Details

Time bar (total: 32.9s)

sample236.0ms

Algorithm
intervals
Results
97.0ms79×body1280valid
70.0ms25×body2560valid
24.0ms49×body640valid
9.0ms33×body320valid
9.0ms111×body80valid
4.0ms67×body80nan
2.0ms12×body160valid

simplify3.5s

Counts
1 → 1
Iterations
IterNodes
done5015
63302
5836
4309
3135
259
125
010

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.4b
(pow (+ 1.0 (/ i n)) n)
8.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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 clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down pow-exp associate-*r/ *-commutative distribute-lft-out
Counts
4 → 281
Calls
4 calls:
431.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
233.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms
(pow (+ 1.0 (/ i n)) n)
377.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts
4 → 12
Calls
4 calls:
595.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
381.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
288.0ms
(pow (+ 1.0 (/ i n)) n)
514.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify3.4s

Counts
293 → 293
Iterations
IterNodes
done5001
24676
11390
0437

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.3b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.4b
(pow (+ 1.0 (/ i n)) n)

rewrite943.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
314×add-sqr-sqrt
206×*-un-lft-identity
146×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
32×unpow-prod-down
30×add-cbrt-cube
29×sqr-pow
28×distribute-lft-out--
23×div-exp
18×div-inv
13×associate-/r* associate-*l*
12×cbrt-undiv
10×prod-exp
8×unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down associate-*l/ pow-exp associate-*r/ *-commutative distribute-lft-out
Counts
4 → 310
Calls
4 calls:
301.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
393.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
200.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
29.0ms
(pow (+ 1.0 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
384.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
450.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
279.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
276.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.9s

Counts
322 → 322
Iterations
IterNodes
done5031
24727
11628
0467

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5))))
2.3b
(/ (+ (+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5)))) (* (log 1.0) n)) (/ 1 n))
11.9b
(* (* i i) (* (log 1.0) 0.5))
16.7b
(* (/ 100.0 i) (/ (+ (+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5)))) (* (log 1.0) n)) (/ 1 n)))

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
116×add-sqr-sqrt
90×*-un-lft-identity
88×add-cube-cbrt
60×add-exp-log
45×associate-*r*
42×add-cbrt-cube
23×div-exp
18×pow1 prod-exp
14×associate-*l* cbrt-unprod
13×associate-/r*
12×cbrt-undiv
10×div-inv
9×pow-prod-down add-log-exp
8×unswap-sqr
3×rec-exp 1-exp associate-/l*
2×associate-+r+ associate-+r- sum-log flip3-+ associate-/r/ *-commutative flip-+ associate-/l/
1×frac-times +-commutative clear-num sub-neg frac-2neg diff-log div-sub associate-*l/ associate-*r/ associate-+l-
Counts
4 → 205
Calls
4 calls:
22.0ms
(+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5))))
284.0ms
(/ (+ (+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5)))) (* (log 1.0) n)) (/ 1 n))
23.0ms
(* (* i i) (* (log 1.0) 0.5))
329.0ms
(* (/ 100.0 i) (/ (+ (+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5)))) (* (log 1.0) n)) (/ 1 n)))

series909.0ms

Counts
4 → 12
Calls
4 calls:
346.0ms
(+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5))))
146.0ms
(/ (+ (+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5)))) (* (log 1.0) n)) (/ 1 n))
195.0ms
(* (* i i) (* (log 1.0) 0.5))
221.0ms
(* (/ 100.0 i) (/ (+ (+ (* (* i i) 0.5) (- (* 1.0 i) (* (* i i) (* (log 1.0) 0.5)))) (* (log 1.0) n)) (/ 1 n)))

simplify1.9s

Counts
217 → 217
Iterations
IterNodes
done5007
23957
11205
0366

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))
0.1b
(* 100.0 (/ (* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n) i))
2.2b
(* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n)
16.8b
(/ (* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n) i)

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
15×add-sqr-sqrt
13×associate-*r/
12×associate-*l/ frac-add
11×*-un-lft-identity add-cube-cbrt
10×associate-*r*
9×flip3-+ flip-+ add-log-exp
8×pow1
6×times-frac flip3-- associate-*l* prod-exp cbrt-unprod flip-- associate-/l/
4×cbrt-undiv associate-+r+ div-exp
3×associate-/r* sum-log
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down *-commutative div-inv unswap-sqr
1×+-commutative associate-+l+ clear-num frac-2neg associate-/l*
Counts
4 → 99
Calls
4 calls:
28.0ms
(+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))
55.0ms
(* 100.0 (/ (* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n) i))
74.0ms
(* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n)
45.0ms
(/ (* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n) i)

series683.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))
215.0ms
(* 100.0 (/ (* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n) i))
155.0ms
(* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n)
201.0ms
(/ (* (+ (+ (* n (log 1.0)) (* 1.0 i)) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))) n) i)

simplify2.2s

Counts
111 → 111
Iterations
IterNodes
done5003
23096
1700
0219

prune509.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.8b

regimes306.0ms

Accuracy

41.3% (13.2b remaining)

Error of 23.8b against oracle of 10.6b and baseline of 33.1b

bsearch502.0ms

Steps
ItersRangePoint
7
5.680956200681059e-225
8.96171128476665e-223
8.76599642872152e-223
6
-3.052506018274348e-266
-2.3564052050298823e-267
-4.586926552796908e-267
7
-8.1353853441046
-0.1501579911863904
-1.995072885870678
9
-1.1388694309263412e+60
-6.092716108791962e+53
-1.4219894413191279e+58
5
-5.900767996836685e+175
-2.667336073769385e+175
-2.8131143936191375e+175

simplify25.0ms

Iterations
IterNodes
done109
1109
077

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.0s2498×body1280valid
1.9s957×body2560valid
557.0ms1594×body640valid
548.0ms3121×body80valid
239.0ms875×body320valid
153.0ms2279×body80nan
57.0ms466×body160valid
22.0ms6×body5120valid