Details

sample225.0ms

Algorithm

intervals

Results

60.0ms	109×	body	1280	valid
41.0ms	37×	body	1280	nan
26.0ms	63×	body	640	valid
19.0ms	28×	body	640	nan
19.0ms	129×	body	80	overflowed
11.0ms	106×	body	80	valid
10.0ms	212×	body	80	nan
7.0ms	27×	body	320	valid
7.0ms	17×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	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: 32.6b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 51

Calls

2 calls:

8.0ms	(pow x (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series344.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(pow x (/ 1.0 n))
286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify40.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	404	475
1	1391	461
2	5001	449

prune288.0ms

Filtered

57 candidates to 46 candidates (80.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 23.3b

Counts

58 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow x (/ 1.0 n)) 3))
0.0b	(pow x (/ 1.0 n))
0.0b	(pow (pow x (/ 1.0 n)) 3)
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
53×	`unpow-prod-down`
44×	`cbrt-prod`
27×	`difference-of-squares`
25×	`sqr-pow`
24×	`*-un-lft-identity`
23×	`cube-prod`
22×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`times-frac`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1` `pow-exp` `add-cbrt-cube`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `rem-cbrt-cube` `div-inv` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 129

Calls

4 calls:

4.0ms	(cbrt (pow (pow x (/ 1.0 n)) 3))
4.0ms	(pow x (/ 1.0 n))
4.0ms	(pow (pow x (/ 1.0 n)) 3)
17.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series480.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cbrt (pow (pow x (/ 1.0 n)) 3))
61.0ms	(pow x (/ 1.0 n))
84.0ms	(pow (pow x (/ 1.0 n)) 3)
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify67.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	620	1225
1	2339	1182
2	5001	1164

prune256.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	140	4	144

Merged error: 23.3b

Counts

144 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (* (log x) 1.0) (* x (pow n 2)))
4.3b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.7b	(* x (pow n 2))
9.5b	(/ (/ 0.5 n) (pow x 2))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

7.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
72.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms	(* x (pow n 2))
9.0ms	(/ (/ 0.5 n) (pow x 2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
69.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
29.0ms	(* x (pow n 2))
30.0ms	(/ (/ 0.5 n) (pow x 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1858

prune538.0ms

Filtered

232 candidates to 140 candidates (60.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	230	6	236

Merged error: 23.2b

Counts

236 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (log x) (* x (pow n 2)))
4.3b	(+ (* 1.0 (/ 1 (* x n))) (* 1.0 (/ (log x) (* x (pow n 2)))))
7.7b	(* x (pow n 2))
9.8b	(* (pow x 2) n)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

6.0ms	(/ (log x) (* x (pow n 2)))
7.0ms	(+ (* 1.0 (/ 1 (* x n))) (* 1.0 (/ (log x) (* x (pow n 2)))))
5.0ms	(* x (pow n 2))
5.0ms	(* (pow x 2) n)

series284.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (log x) (* x (pow n 2)))
155.0ms	(+ (* 1.0 (/ 1 (* x n))) (* 1.0 (/ (log x) (* x (pow n 2)))))
30.0ms	(* x (pow n 2))
22.0ms	(* (pow x 2) n)

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	449	609
1	2233	521
2	5001	521

prune257.0ms

Filtered

105 candidates to 69 candidates (65.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	104	7	111

Merged error: 23.2b

Counts

111 → 7

Details

sample225.0ms

simplify35.0ms

prune2.0ms

localize9.0ms

rewrite20.0ms

series344.0ms

simplify40.0ms

prune288.0ms

localize12.0ms

rewrite34.0ms

series480.0ms

simplify67.0ms

prune256.0ms

localize18.0ms

rewrite104.0ms

series215.0ms

simplify51.0ms

prune538.0ms

localize20.0ms

rewrite27.0ms

series284.0ms

simplify75.0ms

prune257.0ms

regimes168.0ms

bsearch3.0ms

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