Details

sample158.0ms

Algorithm

intervals

Results

60.0ms	82×	body	1280	valid
59.0ms	32×	body	2560	valid
14.0ms	46×	body	640	valid
6.0ms	31×	body	320	valid
5.0ms	107×	body	80	valid
2.0ms	62×	body	80	nan
1.0ms	9×	body	160	valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 39.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite83.0ms

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:

31.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
12.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(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:

355.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
246.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms	(pow (+ 1.0 (/ i n)) n)
347.0ms	(/ (- (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	5002	3166

prune767.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.9b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite45.0ms

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:

12.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
9.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
15.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts

4 → 12

Calls

4 calls:

258.0ms	(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
248.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
204.0ms	(pow (+ 1.0 (/ i n)) n)
364.0ms	(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify77.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (66.0ms)

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

prune274.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
6.8b	(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

10.0ms	(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
6.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
6.0ms	(pow (+ 1.0 (/ i n)) n)
28.0ms	(/ (* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series2.9s

Counts

4 → 12

Calls

4 calls:

457.0ms	(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
219.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
215.0ms	(pow (+ 1.0 (/ i n)) n)
2.0s	(/ (* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify95.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	746	1526
1	4147	1254
2	5002	1233

prune322.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

localize21.0ms

Local error

Found 4 expressions with local error:

6.8b	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
6.8b	(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b	(pow (+ 1.0 (/ i n)) n)
10.7b	(/ (* 100.0 (/ (/ (+ (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))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
36×	`add-cbrt-cube`
31×	`times-frac`
28×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`cbrt-undiv` `div-exp`
13×	`associate-/r*`
12×	`unpow-prod-down`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`pow-unpow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r/` `associate-/l/` `associate-/l`

Counts

4 → 105

Calls

4 calls:

7.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
9.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
6.0ms	(pow (+ 1.0 (/ i n)) n)
38.0ms	(/ (* 100.0 (/ (/ (+ (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))

series14.6s

Counts

4 → 12

Calls

4 calls:

212.0ms	(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
215.0ms	(pow (+ 1.0 (/ i n)) (* 2 n))
208.0ms	(pow (+ 1.0 (/ i n)) n)
13.9s	(/ (* 100.0 (/ (/ (+ (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))

simplify111.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	848	2386
1	4865	1861
2	5002	1861

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

regimes142.0ms

Accuracy

46.7% (12.9b remaining)

Error of 31.4b against oracle of 18.5b and baseline of 42.7b

bsearch606.0ms

Steps

Iters	Range		Point
8	2.6233364391768453e+215	7.559003031217257e+219	7.395559138739582e+219
7	8.449789709258891e+21	1.927335547477129e+23	8.532543483832935e+21
6	3.1399496998840866e-125	3.7800925651486635e-124	6.02622510223327e-125
7	1.4967481787327182e-161	2.5387026277821525e-160	2.515912909264607e-160
8	-1.4252965457371644e-10	-5.035330346103121e-14	-1.3992561866449662e-10
8	-1.6450582212898727e+137	-4.094290472995023e+133	-2.561401665352169e+135

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	107	111
1	107	111

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.8s	2560×	body	1280	valid
1.7s	942×	body	2560	valid
465.0ms	1643×	body	640	valid
138.0ms	871×	body	320	valid
125.0ms	3062×	body	80	valid
66.0ms	2190×	body	80	nan
39.0ms	396×	body	160	valid
29.0ms	8×	body	5120	valid