Details

sample148.0ms

Algorithm

intervals

Results

56.0ms	78×	body	1280	valid
45.0ms	24×	body	2560	valid
16.0ms	57×	body	640	valid
6.0ms	32×	body	320	valid
4.0ms	97×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	57×	body	80	nan
2.0ms	15×	body	160	valid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0b	(pow (+ 1.0 (/ i n)) n)
8.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite821.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 281

Calls

4 calls:

329.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
154.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms	(pow (+ 1.0 (/ i n)) n)
300.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

363.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
242.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
207.0ms	(pow (+ 1.0 (/ i n)) n)
334.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune821.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
7.0b	(pow (+ 1.0 (/ i n)) n)
7.0b	(pow (+ 1.0 (/ i n)) (* 2 n))
8.7b	(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite670.0ms

Algorithm

rewrite-expression-head

Rules

717×	`times-frac`
524×	`*-un-lft-identity`
294×	`add-sqr-sqrt` `add-cube-cbrt`
115×	`distribute-lft-out`
38×	`div-inv`
29×	`associate-/r/`
22×	`associate-/l*`
18×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`flip3-+` `flip-+`
13×	`associate-/r*`
8×	`cbrt-undiv` `unpow-prod-down` `div-exp` `add-log-exp`
6×	`pow1` `div-sub`
4×	`pow-unpow`
2×	`neg-sub0` `pow-to-exp` `associate-+r-` `pow-pow` `unsub-neg` `pow-exp` `sum-log` `sqr-pow`
1×	`+-commutative` `frac-2neg` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 394

Calls

4 calls:

117.0ms	(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
19.0ms	(pow (+ 1.0 (/ i n)) n)
19.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
490.0ms	(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.6s

Counts

4 → 12

Calls

4 calls:

259.0ms	(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
208.0ms	(pow (+ 1.0 (/ i n)) n)
223.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
1.9s	(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify125.0ms

Algorithm

egg-herbie

Counts

406 → 406

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1864	10059
1	5002	9637

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize22.0ms

Local error

Found 4 expressions with local error:

7.0b	(pow (+ 1.0 (/ i n)) n)
7.0b	(pow (+ 1.0 (/ i n)) (* 2 n))
7.0b	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
8.7b	(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

3405×	`times-frac`
2121×	`*-un-lft-identity`
1275×	`add-sqr-sqrt` `add-cube-cbrt`
423×	`distribute-lft-out`
150×	`div-inv`
141×	`associate-/r/`
78×	`associate-/l*`
70×	`flip3-+` `flip-+`
28×	`add-exp-log`
25×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
13×	`associate-/r*`
12×	`unpow-prod-down`
9×	`div-sub`
7×	`pow1`
5×	`pow-unpow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
1×	`neg-sub0` `associate-+r-` `frac-2neg` `unsub-neg` `clear-num` `associate-/l/`

Counts

4 → 1182

Calls

4 calls:

17.0ms	(pow (+ 1.0 (/ i n)) n)
18.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
20.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
742.0ms	(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series15.5s

Counts

4 → 12

Calls

4 calls:

205.0ms	(pow (+ 1.0 (/ i n)) n)
203.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
205.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
14.9s	(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify447.0ms

Algorithm

egg-herbie

Counts

1194 → 1194

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5001	54232

prune4.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize32.0ms

Local error

Found 4 expressions with local error:

7.0b	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.0b	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.0b	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
8.7b	(/ (cbrt (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite828.0ms

Algorithm

rewrite-expression-head

Rules

3471×	`times-frac`
2155×	`*-un-lft-identity`
1309×	`add-sqr-sqrt` `add-cube-cbrt`
1092×	`cbrt-prod`
423×	`distribute-lft-out`
153×	`div-inv`
141×	`associate-/r/`
81×	`associate-/l*`
70×	`flip3-+` `flip-+`
13×	`associate-/r*`
12×	`add-exp-log` `unpow-prod-down`
7×	`pow1` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-unpow` `pow-pow` `div-exp` `pow-exp` `sqr-pow`
1×	`cbrt-div` `frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 1211

Calls

4 calls:

18.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
19.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
18.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
639.0ms	(/ (cbrt (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

Details

sample148.0ms

simplify44.0ms

prune2.0ms

localize9.0ms

rewrite821.0ms

series1.1s

simplify64.0ms

prune821.0ms

localize19.0ms

rewrite670.0ms

series2.6s

simplify125.0ms

prune1.2s

localize22.0ms

rewrite919.0ms

series15.5s

simplify447.0ms

prune4.0s

localize32.0ms

rewrite828.0ms

series9.5m