Details

sample68.0ms

Algorithm

intervals

Results

35.0ms	110×	body	1280	valid
16.0ms	88×	body	640	valid
4.0ms	37×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	21×	body	160	valid

simplify159.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (+ n 1.0) (log (+ n 1.0)))
0.3b	(* n (log n))
5.8b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite31.0ms

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:

13.0ms	(* (+ n 1.0) (log (+ n 1.0)))
5.0ms	(* n (log n))
10.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series433.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* (+ n 1.0) (log (+ n 1.0)))
179.0ms	(* n (log n))
184.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (48.0ms)

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

prune182.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
0.8b	(/ 1 (pow n 2))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 141

Calls

3 calls:

311.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
14.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
4.0ms	(/ 1 (pow n 2))

series79.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
24.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
19.0ms	(/ 1 (pow n 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	481	928
1	1943	772
2	5001	683

prune259.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1.0 (- (+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* 1.0 (log (/ 1 n))))) (/ 0.5 n)))
0.0b	(+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* 1.0 (log (/ 1 n)))))
0.7b	(/ 0.16666666666666669 (pow n 2))

rewrite502.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-log-exp`
20×	`add-cube-cbrt`
12×	`unpow-prod-down`
8×	`add-exp-log` `associate-/r*`
7×	`diff-log`
6×	`sum-log`
5×	`add-cbrt-cube` `distribute-lft-out--`
4×	`unpow2` `sqr-pow`
3×	`pow1` `div-exp` `associate-/l*` `associate--r+`
2×	`associate-+r-` `sub-neg` `log-rec` `distribute-rgt-neg-out` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `unsub-neg` `pow-exp` `associate--l+` `clear-num` `flip--` `flip-+` `div-inv` `associate--r-` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

450.0ms	(- 1.0 (- (+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* 1.0 (log (/ 1 n))))) (/ 0.5 n)))
45.0ms	(+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* 1.0 (log (/ 1 n)))))
4.0ms	(/ 0.16666666666666669 (pow n 2))

series417.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(- 1.0 (- (+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* 1.0 (log (/ 1 n))))) (/ 0.5 n)))
346.0ms	(+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* 1.0 (log (/ 1 n)))))
28.0ms	(/ 0.16666666666666669 (pow n 2))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	383	771
1	1332	685
2	5002	666

prune219.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	21	10

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	3716×	body	1280	valid
479.0ms	2614×	body	640	valid
152.0ms	1259×	body	320	valid
69.0ms	8000×	pre	80	true
35.0ms	411×	body	160	valid