Details

Time bar (total: 20.6s)

sample155.0ms

Algorithm
intervals
Results
61.0ms30×body2560valid
50.0ms75×body1280valid
14.0ms48×body640valid
5.0ms107×body80valid
4.0ms1×body5120valid
4.0ms23×body320valid
3.0ms84×body80nan
1.0ms15×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25815
313715
431915
593915
6376015
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

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)
7.8b
(pow (+ 1.0 (/ i n)) n)
10.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite606.0ms

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:
246.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
114.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
217.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
374.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
249.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms
(pow (+ 1.0 (/ i n)) n)
361.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.3s

Counts
293 → 293
Iterations

Useful iterations: 2 (687.0ms)

IterNodesCost
04376469
112216125
237715875
done50005875

prune816.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))))
0.9b
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
7.8b
(pow (+ 1.0 (/ i n)) n)
7.8b
(pow (+ 1.0 (/ i n)) n)

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
31×add-sqr-sqrt
19×associate-*l*
18×add-exp-log sqrt-prod
17×add-cube-cbrt
16×add-cbrt-cube
15×times-frac
11×pow1
10×unpow-prod-down
8×distribute-rgt-in distribute-lft-in distribute-lft-out difference-of-squares
6×pow-unpow associate-*r/ prod-exp cbrt-unprod add-log-exp
5×sub-neg
4×sqr-pow
3×flip3-- pow-prod-down flip--
2×cbrt-undiv frac-times pow-to-exp pow-pow div-exp pow-exp distribute-lft-out--
1×diff-log associate-*r* associate-*l/ *-commutative div-inv
Counts
4 → 109
Calls
4 calls:
441.0ms
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))))
120.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
11.0ms
(pow (+ 1.0 (/ i n)) n)
12.0ms
(pow (+ 1.0 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
593.0ms
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))))
306.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
395.0ms
(pow (+ 1.0 (/ i n)) n)
214.0ms
(pow (+ 1.0 (/ i n)) n)

simplify824.0ms

Counts
121 → 121
Iterations

Useful iterations: done (820.0ms)

IterNodesCost
01992920
15112796
215562068
done50012056

prune320.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)
0.1b
(* 100.0 (* 1 (/ (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n) i)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b
(pow (+ 1.0 (/ i n)) n)

rewrite883.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
21×add-sqr-sqrt
20×add-cbrt-cube
16×prod-exp
15×*-un-lft-identity
12×pow1
10×associate-*l*
9×add-cube-cbrt cbrt-unprod
6×unpow-prod-down add-log-exp difference-of-squares
4×div-exp associate-*r* pow-prod-down
3×pow-unpow 1-exp sqr-pow
2×cbrt-undiv flip3-- associate-*r/ associate-*l/ *-commutative flip-- distribute-lft-out--
1×pow-to-exp sub-neg pow-pow diff-log pow-exp distribute-lft-out unswap-sqr
Counts
4 → 84
Calls
4 calls:
307.0ms
(* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)
447.0ms
(* 100.0 (* 1 (/ (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n) i)))
111.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
15.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
287.0ms
(* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)
364.0ms
(* 100.0 (* 1 (/ (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n) i)))
249.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms
(pow (+ 1.0 (/ i n)) n)

simplify892.0ms

Counts
96 → 96
Iterations

Useful iterations: done (889.0ms)

IterNodesCost
01961675
14901533
215421317
done50011313

prune236.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* 1 (/ (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)))
4.3b
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
12.1b
(* (pow i 2) (log 1.0))
12.5b
(/ (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)

rewrite625.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
27×add-cbrt-cube
22×add-sqr-sqrt
20×prod-exp
14×add-cube-cbrt *-un-lft-identity associate-*l*
12×pow1
11×cbrt-unprod
8×associate-*r*
6×log-prod div-exp
5×unswap-sqr
4×cbrt-undiv unpow-prod-down pow-prod-down associate-*l/ add-log-exp
3×distribute-rgt-in distribute-lft-in times-frac 1-exp associate-/r* *-commutative
2×flip3-- associate-*r/ flip-- associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 103
Calls
4 calls:
265.0ms
(* 100.0 (* 1 (/ (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)))
193.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
7.0ms
(* (pow i 2) (log 1.0))
157.0ms
(/ (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)

series674.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(* 100.0 (* 1 (/ (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)))
143.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
140.0ms
(* (pow i 2) (log 1.0))
188.0ms
(/ (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)

simplify1.1s

Counts
115 → 115
Iterations

Useful iterations: 2 (503.0ms)

IterNodesCost
02183267
15733129
223692512
done50002512

prune307.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.2b

regimes207.0ms

Accuracy

49.3% (11.1b remaining)

Error of 22.5b against oracle of 11.4b and baseline of 33.3b

bsearch314.0ms

Steps
ItersRangePoint
5
2.1156019066638916e+289
4.577855936315765e+289
3.6742312284979153e+289
10
9.229508149002838e+228
6.473625115333604e+243
8.555628525961589e+241
8
2.2017045375507158e-43
1.1217154889271968e-38
1.103714573737295e-38
8
-5.4793573196899966e-14
-2.1205983461440786e-16
-5.434849520670692e-14

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
054126
176122
done76122

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s954×body2560valid
1.7s2510×body1280valid
470.0ms1657×body640valid
143.0ms866×body320valid
128.0ms3029×body80valid
76.0ms2286×body80nan
43.0ms423×body160valid
21.0ms6×body5120valid