Details

sample271.0ms

Algorithm

intervals

Results

104.0ms	80×	body	1280	valid
97.0ms	36×	body	2560	valid
23.0ms	38×	body	640	valid
9.0ms	28×	body	320	valid
8.0ms	102×	body	80	valid
6.0ms	86×	body	80	nan
4.0ms	17×	body	160	valid

simplify4.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	25	15
2	59	15
3	139	15
4	338	15
5	986	15
6	4059	15
done	5000	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b	(pow (+ 1.0 (/ i n)) n)
11.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

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:

514.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
294.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
22.0ms	(pow (+ 1.0 (/ i n)) n)
518.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts

4 → 12

Calls

4 calls:

537.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
383.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
315.0ms	(pow (+ 1.0 (/ i n)) n)
560.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.6s

Counts

293 → 293

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	437	6469
1	1183	6125
2	3764	5875
done	5001	5867

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
10.1b	(* (pow i 2) (log 1.0))
18.9b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
102×	`add-sqr-sqrt`
87×	`add-cube-cbrt` `*-un-lft-identity`
48×	`associate-r`
23×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-/r*`
11×	`associate-l`
9×	`div-inv` `add-log-exp`
7×	`pow1` `unswap-sqr`
6×	`cbrt-undiv` `log-prod` `div-exp` `prod-exp`
4×	`unpow-prod-down` `cbrt-unprod`
3×	`distribute-rgt-in` `distribute-lft-in` `sum-log` `associate-/l*`
2×	`associate-/r/` `*-commutative` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `flip3-+` `div-sub` `associate-*r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `flip--` `flip-+`

Counts

4 → 186

Calls

4 calls:

33.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
517.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
29.0ms	(* (pow i 2) (log 1.0))
446.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series918.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
341.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
243.0ms	(* (pow i 2) (log 1.0))
254.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify2.1s

Counts

198 → 198

Iterations

Useful iterations: 2 (802.0ms)

Iter	Nodes	Cost
0	338	6829
1	902	6613
2	3386	6123
done	5000	6123

prune928.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
3.3b	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
10.1b	(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
10.1b	(* (pow i 2) (log 1.0))

rewrite3.0s

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
38×	`add-cbrt-cube`
37×	`prod-exp`
27×	`add-sqr-sqrt` `associate-l`
21×	`pow1`
19×	`add-cube-cbrt` `*-un-lft-identity` `cbrt-unprod`
12×	`associate-*l/`
10×	`pow-prod-down`
9×	`times-frac` `associate-r/` `associate-r*`
8×	`div-exp`
6×	`log-prod`
5×	`flip3--` `flip--` `unswap-sqr`
4×	`cbrt-undiv` `frac-times` `unpow-prod-down` `rec-exp` `1-exp` `*-commutative` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`unpow2` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `log-pow` `div-inv`

Counts

4 → 129

Calls

4 calls:

1.7s	(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
503.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
722.0ms	(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
23.0ms	(* (pow i 2) (log 1.0))

series731.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
151.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
201.0ms	(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
164.0ms	(* (pow i 2) (log 1.0))

simplify1.6s

Counts

141 → 141

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	240	4476
1	616	4220
2	2483	3407
done	5001	3389

prune467.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
3.3b	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
10.0b	(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
10.1b	(* (pow i 2) (log 1.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1`
10×	`prod-exp`
9×	`times-frac` `add-log-exp`
8×	`associate-r` `cbrt-unprod`
7×	`associate-*l/`
6×	`log-prod`
5×	`unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `sum-log` `*-commutative` `flip--`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `log-pow` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

26.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
490.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
704.0ms	(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
23.0ms	(* (pow i 2) (log 1.0))

series571.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
149.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
216.0ms	(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
163.0ms	(* (pow i 2) (log 1.0))

simplify1.4s

Counts

116 → 116

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	219	3108
1	594	3005
2	2468	2555
done	5002	2551

prune347.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.9b

Details

sample271.0ms

simplify4.3s

prune5.0ms

localize22.0ms

rewrite1.4s

series1.8s

simplify2.6s

prune1.4s

localize20.0ms

rewrite1.0s

series918.0ms

simplify2.1s

prune928.0ms

localize21.0ms

rewrite3.0s

series731.0ms

simplify1.6s

prune467.0ms

localize19.0ms

rewrite1.2s

series571.0ms

simplify1.4s

prune347.0ms

regimes256.0ms

bsearch2.0ms