Details

Time bar (total: 7.4s)

sample108.0ms

Algorithm
intervals
Results
38.0ms64×body1280valid
18.0ms253×body80nan
18.0ms131×body80valid
15.0ms37×body640valid
5.0ms18×body320valid
1.0ms6×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (log (+ N 1)) (log N))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize18.0ms

Local error

Found 1 expressions with local error:

1.8b
(- (log1p N) (log N))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt prod-diff
10×add-cube-cbrt
5×pow1 add-log-exp
4×diff-log log-pow
3×log-prod fma-neg associate--r+
2×log1p-udef distribute-lft-out--
1×expm1-log1p-u sub-neg flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
Calls
1 calls:
Slowest
12.0ms
(- (log1p N) (log N))

series106.0ms

Calls
1 calls:
Slowest
106.0ms
(- (log1p N) (log N))

simplify2.5s

Calls
40 calls:
Slowest
407.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (log N) 1)))
195.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
183.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
170.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
150.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune361.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite48.0ms

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×expm1-log1p-u frac-2neg flip3-+ div-exp rem-log-exp flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
1×cbrt-undiv log-pow
Calls
2 calls:
Slowest
32.0ms
(/ (+ N 1) N)
13.0ms
(log (/ (+ N 1) N))

series131.0ms

Calls
2 calls:
Slowest
82.0ms
(/ (+ N 1) N)
49.0ms
(log (/ (+ N 1) N))

simplify2.3s

Calls
71 calls:
Slowest
342.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
229.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
182.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
171.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
160.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))

prune556.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

11.8b
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
0.6b
(/ -1/2 (* N N))
0.3b
(/ -1/3 (* (* N N) N))
0.1b
(* (* N N) N)

rewrite976.0ms

Algorithm
rewrite-expression-head
Rules
12353×associate-/r*
9020×add-sqr-sqrt
6957×*-un-lft-identity
6523×frac-add
6494×frac-sub
5635×add-cube-cbrt
5316×associate-*l*
3639×associate-/l*
2292×associate-*r*
1900×unswap-sqr
1857×swap-sqr
1627×times-frac
1213×clear-num frac-2neg
1006×*-commutative
792×prod-diff
544×distribute-lft-out
101×div-inv
97×sub-div
34×flip3-+ flip-+
23×pow1 add-cbrt-cube add-exp-log
11×distribute-lft-out--
9×fma-neg add-log-exp
7×prod-exp cbrt-unprod difference-of-squares
6×pow-plus pow-prod-up
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-prod-down
2×pow2 diff-log pow3 associate--l+ pow-sqr
1×+-commutative sum-log sub-neg flip3-- flip--
Calls
4 calls:
Slowest
348.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))
40.0ms
(* (* N N) N)
29.0ms
(/ -1/3 (* (* N N) N))
9.0ms
(/ -1/2 (* N N))

series181.0ms

Calls
4 calls:
Slowest
55.0ms
(* (* N N) N)
52.0ms
(/ -1/2 (* N N))
46.0ms
(/ -1/3 (* (* N N) N))
28.0ms
(- (+ (/ -1/2 (* N N)) (/ 1 N)) (/ -1/3 (* (* N N) N)))