Details

Time bar (total: 32.1s)

sample221.0ms

Algorithm
intervals
Results
72.0ms28×body2560valid
65.0ms71×body1280valid
26.0ms54×body640valid
21.0ms96×body80valid
9.0ms34×body320valid
4.0ms79×body80nan
2.0ms12×body160valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
314015
434715
5151415
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.3b
(pow (+ 1.0 (/ i n)) n)
8.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
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 distribute-lft-out
Counts
4 → 281
Calls
4 calls:
511.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
262.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms
(pow (+ 1.0 (/ i n)) n)
506.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts
4 → 12
Calls
4 calls:
443.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
303.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
291.0ms
(pow (+ 1.0 (/ i n)) n)
436.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify689.0ms

Counts
293 → 293
Iterations

Useful iterations: done (679.0ms)

IterNodesCost
04376469
114166211
done50005919

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 21.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
0.0b
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.3b
(pow (+ 1.0 (/ i n)) n)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
1689×times-frac
1097×add-sqr-sqrt
830×*-un-lft-identity
662×add-cube-cbrt
330×associate-*r*
246×difference-of-squares
86×unpow-prod-down
83×sqr-pow
82×distribute-lft-out--
80×div-inv
59×add-exp-log
34×add-cbrt-cube
32×div-exp
25×associate-/l*
16×cbrt-undiv
13×associate-/r*
9×prod-exp
7×pow1 unswap-sqr
6×add-log-exp
5×cbrt-unprod
4×rec-exp 1-exp
3×pow-unpow associate-*l*
2×div-sub associate-/r/
1×pow-to-exp sub-neg flip3-- pow-pow frac-2neg diff-log associate-*r/ pow-prod-down pow-exp clear-num *-commutative flip-- associate-/l/ distribute-lft-out
Counts
4 → 786
Calls
4 calls:
488.0ms
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
302.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
225.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms
(pow (+ 1.0 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
435.0ms
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
497.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
305.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
304.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.2s

Counts
798 → 798
Iterations

Useful iterations: done (2.2s)

IterNodesCost
0104822000
1378419552
done500219238

prune3.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
0.2b
(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
12.2b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.8b
(* (pow i 2) (log 1.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
846×times-frac
428×add-sqr-sqrt
399×*-un-lft-identity
397×add-cube-cbrt
178×associate-*r*
65×add-exp-log
57×div-inv
38×add-cbrt-cube
33×div-exp
17×cbrt-undiv
16×associate-/r* associate-/l*
12×prod-exp
11×associate-*l* unswap-sqr
7×pow1
6×log-prod cbrt-unprod
4×unpow-prod-down rec-exp 1-exp add-log-exp
3×distribute-rgt-in distribute-lft-in div-sub associate-/l/
2×frac-2neg clear-num associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp flip3-- associate-*r/ pow-prod-down pow-exp log-pow flip--
Counts
4 → 492
Calls
4 calls:
420.0ms
(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
322.0ms
(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
382.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
22.0ms
(* (pow i 2) (log 1.0))

series968.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
293.0ms
(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
197.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
196.0ms
(* (pow i 2) (log 1.0))

simplify1.5s

Counts
504 → 504
Iterations

Useful iterations: done (1.5s)

IterNodesCost
071622321
1246420781
done500019496

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
0.1b
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
12.2b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.8b
(* (pow i 2) (log 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod unswap-sqr
4×unpow-prod-down pow-prod-down add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*l/ pow-exp clear-num log-pow flip--
Counts
4 → 117
Calls
4 calls:
367.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
369.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
334.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms
(* (pow i 2) (log 1.0))

series732.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
234.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
144.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
190.0ms
(* (pow i 2) (log 1.0))

simplify1.7s

Counts
129 → 129
Iterations

Useful iterations: 2 (494.0ms)

IterNodesCost
02183765
15643690
230923161
done50013161

prune898.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.3b

regimes291.0ms

Accuracy

46.3% (12.1b remaining)

Error of 23.3b against oracle of 11.2b and baseline of 33.7b

bsearch715.0ms

Steps
ItersRangePoint
10
5.527224725001059e+164
3.61215045040521e+174
2.0375480860394606e+169
10
8066803396.000897
8.375463895322616e+20
8143434713.669914
9
-1.074406417091718e-51
-9.55145155808955e-59
-1.0591314467102691e-51

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04089
15689
done5689

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.3s2535×body1280valid
2.2s948×body2560valid
709.0ms1613×body640valid
500.0ms2995×body80valid
325.0ms888×body320valid
133.0ms2115×body80nan
92.0ms425×body160valid
37.0ms7×body5120valid