Details

Time bar (total: 26.1s)

sample234.0ms

Algorithm
intervals
Results
89.0ms33×body2560valid
84.0ms72×body1280valid
24.0ms54×body640valid
9.0ms34×body320valid
6.0ms90×body80valid
3.0ms54×body80nan
2.0ms14×body160valid

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5005
52617
4533
3154
259
128
010

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.7b
(fma 100 (pow (+ 1 (/ i n)) n) -100)
5.3b
(pow (+ 1 (/ i n)) n)
10.7b
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
49×*-un-lft-identity
47×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
9×add-exp-log
8×add-cbrt-cube
5×div-inv
4×pow1 unpow-prod-down
3×expm1-log1p-u cbrt-undiv pow-unpow div-exp insert-posit16 log1p-expm1-u associate-/l* add-log-exp
1×pow-to-exp clear-num pow-pow frac-2neg pow-exp associate-/r/ fma-udef distribute-lft-out sqr-pow
Counts
3 → 105
Calls
3 calls:
0.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
26.0ms
(pow (+ 1 (/ i n)) n)
11.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

series1.0s

Counts
3 → 9
Calls
3 calls:
321.0ms
(fma 100 (pow (+ 1 (/ i n)) n) -100)
271.0ms
(pow (+ 1 (/ i n)) n)
444.0ms
(/ (fma 100 (pow (+ 1 (/ i n)) n) -100) (/ i n))

simplify2.0s

Counts
114 → 114
Iterations
IterNodes
done5001
21605
1528
0222

prune721.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.2b

localize37.0ms

Local error

Found 4 expressions with local error:

1.9b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
4.6b
(log1p (/ i n))
10.7b
(* n (log1p (/ i n)))
10.7b
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

rewrite48.0ms

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)
1.0ms
(log1p (/ i n))
14.0ms
(* n (log1p (/ i n)))
26.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
343.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
66.0ms
(log1p (/ i n))
97.0ms
(* n (log1p (/ i n)))
552.0ms
(/ (fma 100 (exp (* n (log1p (/ i n)))) -100) (/ i n))

simplify2.0s

Counts
129 → 129
Iterations
IterNodes
done5000
22183
1636
0257

prune680.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.9b
(fma 100 (exp (* n (log1p (/ i n)))) -100)
4.6b
(log1p (/ i n))
9.7b
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
10.7b
(* n (log1p (/ i n)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
50×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
13×associate-/l*
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 associate-/r* div-exp associate-*r* associate-*l*
1×log1p-udef clear-num frac-2neg pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod fma-udef unswap-sqr associate-/l/
Counts
4 → 117
Calls
4 calls:
0.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
0.0ms
(log1p (/ i n))
11.0ms
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
8.0ms
(* n (log1p (/ i n)))

series1.6s

Counts
4 → 12
Calls
4 calls:
308.0ms
(fma 100 (exp (* n (log1p (/ i n)))) -100)
73.0ms
(log1p (/ i n))
1.2s
(/ (/ i n) (fma 100 (exp (* n (log1p (/ i n)))) -100))
84.0ms
(* n (log1p (/ i n)))

simplify2.2s

Counts
129 → 129
Iterations
IterNodes
done5001
21969
1671
0277

prune844.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n))))
0.3b
(fma (/ i (* n n)) 1/200 (/ 1/100 n))
2.7b
(fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n)))
8.2b
(/ i (* n n))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×add-exp-log
12×times-frac
11×add-cbrt-cube
6×associate-/l*
5×pow1
4×expm1-log1p-u associate-/r* div-exp insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv
2×clear-num frac-2neg fma-udef div-inv
1×rec-exp 1-exp prod-exp cbrt-unprod pow-flip inv-pow
Counts
4 → 80
Calls
4 calls:
5.0ms
(/ 1 (fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n))))
0.0ms
(fma (/ i (* n n)) 1/200 (/ 1/100 n))
0.0ms
(fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n)))
9.0ms
(/ i (* n n))

series229.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ 1 (fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n))))
69.0ms
(fma (/ i (* n n)) 1/200 (/ 1/100 n))
58.0ms
(fma (/ i n) -1/200 (fma (/ i (* n n)) 1/200 (/ 1/100 n)))
44.0ms
(/ i (* n n))

simplify1.7s

Counts
92 → 92
Iterations
IterNodes
done5220
32519
2687
1259
0133

prune394.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 2.9b

regimes433.0ms

Accuracy

54.7% (9.0b remaining)

Error of 12.1b against oracle of 3.1b and baseline of 23.0b

bsearch571.0ms

Steps
ItersRangePoint
8
9.610018365276117e+272
9.38229576005854e+276
2.695991510921252e+276
11
3.5125362636478824e-11
2.0729826645785407e+19
0.5685613637685243
9
-1.1375194732999505
-2.46215381836168e-09
-6.985621920368718e-06

simplify33.0ms

Iterations
IterNodes
done89
189
067

end0.0ms

sample7.8s

Algorithm
intervals
Results
3.0s941×body2560valid
2.7s2503×body1280valid
924.0ms1621×body640valid
326.0ms832×body320valid
298.0ms3022×body80valid
133.0ms2288×body80nan
75.0ms423×body160valid
55.0ms11×body5120valid