Details

sample113.0ms

Algorithm

intervals

Results

44.0ms	64×	body	1280	valid
20.0ms	253×	body	80	nan
17.0ms	37×	body	640	valid
15.0ms	131×	body	80	valid
6.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify11.0ms

Calls

1 calls:

Slowest

11.0ms

(- (log (+ N 1)) (log N))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize12.0ms

Local error

Found 2 expressions with local error:

3.3b	(log (+ N 1))
1.8b	(- (log (+ N 1)) (log N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
6×	`add-log-exp`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `diff-log` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `distribute-lft-out`
1×	`sub-neg` `flip3--` `rem-log-exp` `flip--` `difference-of-squares`

Calls

2 calls:

Slowest

24.0ms	(- (log (+ N 1)) (log N))
3.0ms	(log (+ N 1))

series109.0ms

Calls

2 calls:

Slowest

76.0ms	(- (log (+ N 1)) (log N))
32.0ms	(log (+ N 1))

simplify1.8s

Calls

32 calls:

Slowest

333.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
284.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
233.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
193.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
152.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune480.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

1.7b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
12×	`log-div`
10×	`associate-/l*`
9×	`distribute-lft-out`
7×	`add-exp-log`
6×	`associate-/r*`
4×	`add-cbrt-cube` `associate-/l/`
3×	`pow1` `clear-num` `log-rec`
2×	`frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `flip-+` `insert-posit16` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `log-pow`

Calls

2 calls:

Slowest

25.0ms	(/ (+ 1 N) N)
17.0ms	(log (/ (+ 1 N) N))

series103.0ms

Calls

2 calls:

Slowest

59.0ms	(/ (+ 1 N) N)
45.0ms	(log (/ (+ 1 N) N))

simplify2.1s

Calls

71 calls:

Slowest

304.0ms	(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
225.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
179.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
138.0ms	(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))
105.0ms	(- N (+ (log N) (* 1/2 (pow N 2))))

prune600.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

3.3b	(log (+ 1 N))
1.8b	(- (log (+ 1 N)) (log N))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
6×	`add-log-exp`
5×	`log-pow` `add-cube-cbrt`
4×	`log-div` `diff-log` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `insert-posit16` `distribute-lft-out`
1×	`sub-neg` `flip3--` `rem-log-exp` `flip--` `difference-of-squares`

Calls

2 calls:

Slowest

12.0ms	(- (log (+ 1 N)) (log N))
6.0ms	(log (+ 1 N))

series106.0ms

Calls

2 calls:

Slowest

72.0ms	(- (log (+ 1 N)) (log N))
34.0ms	(log (+ 1 N))

simplify1.7s

Calls

32 calls:

Slowest

362.0ms	(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
240.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
192.0ms	(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
176.0ms	(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
162.0ms	(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune395.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

11.8b	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
0.6b	(/ 1/3 (* N N))
0.6b	(/ -1/2 (* N N))
0.1b	(/ (/ 1/3 (* N N)) N)

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

28880×	`frac-add`
18534×	`associate-/r*`
17751×	`add-sqr-sqrt`
16830×	`associate-/l*`
14835×	`*-un-lft-identity`
14813×	`add-cube-cbrt`
9024×	`times-frac`
4410×	`associate-l`
4407×	`swap-sqr` `associate-r`
4032×	`associate-/l/`
2666×	`clear-num` `frac-2neg`
1469×	`*-commutative` `unswap-sqr`
199×	`div-inv`
77×	`flip3-+` `flip-+`
23×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`pow1` `insert-posit16`
3×	`sum-log` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `associate-+l+`

Calls

4 calls:

Slowest

230.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
18.0ms	(/ (/ 1/3 (* N N)) N)
11.0ms	(/ 1/3 (* N N))
11.0ms	(/ -1/2 (* N N))

series172.0ms

Calls

4 calls:

Slowest

61.0ms	(/ (/ 1/3 (* N N)) N)
50.0ms	(/ 1/3 (* N N))
31.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 (* N N)) N))
29.0ms	(/ -1/2 (* N N))