Details

Time bar (total: 20.4s)

sample226.0ms

Algorithm
intervals
Results
85.0ms35×body2560valid
70.0ms76×body1280valid
27.0ms53×body640valid
7.0ms96×body80valid
6.0ms25×body320valid
5.0ms90×body80nan
2.0ms15×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5159315
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

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 clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down pow-exp associate-*r/ *-commutative
Counts
4 → 321
Calls
4 calls:
440.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
286.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms
(pow (+ 1.0 (/ i n)) n)
391.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
507.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
355.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
294.0ms
(pow (+ 1.0 (/ i n)) n)
578.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify749.0ms

Counts
333 → 333
Iterations

Useful iterations: done (735.0ms)

IterNodesCost
04797415
115216929
done50016479

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (* 0.5 (pow i 2)))
0.1b
(* 100.0 (/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
10.4b
(* (log 1.0) (pow i 2))
17.2b
(/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
100×add-sqr-sqrt
85×*-un-lft-identity add-cube-cbrt
52×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
9×div-inv
7×pow1 associate-*l* unswap-sqr
6×cbrt-undiv div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow associate-/l/
1×pow-to-exp clear-num frac-2neg flip3-- div-sub pow-prod-down pow-exp associate-*r/ log-pow fma-udef flip--
Counts
4 → 183
Calls
4 calls:
0.0ms
(fma 1.0 i (* 0.5 (pow i 2)))
31.0ms
(* 100.0 (/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
17.0ms
(* (log 1.0) (pow i 2))
16.0ms
(/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

series635.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(fma 1.0 i (* 0.5 (pow i 2)))
219.0ms
(* 100.0 (/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n)))
157.0ms
(* (log 1.0) (pow i 2))
191.0ms
(/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ i n))

simplify386.0ms

Counts
195 → 195
Iterations

Useful iterations: done (378.0ms)

IterNodesCost
03206274
19646123
done50015675

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (* 0.5 (pow i 2)))
2.5b
(/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n))
10.4b
(* (log 1.0) (pow i 2))
13.0b
(* (/ 100.0 i) (/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
125×add-sqr-sqrt
93×*-un-lft-identity
91×add-cube-cbrt
53×add-exp-log
52×associate-*r*
32×add-cbrt-cube
23×div-exp
17×associate-*l*
13×associate-/r* prod-exp
12×cbrt-undiv unswap-sqr
10×div-inv
7×pow1 cbrt-unprod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow associate-/l/
1×frac-times pow-to-exp clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*l/ pow-exp associate-*r/ log-pow fma-udef flip--
Counts
4 → 212
Calls
4 calls:
0.0ms
(fma 1.0 i (* 0.5 (pow i 2)))
18.0ms
(/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n))
11.0ms
(* (log 1.0) (pow i 2))
49.0ms
(* (/ 100.0 i) (/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n)))

series586.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma 1.0 i (* 0.5 (pow i 2)))
145.0ms
(/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n))
159.0ms
(* (log 1.0) (pow i 2))
215.0ms
(* (/ 100.0 i) (/ (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) (/ 1 n)))

simplify436.0ms

Counts
224 → 224
Iterations

Useful iterations: done (428.0ms)

IterNodesCost
03607676
111897265
done50016417

prune999.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.4b

localize38.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)
4.9b
(* (/ (sqrt 100.0) (cbrt i)) (* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n))
7.5b
(* (/ (sqrt 100.0) (* (cbrt i) (cbrt i))) (* (/ (sqrt 100.0) (cbrt i)) (* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)))
10.4b
(* (log 1.0) (pow i 2))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log
71×add-cbrt-cube
57×associate-*l*
48×prod-exp
46×cbrt-unprod
45×add-sqr-sqrt
42×times-frac
37×*-un-lft-identity add-cube-cbrt
21×pow1 sqrt-prod
18×cbrt-prod cbrt-undiv div-exp associate-*l/
13×associate-*r*
11×frac-times associate-*r/
10×pow-prod-down
7×flip3-- flip--
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down *-commutative log1p-expm1-u add-log-exp
2×div-inv unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow
Counts
4 → 183
Calls
4 calls:
14.0ms
(* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)
43.0ms
(* (/ (sqrt 100.0) (cbrt i)) (* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n))
118.0ms
(* (/ (sqrt 100.0) (* (cbrt i) (cbrt i))) (* (/ (sqrt 100.0) (cbrt i)) (* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)))
11.0ms
(* (log 1.0) (pow i 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)
334.0ms
(* (/ (sqrt 100.0) (cbrt i)) (* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n))
465.0ms
(* (/ (sqrt 100.0) (* (cbrt i) (cbrt i))) (* (/ (sqrt 100.0) (cbrt i)) (* (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))) n)))
160.0ms
(* (log 1.0) (pow i 2))

simplify339.0ms

Counts
195 → 195
Iterations

Useful iterations: done (332.0ms)

IterNodesCost
03397699
110747369
done50005970

prune1.0s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.4b

regimes587.0ms

Accuracy

43.9% (12.6b remaining)

Error of 23.5b against oracle of 11.0b and baseline of 33.3b

bsearch454.0ms

Steps
ItersRangePoint
7
1.2245728681896357e-155
1.2152850197652755e-153
1.4183297845116364e-154
7
-22.8286883066892
-0.10952899301968014
-1.8594290872480363
8
-8.389936357340607e+106
-5.720382841890011e+103
-8.23875326441092e+106
7
-4.1468841507459867e+123
-2.615624459402513e+121
-6.142887410522618e+122

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
046142
161116
done61116

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.1s2450×body1280valid
1.9s995×body2560valid
612.0ms1640×body640valid
260.0ms3041×body80valid
179.0ms835×body320valid
141.0ms2189×body80nan
52.0ms454×body160valid
23.0ms7×body5120valid