Details

sample36.0s

Algorithm

intervals

Results

87.0ms	44×	body	2560	valid
69.0ms	82×	body	1280	valid
21.0ms	54×	body	640	valid
8.0ms	36×	body	320	valid
5.0ms	66×	body	80	valid
3.0ms	59×	body	80	nan
2.0ms	12×	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

prune3.0ms

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: 50.2b

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)))
1.0b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.8b	(pow (+ 1.0 (/ i n)) n)
12.9b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite79.0ms

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:

29.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0ms	(pow (+ 1.0 (/ i n)) n)
15.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series187.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
35.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms	(pow (+ 1.0 (/ i n)) n)
62.0ms	(/ (- (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

prune604.0ms

Filtered

223 candidates to 293 candidates (-31.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	286	7	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	7	294

Merged error: 24.2b

Counts

294 → 7

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)))
10.6b	(* (pow i 2) (log 1.0))
18.5b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite53.0ms

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)))
9.0ms	(* (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))

series60.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
25.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
12.0ms	(* (pow i 2) (log 1.0))
20.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify152.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (26.0ms)

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

prune805.0ms

Filtered

157 candidates to 212 candidates (-35.0%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	199	13	212
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	200	19	219

Merged error: 11.0b

Counts

219 → 19

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))
10.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.6b	(* (pow i 2) (log 1.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

5.0ms	(* 0.5 (pow i 2))
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))

series54.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 0.5 (pow i 2))
21.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms	(* (pow i 2) (log 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	518	1449
1	2468	1227
2	5001	1223

prune337.0ms

Filtered

79 candidates to 124 candidates (-57.0%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	17	18
Picked	0	1	1
Done	0	0	0
Total	124	19	143

Merged error: 11.0b

Counts

143 → 19

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (* (cbrt (pow (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 3)) n))
10.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
10.6b	(* (pow i 2) (log 1.0))
13.3b	(cbrt (pow (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
27×	`times-frac`
17×	`unpow-prod-down`
16×	`add-exp-log`
13×	`cube-prod`
12×	`add-cbrt-cube`
11×	`associate-l`
10×	`pow1`
6×	`log-prod` `prod-exp`
5×	`associate-r`
4×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-/r` `div-inv` `associate-/l` `sqr-pow`
2×	`cube-div` `cbrt-div` `*-commutative` `associate-/l/` `unpow2`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `unpow3` `div-sub` `associate-r/` `div-exp` `associate-l/` `pow-exp` `clear-num` `log-pow` `flip--` `rem-cbrt-cube`

Counts

4 → 125

Calls

4 calls:

17.0ms	(* 100.0 (* (cbrt (pow (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 3)) 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))
9.0ms	(cbrt (pow (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 3))

series71.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 100.0 (* (cbrt (pow (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 3)) n))
15.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.0ms	(* (pow i 2) (log 1.0))
18.0ms	(cbrt (pow (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 3))

simplify110.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	702	2324
1	3347	2205
2	5001	2205

prune330.0ms

Filtered

84 candidates to 137 candidates (-63.1%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	16	17
Picked	0	1	1
Done	0	1	1
Total	137	19	156

Merged error: 11.0b

Counts

156 → 19

regimes576.0ms

bsearch1.6min

Steps

Iters	Range		Point
10	102741.10950634319	1.8891606911836606e+20	104363.90759147814
9	-5.190150388366246	-2.8132226043098912e-08	-0.03763215011753982

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	31
1	47	31

end0.0ms

sample13.8s

Algorithm

intervals

Results

Details

sample36.0s

simplify44.0ms

prune3.0ms

localize9.0ms

rewrite79.0ms

series187.0ms

simplify63.0ms

prune604.0ms

localize16.0ms

rewrite53.0ms

series60.0ms

simplify152.0ms

prune805.0ms

localize16.0ms

rewrite36.0ms

series54.0ms

simplify81.0ms

prune337.0ms

localize19.0ms

rewrite46.0ms

series71.0ms

simplify110.0ms

prune330.0ms

regimes576.0ms

bsearch1.6min

simplify1.0ms

end0.0ms

sample13.8s

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