Details

Time bar (total: 6.6m)

sample307.0ms

Algorithm
intervals
Results
109.0ms32×body2560valid
99.0ms57×body1280valid
45.0ms58×body640valid
14.0ms116×body80valid
10.0ms24×body320valid
10.0ms79×body80nan
6.0ms16×body160valid

simplify178.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
178.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize402.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
9.1b
(pow (+ 1 (/ i n)) n)
0.9b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite558.0ms

Algorithm
rewrite-expression-head
Rules
584×times-frac
485×add-sqr-sqrt
366×*-un-lft-identity
224×add-cube-cbrt
174×associate-*r*
168×difference-of-squares
88×unpow-prod-down
85×sqr-pow
84×difference-of-sqr-1
29×div-inv
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
13×associate-/r* associate-/l*
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×insert-posit16
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 → 453
Calls
4 calls:
Slowest
217.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
212.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
98.0ms
(- (pow (+ 1 (/ i n)) n) 1)
10.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
433.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
418.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
301.0ms
(pow (+ 1 (/ i n)) n)
288.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.3m

Counts
595 → 465
Calls
595 calls:
Slowest
801.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) i)
635.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (cbrt n)))
619.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (cbrt i) (sqrt n)))
610.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (* (cbrt n) (cbrt n))))
607.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) n))

prune3.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.2b

localize26.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (log (exp (- (pow (+ (/ i n) 1) n) 1))) (/ i n))
9.1b
(pow (+ (/ i n) 1) n)
0.9b
(- (pow (+ (/ i n) 1) n) 1)
0.9b
(log (exp (- (pow (+ (/ i n) 1) n) 1)))

rewrite921.0ms

Algorithm
rewrite-expression-head
Rules
383×times-frac
306×add-sqr-sqrt
244×*-un-lft-identity
210×log-pow
195×exp-prod
162×add-cube-cbrt
96×difference-of-squares
52×unpow-prod-down
49×sqr-pow
48×difference-of-sqr-1
20×pow1
19×div-inv
17×associate-/l*
16×distribute-lft-out--
13×associate-/r*
10×add-exp-log
9×add-cbrt-cube
6×add-log-exp
5×log-prod
4×insert-posit16
3×cbrt-undiv pow-unpow div-exp
2×log-div sub-neg exp-diff exp-sum
1×pow-to-exp clear-num pow-pow frac-2neg flip3-- diff-log div-sub rem-log-exp pow-exp associate-/r/ flip-- distribute-lft-out
Counts
4 → 339
Calls
4 calls:
Slowest
600.0ms
(/ (log (exp (- (pow (+ (/ i n) 1) n) 1))) (/ i n))
200.0ms
(log (exp (- (pow (+ (/ i n) 1) n) 1)))
99.0ms
(- (pow (+ (/ i n) 1) n) 1)
14.0ms
(pow (+ (/ i n) 1) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
539.0ms
(/ (log (exp (- (pow (+ (/ i n) 1) n) 1))) (/ i n))
215.0ms
(log (exp (- (pow (+ (/ i n) 1) n) 1)))
212.0ms
(- (pow (+ (/ i n) 1) n) 1)
202.0ms
(pow (+ (/ i n) 1) n)

simplify1.8m

Counts
532 → 351
Calls
532 calls:
Slowest
628.0ms
(/ (log (exp (+ (pow (+ (/ i n) 1) (/ n 2)) 1))) (/ i (cbrt n)))
611.0ms
(- (pow (sqrt (+ (/ i n) 1)) n) 1)
585.0ms
(/ (log (exp (sqrt (- (pow (+ (/ i n) 1) n) 1)))) (/ i n))
491.0ms
(/ (- (sqrt (pow (+ (/ i n) 1) n)) (sqrt 1)) (/ (sqrt i) (sqrt n)))
474.0ms
(/ (log (exp (+ (pow (sqrt (+ (/ i n) 1)) n) (sqrt 1)))) (cbrt (/ i n)))

