Details

sample180.0ms

Algorithm

intervals

Results

75.0ms	95×	body	1280	valid
51.0ms	24×	body	2560	valid
23.0ms	63×	body	640	valid
7.0ms	31×	body	320	valid
5.0ms	70×	body	80	valid
3.0ms	67×	body	80	nan
2.0ms	13×	body	160	valid

simplify42.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 48.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.1b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
8.2b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite85.0ms

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:

34.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
16.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

366.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms	(pow (+ 1.0 (/ i n)) n)
366.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune709.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	9	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	9	294

Merged error: 22.9b

Counts

294 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
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)))
11.1b	(* (pow i 2) (log 1.0))
15.9b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

5.0ms	(* 0.5 (pow i 2))
18.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
13.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series563.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 0.5 (pow i 2))
204.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
138.0ms	(* (pow i 2) (log 1.0))
191.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify146.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune697.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	196	16	212
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	197	24	221

Merged error: 14.4b

Counts

221 → 24

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 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))
10.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

11.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
11.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms	(* (pow i 2) (log 1.0))

series938.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
253.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
319.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
139.0ms	(* (pow i 2) (log 1.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	529	1979
1	2435	1684
2	5001	1679

prune367.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	4	19	23
Picked	0	1	1
Done	0	0	0
Total	130	23	153

Merged error: 14.4b

Counts

153 → 23

localize24.0ms

Local error

Found 4 expressions with local error:

10.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b	(* (pow i 2) (log 1.0))
11.1b	(* (pow i 2) (log 1.0))
11.1b	(* (pow i 2) (log 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
21×	`add-exp-log`
18×	`log-prod`
12×	`unpow-prod-down` `associate-r` `add-cbrt-cube` `unswap-sqr`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `prod-exp`
7×	`pow1`
6×	`unpow2` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/r` `log-pow` `-commutative` `cbrt-unprod` `associate-/l*`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 132

Calls

4 calls:

11.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))
6.0ms	(* (pow i 2) (log 1.0))

series576.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
140.0ms	(* (pow i 2) (log 1.0))
135.0ms	(* (pow i 2) (log 1.0))
169.0ms	(* (pow i 2) (log 1.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	299	1229
1	1359	1100
2	5002	1086

prune471.0ms

Filtered

144 candidates to 93 candidates (64.6%)

Pruning

23 alts after pruning (21 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	21	21
Picked	0	1	1
Done	0	1	1
Total	144	23	167

Merged error: 14.4b

Counts

167 → 23

Details

sample180.0ms

simplify42.0ms

prune2.0ms

localize9.0ms

rewrite85.0ms

series1.2s

simplify63.0ms

prune709.0ms

localize16.0ms

rewrite55.0ms

series563.0ms

simplify146.0ms

prune697.0ms

localize16.0ms

rewrite43.0ms

series938.0ms

simplify84.0ms

prune367.0ms

localize24.0ms

rewrite34.0ms

series576.0ms

simplify58.0ms

prune471.0ms

regimes332.0ms

bsearch4.0ms

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