Details

sample177.0ms

Algorithm

intervals

Results

80.0ms	115×	body	1280	valid
43.0ms	89×	body	640	valid
25.0ms	256×	pre	80	true
13.0ms	37×	body	320	valid
3.0ms	15×	body	160	valid

simplify255.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

255.0ms

(- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize18.0ms

Local error

Found 3 expressions with local error:

4.9b	(- (log1p n) (log n))
1.1b	(fma n (- (log1p n) (log n)) -1)
0.0b	(+ (fma n (- (log1p n) (log n)) -1) (log1p n))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`prod-diff`
7×	`pow1` `add-log-exp`
4×	`log-pow`
3×	`expm1-log1p-u` `log-prod` `fma-def` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u` `associate--r+`
2×	`log1p-udef` `sum-log` `diff-log` `fma-udef` `distribute-lft-out--`
1×	`+-commutative` `associate-+l+` `sub-neg` `flip3-+` `flip3--` `flip-+` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

3 → 68

Calls

3 calls:

Slowest

6.0ms	(- (log1p n) (log n))
4.0ms	(+ (fma n (- (log1p n) (log n)) -1) (log1p n))
0.0ms	(fma n (- (log1p n) (log n)) -1)

series355.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

137.0ms	(fma n (- (log1p n) (log n)) -1)
132.0ms	(+ (fma n (- (log1p n) (log n)) -1) (log1p n))
86.0ms	(- (log1p n) (log n))

simplify9.3s

Counts

90 → 77

Calls

90 calls:

Slowest

492.0ms	(* (exp (fma n (- (log1p n) (log n)) -1)) (+ 1 n))
486.0ms	(* (* (- (log1p n) (log n)) (- (log1p n) (log n))) (- (log1p n) (log n)))
454.0ms	(- (+ n (* 1/2 (pow n 2))) (+ (* n (log n)) 1))
412.0ms	(exp (+ (fma n (- (log1p n) (log n)) -1) (log1p n)))
380.0ms	(* (exp (fma n (- (log1p n) (log n)) -1)) (exp (log1p n)))

prune717.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 1 expressions with local error:

0.8b	(/ 1/6 (* n n))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `times-frac` `add-cube-cbrt` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`expm1-log1p-u` `pow1` `clear-num` `associate-/r*` `frac-2neg` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

Slowest

7.0ms

(/ 1/6 (* n n))

series35.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

35.0ms

(/ 1/6 (* n n))

simplify1.2s

Counts

31 → 27

Calls

31 calls:

Slowest

322.0ms	(/ (* (* 1/6 1/6) 1/6) (* (* (* n n) n) (* (* n n) n)))
289.0ms	(/ (* (* 1/6 1/6) 1/6) (* (* (* n n) (* n n)) (* n n)))
141.0ms	(* (* (/ 1/6 (* n n)) (/ 1/6 (* n n))) (/ 1/6 (* n n)))
53.0ms	(log (/ 1/6 (* n n)))
50.0ms	(- (log 1/6) (log (* n n)))

prune264.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	3604×	body	1280	valid
1.8s	2628×	body	640	valid
522.0ms	1327×	body	320	valid
231.0ms	8000×	pre	80	true
95.0ms	441×	body	160	valid