Details

Time bar (total: 1.3m)

sample209.0ms

Algorithm
intervals
Results
82.0ms74×body1280valid
54.0ms22×body2560valid
35.0ms66×body640valid
7.0ms100×body80valid
5.0ms21×body320valid
3.0ms49×body80nan
2.0ms13×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
314015
434715
5151415
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
8.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

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:
504.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
272.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
468.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
551.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
381.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
285.0ms
(pow (+ 1.0 (/ i n)) n)
525.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify915.0ms

Counts
293 → 293
Iterations

Useful iterations: done (900.0ms)

IterNodesCost
04376469
114166211
done50005919

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize38.0ms

Local error

Found 4 expressions with local error:

6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) n)
7.7b
(/ (- (* (pow (+ 1.0 (/ i n)) n) (pow (+ 1.0 (/ i n)) n)) (* 1.0 1.0)) (* (/ i n) (+ (pow (+ 1.0 (/ i n)) n) 1.0)))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down
9×pow-unpow
7×pow1
5×associate-/r/
4×cbrt-undiv times-frac div-exp associate-/l* add-log-exp
3×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
2×frac-times flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ associate-/l/ difference-of-squares
1×flip3-- frac-2neg div-sub associate-*l/ clear-num associate-/r* flip-- div-inv
Counts
4 → 87
Calls
4 calls:
19.0ms
(pow (+ 1.0 (/ i n)) n)
20.0ms
(pow (+ 1.0 (/ i n)) n)
22.0ms
(pow (+ 1.0 (/ i n)) n)
256.0ms
(/ (- (* (pow (+ 1.0 (/ i n)) n) (pow (+ 1.0 (/ i n)) n)) (* 1.0 1.0)) (* (/ i n) (+ (pow (+ 1.0 (/ i n)) n) 1.0)))

series3.4s

Counts
4 → 12
Calls
4 calls:
313.0ms
(pow (+ 1.0 (/ i n)) n)
298.0ms
(pow (+ 1.0 (/ i n)) n)
274.0ms
(pow (+ 1.0 (/ i n)) n)
2.5s
(/ (- (* (pow (+ 1.0 (/ i n)) n) (pow (+ 1.0 (/ i n)) n)) (* 1.0 1.0)) (* (/ i n) (+ (pow (+ 1.0 (/ i n)) n) 1.0)))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01642324
15311958
225301721
done50001711

prune375.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.4b

localize42.0ms

Local error

Found 4 expressions with local error:

6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.7b
(/ (- (pow (* (pow (+ 1.0 (/ i n)) n) (pow (+ 1.0 (/ i n)) n)) 3) (pow (* 1.0 1.0) 3)) (/ (* (+ (pow (pow (+ 1.0 (/ i n)) n) 4) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (+ 1.0 (/ i n)) (* 2 n))))) (* i (+ (pow (+ 1.0 (/ i n)) n) 1.0))) n))

rewrite759.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
128×difference-of-squares
125×add-sqr-sqrt
83×*-un-lft-identity
76×unpow-prod-down
67×sqr-pow
64×cube-prod
61×add-cube-cbrt
23×div-inv
21×add-exp-log associate-/l*
18×add-cbrt-cube
8×difference-cubes distribute-lft-out--
7×pow1 cbrt-undiv pow-unpow div-exp associate-/r*
4×add-log-exp
3×pow-to-exp pow-pow pow-exp prod-exp cbrt-unprod distribute-lft-out
2×associate-/l/
1×flip3-- frac-2neg div-sub clear-num associate-/r/ flip--
Counts
4 → 249
Calls
4 calls:
29.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(pow (+ 1.0 (/ i n)) n)
35.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
647.0ms
(/ (- (pow (* (pow (+ 1.0 (/ i n)) n) (pow (+ 1.0 (/ i n)) n)) 3) (pow (* 1.0 1.0) 3)) (/ (* (+ (pow (pow (+ 1.0 (/ i n)) n) 4) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (+ 1.0 (/ i n)) (* 2 n))))) (* i (+ (pow (+ 1.0 (/ i n)) n) 1.0))) n))

series52.0s

Counts
4 → 12
Calls
4 calls:
235.0ms
(pow (+ 1.0 (/ i n)) n)
224.0ms
(pow (+ 1.0 (/ i n)) n)
239.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
51.3s
(/ (- (pow (* (pow (+ 1.0 (/ i n)) n) (pow (+ 1.0 (/ i n)) n)) 3) (pow (* 1.0 1.0) 3)) (/ (* (+ (pow (pow (+ 1.0 (/ i n)) n) 4) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (+ 1.0 (/ i n)) (* 2 n))))) (* i (+ (pow (+ 1.0 (/ i n)) n) 1.0))) n))

simplify590.0ms

Counts
261 → 261
Iterations

Useful iterations: done (574.0ms)

IterNodesCost
045120361
1143418415
done500017134

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)

rewrite883.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
28×associate-*r*
22×times-frac
19×add-exp-log add-cube-cbrt
18×add-cbrt-cube
12×pow1 difference-of-squares
8×unpow-prod-down
7×prod-exp cbrt-unprod
6×add-log-exp
5×sqr-pow
4×associate-*l* pow-prod-down distribute-lft-out--
3×pow-unpow
2×cbrt-undiv associate-*r/ div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*l/ pow-exp flip-- div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
368.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
323.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
170.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)

series994.0ms

Counts
4 → 12
Calls
4 calls:
367.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
157.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
250.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.4s

Counts
111 → 111
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02241903
16171820
230361610
done50001602

prune272.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

regimes138.0ms

Accuracy

54.5% (11.6b remaining)

Error of 20.1b against oracle of 8.6b and baseline of 34.0b

bsearch318.0ms

Steps
ItersRangePoint
8
3162079221.758062
63527163486164.19
3222196569.8044276
6
-1.263328474033804e-18
-8.622232208669777e-20
-1.2371314562791146e-18

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04375
16175
done6175

end0.0ms

sample5.7s

Algorithm
intervals
Results
1.9s2439×body1280valid
1.9s977×body2560valid
919.0ms1632×body640valid
156.0ms3056×body80valid
151.0ms807×body320valid
121.0ms2361×body80nan
87.0ms483×body160valid
40.0ms12×body5120valid