (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)))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

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

simplify95.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	280	352
1	785	337
2	3548	329
3	5001	329

prune81.0ms

Filtered

23 candidates to 27 candidates (-17.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	4	28

Merged error: 24.1b

Counts

28 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.0b	(- (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`
15×	`log-prod` `exp-sum`
12×	`sqr-pow`
6×	`distribute-lft-out--`
4×	`add-cube-cbrt` `exp-prod` `add-log-exp`
3×	`pow1`
2×	`add-exp-log` `log-div` `flip3--` `exp-diff` `add-cbrt-cube` `flip--` `distribute-lft-out`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

2 → 53

Calls

2 calls:

10.0ms	(exp (log (- (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)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify132.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	358	760
1	954	730
2	4218	699
3	5001	693

prune144.0ms

Filtered

45 candidates to 59 candidates (-31.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	57	6	63

Merged error: 24.1b

Counts

63 → 6

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(pow E (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`unpow-prod-down`
19×	`*-un-lft-identity`
18×	`difference-of-squares`
15×	`unpow-prod-up` `log-prod`
13×	`sqr-pow`
6×	`distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`pow1` `pow-unpow` `add-log-exp`
3×	`add-exp-log`
2×	`log-div` `flip3--` `pow-exp` `add-cbrt-cube` `flip--` `distribute-lft-out` `pow-sub`
1×	`pow-to-exp` `sub-neg` `e-exp-1` `pow-pow` `diff-log` `log-pow`

Counts

2 → 60

Calls

2 calls:

13.0ms	(pow E (log (- (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)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(pow E (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify47.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	522	966
1	1551	941
2	5002	906

prune182.0ms

Filtered

51 candidates to 66 candidates (-29.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Merged error: 24.1b

Counts

72 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (log (/ 1 x)) (* x (pow n 2)))
3.0b	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
7.6b	(/ (/ 0.5 n) (pow x 2))
9.7b	(* x (pow n 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 223

Calls

4 calls:

7.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
14.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
8.0ms	(/ (/ 0.5 n) (pow x 2))
6.0ms	(* x (pow n 2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
13.0ms	(+ (/ (/ 1.0 n) x) (* 1.0 (- 0 (/ (log (/ 1 x)) (* x (pow n 2))))))
10.0ms	(/ (/ 0.5 n) (pow x 2))
7.0ms	(* x (pow n 2))

simplify153.0ms

Algorithm

egg-herbie

Counts

235 → 235

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	1037	1834
1	4830	1606
2	5001	1605

prune427.0ms

Filtered

147 candidates to 235 candidates (-59.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	231	4	235
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	232	9	241

Merged error: 23.8b

Counts

241 → 9

Details

analyze3.9s

sample236.0ms

simplify33.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series40.0ms

simplify95.0ms

prune81.0ms

localize10.0ms

rewrite22.0ms

series78.0ms

simplify132.0ms

prune144.0ms

localize11.0ms

rewrite25.0ms

series136.0ms

simplify47.0ms

prune182.0ms

localize20.0ms

rewrite45.0ms

series42.0ms

simplify153.0ms

prune427.0ms

regimes355.0ms

bsearch1.0ms

Profiling