Details

Time bar (total: 27.3s)

sample257.0ms

Algorithm
intervals
Results
105.0ms35×body2560valid
79.0ms76×body1280valid
28.0ms53×body640valid
8.0ms96×body80valid
8.0ms25×body320valid
5.0ms90×body80nan
2.0ms15×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5000
51593
4364
3144
260
125
010

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.4b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite833.0ms

Algorithm
rewrite-expression-head
Rules
1070×times-frac
777×add-sqr-sqrt
586×*-un-lft-identity
442×add-cube-cbrt
201×difference-of-squares
104×associate-/r*
87×unpow-prod-down
72×sqr-pow
67×distribute-lft-out--
42×div-inv
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
16×associate-/l*
11×associate-/r/
9×cbrt-undiv div-exp
8×fma-neg
6×flip3-- flip-- add-log-exp
5×pow1 distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
2×clear-num frac-2neg
1×pow-to-exp sub-neg pow-pow diff-log pow-exp associate-/l/
Counts
4 → 610
Calls
4 calls:
212.0ms
(/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0))
224.0ms
(/ n (/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0)))
325.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)

series2.8s

Counts
4 → 12
Calls
4 calls:
1.8s
(/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0))
267.0ms
(/ n (/ (/ i 100.0) (- (pow (+ 1.0 (/ i n)) n) 1.0)))
378.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
329.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.8s

Counts
622 → 622
Iterations
IterNodes
done5000
13100
01050

prune3.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (* 0.5 (pow i 2)))
0.1b
(/ n (/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2))))))
9.9b
(/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))))
10.4b
(* (log 1.0) (pow i 2))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
241×add-sqr-sqrt
235×*-un-lft-identity add-cube-cbrt
48×associate-/r*
23×add-exp-log
22×div-inv
20×add-cbrt-cube
16×associate-/l*
11×associate-/r/
9×cbrt-undiv div-exp
8×associate-*r*
5×pow1 flip3-- flip--
4×expm1-log1p-u unpow-prod-down associate-*l* log1p-expm1-u add-log-exp unswap-sqr
3×prod-exp
2×clear-num frac-2neg unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow *-commutative cbrt-unprod fma-udef associate-/l/
Counts
4 → 316
Calls
4 calls:
0.0ms
(fma 1.0 i (* 0.5 (pow i 2)))
26.0ms
(/ n (/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2))))))
18.0ms
(/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))))
11.0ms
(* (log 1.0) (pow i 2))

series1.1s

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma 1.0 i (* 0.5 (pow i 2)))
233.0ms
(/ n (/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2))))))
579.0ms
(/ (/ i 100.0) (- (fma (log 1.0) n (fma 1.0 i (* 0.5 (pow i 2)))) (* 0.5 (* (log 1.0) (pow i 2)))))
184.0ms
(* (log 1.0) (pow i 2))

simplify626.0ms

Counts
328 → 328
Iterations
IterNodes
done5001
11647
0569

prune2.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 i) 100.0)
2.4b
(* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i)))))
10.4b
(* (log 1.0) (* 0.5 (* i i)))
13.0b
(* (* (/ 1 i) 100.0) (* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i))))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
41×add-cbrt-cube
34×prod-exp
30×distribute-rgt-in add-sqr-sqrt pow1 distribute-lft-in
22×*-un-lft-identity cbrt-unprod
21×associate-*l* add-cube-cbrt
18×prod-diff
16×pow-prod-down
11×times-frac
8×associate-*r* associate-*r/
6×sub-neg div-exp associate--l+ fma-udef
5×associate-*l/
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp unswap-sqr
3×cbrt-undiv rec-exp flip3-- 1-exp flip--
2×frac-times
1×log-pow div-inv
Counts
4 → 156
Calls
4 calls:
15.0ms
(* (/ 1 i) 100.0)
15.0ms
(* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i)))))
36.0ms
(* (log 1.0) (* 0.5 (* i i)))
53.0ms
(* (* (/ 1 i) 100.0) (* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i))))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (/ 1 i) 100.0)
146.0ms
(* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i)))))
173.0ms
(* (log 1.0) (* 0.5 (* i i)))
206.0ms
(* (* (/ 1 i) 100.0) (* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i))))))

simplify359.0ms

Counts
168 → 168
Iterations
IterNodes
done5001
1884
0285

prune789.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 9.2b

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (/ 100.0 i))
2.4b
(* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i)))))
10.4b
(* (log 1.0) (* 0.5 (* i i)))
13.0b
(* (* (* (cbrt (/ 100.0 i)) (cbrt (/ 100.0 i))) (cbrt (/ 100.0 i))) (* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i))))))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
37×pow1 cbrt-div
36×add-exp-log
30×distribute-rgt-in distribute-lft-in
29×frac-times associate-*r/
28×add-cbrt-cube
22×add-sqr-sqrt pow-prod-down associate-*l/ prod-exp cbrt-unprod
20×*-un-lft-identity add-cube-cbrt
18×prod-diff
13×cbrt-prod
9×times-frac flip3-- flip--
8×associate-*l*
6×sub-neg associate--l+ fma-udef
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
1×pow1/3 log-pow div-inv unswap-sqr
Counts
4 → 159
Calls
4 calls:
2.0ms
(cbrt (/ 100.0 i))
15.0ms
(* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i)))))
36.0ms
(* (log 1.0) (* 0.5 (* i i)))
151.0ms
(* (* (* (cbrt (/ 100.0 i)) (cbrt (/ 100.0 i))) (cbrt (/ 100.0 i))) (* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i))))))

series806.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(cbrt (/ 100.0 i))
144.0ms
(* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i)))))
172.0ms
(* (log 1.0) (* 0.5 (* i i)))
280.0ms
(* (* (* (cbrt (/ 100.0 i)) (cbrt (/ 100.0 i))) (cbrt (/ 100.0 i))) (* n (- (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i))) (* (log 1.0) (* 0.5 (* i i))))))

simplify1.3s

Counts
171 → 171
Iterations
IterNodes
done5000
24879
1963
0323

prune648.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 9.2b

regimes831.0ms

Accuracy

45.6% (13.1b remaining)

Error of 22.1b against oracle of 9.0b and baseline of 33.1b

bsearch1.2s

Steps
ItersRangePoint
9
1.9810384541203628e-14
1.3953242987786103e-06
2.017216558646519e-14
7
5.714800893424793e-72
1.5611864490473165e-70
6.309945584301677e-71
10
2.6930047707368117e-129
2.2238472426831852e-116
5.768185076220756e-118
11
-2.7466970801947033e-308
1.8451777477141087e-282
-1.23685988632567e-310
9
-2.888724852950189e+30
-1.9220603911752233e+24
-8.577935915550075e+29
8
-8.389936357340607e+106
-5.720382841890011e+103
-8.23875326441092e+106
7
-4.1468841507459867e+123
-2.615624459402513e+121
-6.142887410522618e+122

simplify19.0ms

Iterations
IterNodes
done132
3132
2129
1126
0106

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.1s2450×body1280valid
1.9s995×body2560valid
525.0ms1640×body640valid
177.0ms835×body320valid
146.0ms3041×body80valid
107.0ms2189×body80nan
74.0ms454×body160valid
23.0ms7×body5120valid