Details

Time bar (total: 34.3s)

sample158.0ms

Algorithm
intervals
Results
63.0ms82×body1280valid
53.0ms26×body2560valid
15.0ms51×body640valid
4.0ms100×body80valid
3.0ms20×body320valid
3.0ms83×body80nan
2.0ms16×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.6b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite901.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 321
Calls
4 calls:
335.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
193.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
337.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
363.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
244.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms
(pow (+ 1.0 (/ i n)) n)
351.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify65.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150023446

prune857.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.3b

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
7.6b
(pow (+ 1.0 (/ i n)) n)
7.6b
(pow (+ 1.0 (/ i n)) (* 2 n))
9.2b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite700.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
528×*-un-lft-identity
296×add-sqr-sqrt add-cube-cbrt
116×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
12×unpow-prod-down
8×cbrt-undiv fma-def div-exp add-log-exp
6×pow1 div-sub
4×expm1-log1p-u pow-unpow log1p-expm1-u
3×sqr-pow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 410
Calls
4 calls:
134.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
18.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
499.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.8s

Counts
4 → 12
Calls
4 calls:
269.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
220.0ms
(pow (+ 1.0 (/ i n)) n)
232.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
2.0s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify116.0ms

Algorithm
egg-herbie
Counts
422 → 422
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0188610118
150019695

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.3b

localize18.0ms

Local error

Found 4 expressions with local error:

7.6b
(pow (+ 1.0 (/ i n)) n)
7.6b
(pow (+ 1.0 (/ i n)) n)
7.6b
(pow (+ 1.0 (/ i n)) (* 2 n))
11.1b
(- (/ (pow (+ 1.0 (/ i n)) (* 2 n)) (* (/ i n) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ (/ (* 1.0 1.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
5720×times-frac
2788×*-un-lft-identity
2295×prod-diff
2082×add-sqr-sqrt
2066×add-cube-cbrt
1141×associate-/r/
556×unpow-prod-down
544×div-inv
493×flip3-+ flip-+
360×distribute-lft-out
272×frac-times associate-*r/
139×sqr-pow
137×associate-*l/
17×fma-neg
7×pow1 add-exp-log pow-unpow
6×add-log-exp
5×difference-of-squares
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow-pow pow-exp
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- distribute-lft-out--
Counts
4 → 2392
Calls
4 calls:
17.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
743.0ms
(- (/ (pow (+ 1.0 (/ i n)) (* 2 n)) (* (/ i n) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ (/ (* 1.0 1.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n)))

series3.0s

Counts
4 → 12
Calls
4 calls:
225.0ms
(pow (+ 1.0 (/ i n)) n)
215.0ms
(pow (+ 1.0 (/ i n)) n)
219.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
2.3s
(- (/ (pow (+ 1.0 (/ i n)) (* 2 n)) (* (/ i n) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ (/ (* 1.0 1.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n)))

simplify1.7s

Algorithm
egg-herbie
Counts
2404 → 2404
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
05001193329

prune11.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.6b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite856.0ms

Algorithm
rewrite-expression-head
Rules
323×times-frac
315×add-sqr-sqrt
223×*-un-lft-identity
157×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp associate-*l* sqrt-prod add-log-exp unswap-sqr
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow prod-exp cbrt-unprod
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
Counts
4 → 327
Calls
4 calls:
322.0ms
(* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
181.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
319.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts
4 → 12
Calls
4 calls:
528.0ms
(* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
239.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
204.0ms
(pow (+ 1.0 (/ i n)) n)
334.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify57.0ms

Algorithm
egg-herbie
Counts
339 → 339
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013563952
150023668

prune844.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.5b

regimes232.0ms

Accuracy

55.1% (11.1b remaining)

Error of 29.3b against oracle of 18.2b and baseline of 42.9b

bsearch749.0ms

Steps
ItersRangePoint
10
4.756375948439579e+148
6.004700300407403e+161
1.3538891898856935e+154
10
1.6508802098011257e-110
7.205480219419598e-99
4.687031455960939e-109
9
-3096.4512561506854
-5.8848704152608634e-05
-1.4440406082333634
8
-2.6107605323010537e+144
-6.787307901665572e+139
-1.2425716031584474e+142

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010594
110794
210794

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.7s961×body2560valid
1.7s2505×body1280valid
456.0ms1626×body640valid
134.0ms870×body320valid
123.0ms3006×body80valid
66.0ms2271×body80nan
41.0ms408×body160valid
7.0ms2×body5120valid