Details

Time bar (total: 31.8s)

sample230.0ms

Algorithm
intervals
Results
88.0ms82×body1280valid
74.0ms28×body2560valid
27.0ms49×body640valid
7.0ms97×body80valid
7.0ms26×body320valid
5.0ms91×body80nan
2.0ms13×body160valid

simplify4.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

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:
495.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
260.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
31.0ms
(pow (+ 1.0 (/ i n)) n)
536.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
448.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
305.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
262.0ms
(pow (+ 1.0 (/ i n)) n)
540.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.4s

Counts
333 → 333
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ n (/ i (- (pow (/ i n) n) 1.0)))
0.1b
(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
1.1b
(- (pow (/ i n) n) 1.0)
4.6b
(pow (/ i n) n)

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
418×times-frac
393×add-sqr-sqrt
252×*-un-lft-identity
208×add-cube-cbrt
109×unpow-prod-down
95×associate-*r*
88×difference-of-squares
51×prod-diff
30×associate-/r*
27×sqr-pow
22×distribute-lft-out--
21×add-exp-log
18×add-cbrt-cube
17×fma-neg
16×associate-/r/
14×div-inv
8×flip3-- flip--
7×pow1 div-exp
6×cbrt-undiv add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* prod-exp cbrt-unprod associate-/l* unswap-sqr
2×pow-exp
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 376
Calls
4 calls:
56.0ms
(/ n (/ i (- (pow (/ i n) n) 1.0)))
134.0ms
(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
60.0ms
(- (pow (/ i n) n) 1.0)
7.0ms
(pow (/ i n) n)

series385.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ n (/ i (- (pow (/ i n) n) 1.0)))
135.0ms
(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
73.0ms
(- (pow (/ i n) n) 1.0)
55.0ms
(pow (/ i n) n)

simplify1.1s

Counts
388 → 388
Iterations

Useful iterations: done (1.1s)

IterNodesCost
06578161
115987226
done50016788

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
0.1b
(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
1.1b
(- (pow (/ i n) n) 1.0)
4.6b
(pow (/ i n) n)

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
415×times-frac
383×add-sqr-sqrt
251×*-un-lft-identity
207×add-cube-cbrt
109×unpow-prod-down
95×associate-*r*
88×difference-of-squares
63×add-exp-log
51×prod-diff
30×associate-/r* add-cbrt-cube
27×sqr-pow
22×div-exp distribute-lft-out--
21×prod-exp
17×fma-neg
16×associate-/r/
14×div-inv
11×pow1
9×cbrt-undiv cbrt-unprod
8×flip3-- flip--
6×rec-exp 1-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow pow-prod-down associate-/l*
2×pow-exp
1×pow-to-exp sub-neg pow-flip pow-pow frac-2neg diff-log associate-*r/ associate-*l* clear-num un-div-inv *-commutative inv-pow
Counts
4 → 393
Calls
4 calls:
67.0ms
(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
122.0ms
(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
61.0ms
(- (pow (/ i n) n) 1.0)
7.0ms
(pow (/ i n) n)

series344.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
133.0ms
(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
75.0ms
(- (pow (/ i n) n) 1.0)
55.0ms
(pow (/ i n) n)

simplify3.2s

Counts
405 → 405
Iterations

Useful iterations: done (3.1s)

IterNodesCost
06618676
117697090
248406381
done50006376

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
0.0b
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
0.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*l*
24×unpow-prod-down prod-diff
22×times-frac
19×add-exp-log
18×add-cbrt-cube
12×pow1 difference-of-squares
9×sqr-pow
8×fma-neg
7×prod-exp cbrt-unprod
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u distribute-lft-out--
3×pow-unpow
2×cbrt-undiv div-exp associate-*l/ *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*r/ pow-exp flip-- div-inv
Counts
4 → 139
Calls
4 calls:
565.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
384.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
211.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms
(pow (+ 1.0 (/ i n)) n)

series1.6s

Counts
4 → 12
Calls
4 calls:
474.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
461.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
336.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
303.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.6s

Counts
151 → 151
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02522834
16182497
216482138
done50002078

prune448.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.1b

regimes282.0ms

Accuracy

52.9% (12.8b remaining)

Error of 19.0b against oracle of 6.2b and baseline of 33.3b

bsearch719.0ms

Steps
ItersRangePoint
7
1.466106254315184e+230
4.2050101804867395e+231
1.804564161742965e+231
11
3.173232095275158e+114
4.61796087672408e+142
1.4940919618286633e+142
7
3.39002248453449e-27
2.9088581115424155e-25
2.8575028267387598e-25
9
-123126161593.44334
-41918.349557210015
-42606.74875587942

simplify20.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
085246
1112246
done112246

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.8s2515×body1280valid
2.3s989×body2560valid
687.0ms1615×body640valid
262.0ms2337×body80nan
205.0ms856×body320valid
190.0ms2973×body80valid
65.0ms443×body160valid
15.0ms4×body5120valid