Details

sample200.0ms

Algorithm

intervals

Results

82.0ms	90×	body	1280	valid
62.0ms	27×	body	2560	valid
21.0ms	49×	body	640	valid
10.0ms	100×	body	80	valid
5.0ms	76×	body	80	nan
5.0ms	18×	body	320	valid
3.0ms	17×	body	160	valid

simplify41.0ms

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: 41.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
10.1b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite570.0ms

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:

231.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
106.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
202.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

376.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms	(pow (+ 1.0 (/ i n)) n)
348.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify58.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5001	3166

prune785.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
2.6b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
10.2b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite416.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
31×	`times-frac`
28×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`associate-/r*`
7×	`pow1` `associate-r`
6×	`cbrt-undiv` `unpow-prod-down` `div-exp` `add-log-exp` `difference-of-squares`
4×	`associate-*r/`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `sqr-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `clear-num` `associate-/r/` `-commutative` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 110

Calls

4 calls:

201.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
105.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms	(pow (+ 1.0 (/ i n)) n)
95.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

276.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
261.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms	(pow (+ 1.0 (/ i n)) n)
361.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify81.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	651	1023
1	3174	917
2	5001	912

prune295.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (/ i n) n) 1.0))
0.1b	(/ (* 100.0 (- (pow (/ i n) n) 1.0)) (/ i n))
3.1b	(- (pow (/ i n) n) 1.0)
6.3b	(pow (/ i n) n)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
42×	`times-frac`
32×	`*-un-lft-identity`
28×	`add-cube-cbrt`
21×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`unpow-prod-down`
13×	`associate-/r*`
8×	`associate-r` `difference-of-squares`
7×	`pow1` `div-exp`
6×	`cbrt-undiv` `add-log-exp`
4×	`associate-*r/` `div-inv`
3×	`sub-neg` `pow-unpow` `flip3--` `associate-l` `prod-exp` `flip--` `cbrt-unprod` `sqr-pow`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-exp` `associate-/l/` `distribute-lft-out--`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `associate-/r/` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 122

Calls

4 calls:

63.0ms	(* 100.0 (- (pow (/ i n) n) 1.0))
33.0ms	(/ (* 100.0 (- (pow (/ i n) n) 1.0)) (/ i n))
28.0ms	(- (pow (/ i n) n) 1.0)
4.0ms	(pow (/ i n) n)

series359.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* 100.0 (- (pow (/ i n) n) 1.0))
153.0ms	(/ (* 100.0 (- (pow (/ i n) n) 1.0)) (/ i n))
74.0ms	(- (pow (/ i n) n) 1.0)
46.0ms	(pow (/ i n) n)

simplify117.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	932	1127
1	4685	1027
2	5001	1007

prune369.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (/ i n) n) 1.0))
3.4b	(+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0)))
6.3b	(pow (/ i n) n)
6.3b	(pow (/ i n) (* 2 n))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
34×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`unpow-prod-down`
12×	`add-exp-log`
11×	`distribute-lft-out`
8×	`add-log-exp`
6×	`pow1` `add-cbrt-cube`
4×	`pow-unpow` `pow-exp` `associate-/r` `associate-/l`
3×	`flip3-+` `div-sub` `div-exp` `flip-+` `div-inv`
2×	`neg-sub0` `pow-to-exp` `associate-+r-` `pow-pow` `unsub-neg` `sum-log` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `neg-log` `clear-num`

Counts

4 → 113

Calls

4 calls:

89.0ms	(/ (+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (/ i n) n) 1.0))
27.0ms	(+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0)))
3.0ms	(pow (/ i n) n)
4.0ms	(pow (/ i n) (* 2 n))

series323.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (/ i n) n) 1.0))
82.0ms	(+ (pow (/ i n) (* 2 n)) (- (* 1.0 1.0)))
46.0ms	(pow (/ i n) n)
55.0ms	(pow (/ i n) (* 2 n))

simplify94.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	750	1352
1	3339	1253
2	5001	1233

prune383.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.5b

regimes219.0ms

Accuracy

51.5% (13.2b remaining)

Error of 29.8b against oracle of 16.6b and baseline of 43.9b

bsearch935.0ms

Steps

Iters	Range		Point
8	1.9388806651223434e+173	8.867436241502294e+176	4.7215330661381895e+175
9	3.1383368649600063e-111	2.221497081354824e-102	1.862196599311927e-104
10	-5.360679504985299e-297	2.1728968967176598e-303	-7.7041642639419e-311
7	-3529.757956125628	-29.541817090935037	-29.971639032111977
8	-1.7636691380633754e+18	-2542138303994675.5	-8.549866216582126e+17
8	-5.1499886097089576e+153	-1.8010740352434605e+151	-2.5145781368598933e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	126	118
1	126	118

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.2s	2457×	body	1280	valid
2.1s	984×	body	2560	valid
719.0ms	1628×	body	640	valid
301.0ms	3001×	body	80	valid
258.0ms	877×	body	320	valid
166.0ms	2279×	body	80	nan
79.0ms	407×	body	160	valid
26.0ms	6×	body	5120	valid