Details

sample100.0ms

Algorithm

intervals

Results

47.0ms	108×	body	1280	valid
28.0ms	90×	body	640	valid
10.0ms	43×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	15×	body	160	valid

simplify157.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	8
1	43	8
2	123	8
3	212	8
4	374	8
5	496	8
6	715	8
7	967	8
8	1121	8
9	1221	8
10	1497	8
11	1752	8
12	2132	8
13	2469	8
14	3314	8
15	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
6.8b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`log-prod`
25×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r` `associate--l+`
7×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`associate--r+`
5×	`distribute-lft-out` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `log-pow` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 81

Calls

3 calls:

4.0ms	(* n (log n))
14.0ms	(* (+ n 1.0) (log (+ n 1.0)))
11.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series437.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(* n (log n))
69.0ms	(* (+ n 1.0) (log (+ n 1.0)))
185.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	419	643
1	1786	587
2	5001	568

prune198.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
0.0b	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
0.5b	(/ 1 (pow n 2))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`times-frac`
52×	`*-un-lft-identity`
37×	`add-cube-cbrt`
33×	`add-exp-log`
28×	`associate-r`
23×	`unpow-prod-down` `add-log-exp`
12×	`div-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`diff-log` `associate-/r*`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp`
5×	`sum-log` `distribute-lft-out--`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `associate--r+` `inv-pow`

Counts

4 → 157

Calls

4 calls:

327.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
8.0ms	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
15.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series450.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
367.0ms	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
25.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
21.0ms	(/ 1 (pow n 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	545	1163
1	2183	985
2	5001	902

prune351.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ 0.16666666666666669 (pow n 2))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`associate-/r*`
6×	`add-exp-log`
4×	`unpow2` `sqr-pow`
3×	`div-exp` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 49

Calls

1 calls:

4.0ms

(/ 0.16666666666666669 (pow n 2))

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

(/ 0.16666666666666669 (pow n 2))

simplify106.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	153	244
1	571	217
2	3249	208
3	5002	208

prune113.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3630×	body	1280	valid
842.0ms	2608×	body	640	valid
314.0ms	1346×	body	320	valid
106.0ms	8000×	pre	80	true
67.0ms	416×	body	160	valid