Details

Time bar (total: 26.8s)

sample279.0ms

Algorithm
intervals
Results
109.0ms75×body1280valid
83.0ms24×body2560valid
34.0ms51×body640valid
14.0ms105×body80valid
11.0ms24×body320valid
8.0ms69×body80nan
4.0ms12×body160valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2016
52016
4533
3154
259
128
010

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (/ i n))
1.2b
(fma 100 (pow (+ 1 (/ i n)) n) -100)
7.4b
(pow (+ 1 (/ i n)) n)
8.4b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
53×*-un-lft-identity
49×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
10×add-exp-log
9×add-cbrt-cube
6×add-log-exp
5×pow1 div-inv
4×expm1-log1p-u unpow-prod-down insert-posit16 log1p-expm1-u
3×cbrt-undiv pow-unpow fma-def div-exp associate-/l*
2×distribute-lft-out
1×pow-to-exp +-commutative clear-num sum-log pow-pow frac-2neg flip3-+ pow-exp associate-/r/ flip-+ fma-udef sqr-pow
Counts
4 → 123
Calls
4 calls:
6.0ms
(+ 1 (/ i n))
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
18.0ms
(pow (+ 1 (/ i n)) n)
17.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ 1 (/ i n))
318.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
310.0ms
(pow (+ 1 (/ i n)) n)
440.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify1.5s

Counts
135 → 135
Iterations
IterNodes
done2000
32000
21814
1600
0241

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize35.0ms

Local error

Found 4 expressions with local error:

2.5b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
6.1b
(log1p (/ i n))
8.5b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
8.5b
(* n (log1p (/ i n)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1
5×expm1-log1p-u div-inv
4×insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
1×log1p-udef clear-num frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 117
Calls
4 calls:
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
0.0ms
(log1p (/ i n))
15.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
12.0ms
(* n (log1p (/ i n)))

series1.1s

Counts
4 → 12
Calls
4 calls:
352.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
68.0ms
(log1p (/ i n))
592.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))
85.0ms
(* n (log1p (/ i n)))

simplify1.2s

Counts
129 → 129
Iterations
IterNodes
done2000
22000
1635
0257

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.3b

localize38.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
6.1b
(log1p (/ i n))
8.5b
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
8.5b
(* n (log1p (/ i n)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/r*
11×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
5×expm1-log1p-u div-inv
4×insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-*r* associate-*l* associate-/l*
2×flip3-+ flip-+ associate-/l/
1×+-commutative log1p-udef clear-num sum-log fma-def frac-2neg pow-prod-down prod-exp log1p-expm1 associate-/r/ *-commutative cbrt-unprod unswap-sqr
Counts
4 → 123
Calls
4 calls:
19.0ms
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
1.0ms
(log1p (/ i n))
51.0ms
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
12.0ms
(* n (log1p (/ i n)))

series1.0s

Counts
4 → 12
Calls
4 calls:
349.0ms
(+ (* 100 (exp (* n (log1p (/ i n))))) -100)
94.0ms
(log1p (/ i n))
464.0ms
(/ (+ (* 100 (exp (* n (log1p (/ i n))))) -100) (/ i n))
96.0ms
(* n (log1p (/ i n)))

simplify1.2s

Counts
135 → 135
Iterations
IterNodes
done2000
22000
1723
0272

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

localize88.0ms

Local error

Found 4 expressions with local error:

8.5b
(* n (log1p (/ i n)))
8.5b
(* n (log1p (/ i n)))
8.5b
(* n (log1p (/ i n)))
8.5b
(* n (log1p (/ i n)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
12×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
4×expm1-log1p-u pow-prod-down prod-exp *-commutative cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
Counts
4 → 84
Calls
4 calls:
6.0ms
(* n (log1p (/ i n)))
6.0ms
(* n (log1p (/ i n)))
6.0ms
(* n (log1p (/ i n)))
6.0ms
(* n (log1p (/ i n)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* n (log1p (/ i n)))
93.0ms
(* n (log1p (/ i n)))
97.0ms
(* n (log1p (/ i n)))
70.0ms
(* n (log1p (/ i n)))

simplify1.5s

Counts
96 → 96
Iterations
IterNodes
done2000
52000
4932
3346
2146
172
039

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

regimes252.0ms

Accuracy

37.7% (16.2b remaining)

Error of 29.4b against oracle of 13.2b and baseline of 39.2b

bsearch1.5s

Steps
ItersRangePoint
8
5.070728200186422e+194
1.7112199524119634e+199
7.855089357782943e+198
7
4.091483816042697e-45
1.1226141387625792e-43
4.809293212884638e-44
10
1.7939671322110348e-104
7.546456747018334e-93
3.2388182495466635e-96
12
6.77630104842725e-252
1.5629148595638114e-211
1.547355740653275e-211
11
-2.3547009421769087e-299
6.119726840572462e-296
1.9360594076256e-310
6
-8.564238649774633e+137
-7.70551469089499e+136
-4.6511036455496e+137

simplify79.0ms

Iterations
IterNodes
done145
1145
0111

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.0s2490×body1280valid
2.6s953×body2560valid
1.4s1574×body640valid
362.0ms3068×body80valid
330.0ms2254×body80nan
310.0ms831×body320valid
131.0ms450×body160valid
37.0ms8×body5120valid