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.2b

localize31.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ i n))
9.1b
(pow (+ (/ i n) 1) n)
9.1b
(pow (+ (/ i n) 1) n)
9.1b
(pow (+ (/ i n) 1) n)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
97×times-frac
65×*-un-lft-identity
59×add-sqr-sqrt add-cube-cbrt
14×cbrt-prod
13×associate-/r*
12×unpow-prod-down add-exp-log
9×pow-unpow
7×pow1 add-cbrt-cube
6×div-inv
4×insert-posit16 associate-/l* add-log-exp
3×pow-to-exp cbrt-undiv pow-pow div-exp pow-exp distribute-lft-out sqr-pow
1×clear-num frac-2neg associate-/r/
Counts
4 → 142
Calls
4 calls:
Slowest
17.0ms
(pow (+ (/ i n) 1) n)
13.0ms
(pow (+ (/ i n) 1) n)
13.0ms
(pow (+ (/ i n) 1) n)
9.0ms
(/ (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ i n))

series914.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(/ (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ i n))
210.0ms
(pow (+ (/ i n) 1) n)
209.0ms
(pow (+ (/ i n) 1) n)
205.0ms
(pow (+ (/ i n) 1) n)

simplify32.8s

Counts
160 → 154
Calls
160 calls:
Slowest
564.0ms
(/ (cbrt (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ (sqrt i) (sqrt n)))
560.0ms
(/ (sqrt (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))))) (/ 1 1))
396.0ms
(/ (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ 1 n))
395.0ms
(/ (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ i (cbrt n)))
393.0ms
(/ (cbrt (* (* (log (exp (- (pow (+ (/ i n) 1) n) 1))) (log (exp (- (pow (+ (/ i n) 1) n) 1)))) (log (exp (- (pow (+ (/ i n) 1) n) 1))))) (/ i (sqrt n)))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.2b

localize26.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
9.1b
(pow (+ 1 (/ i n)) n)
0.9b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* (sqrt 100) (* (sqrt 100) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
295×times-frac
255×add-sqr-sqrt
197×*-un-lft-identity
120×add-cube-cbrt
90×difference-of-squares
49×unpow-prod-down
46×sqr-pow
45×difference-of-sqr-1
24×add-exp-log
23×add-cbrt-cube
15×div-inv distribute-lft-out--
13×associate-/r* associate-/l*
10×pow1
7×prod-exp cbrt-unprod
6×cbrt-undiv div-exp associate-*l* add-log-exp
4×insert-posit16
3×pow-unpow pow-prod-down sqrt-prod
2×flip3-- associate-*r/ flip-- associate-/l/
1×pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub associate-*r* pow-exp associate-/r/ *-commutative distribute-lft-out
Counts
4 → 283
Calls
4 calls:
Slowest
146.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
134.0ms
(* (sqrt 100) (* (sqrt 100) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))))
75.0ms
(- (pow (+ 1 (/ i n)) n) 1)
9.0ms
(pow (+ 1 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(* (sqrt 100) (* (sqrt 100) (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))))
287.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
216.0ms
(- (pow (+ 1 (/ i n)) n) 1)
209.0ms
(pow (+ 1 (/ i n)) n)

simplify1.4m

Counts
423 → 295
Calls
423 calls:
Slowest
641.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) n))
571.0ms
(* (* (* (sqrt 100) (sqrt 100)) (sqrt 100)) (* (* (* (sqrt 100) (sqrt 100)) (sqrt 100)) (/ (* (* (- (pow (+ 1 (/ i n)) n) 1) (- (pow (+ 1 (/ i n)) n) 1)) (- (pow (+ 1 (/ i n)) n) 1)) (* (* (/ i n) (/ i n)) (/ i n)))))
522.0ms
(/ (+ (pow (+ 1 (/ i n)) (/ n 2)) (sqrt 1)) (/ (* (cbrt i) (cbrt i)) (sqrt n)))
463.0ms
(/ (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ 1 (* (cbrt n) (cbrt n))))
449.0ms
(/ (+ (pow (sqrt (+ 1 (/ i n))) n) (sqrt 1)) (/ (sqrt i) (sqrt n)))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.2b

regimes113.0ms

Accuracy

55.7% (10.6b remaining)

Error of 29.3b against oracle of 18.7b and baseline of 42.7b

bsearch244.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.6s2491×body1280valid
2.2s1010×body2560valid
807.0ms1585×body640valid
317.0ms3031×body80valid
275.0ms835×body320valid
203.0ms2382×body80nan
99.0ms453×body160valid
26.0ms7×body5120valid