Details

Time bar (total: 3.5m)

sample325.0ms

Algorithm
intervals
Results
112.0ms73×body1280valid
84.0ms26×body2560valid
70.0ms65×body640valid
14.0ms103×body80valid
12.0ms27×body320valid
9.0ms78×body80nan
6.0ms21×body160valid

simplify193.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
193.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize20.0ms

Local error

Found 4 expressions with local error:

9.9b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.2b
(pow (+ 1 (/ i n)) n)
1.9b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite566.0ms

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
224.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
169.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
142.0ms
(- (pow (+ 1 (/ i n)) n) 1)
17.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
407.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
400.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
331.0ms
(pow (+ 1 (/ i n)) n)
285.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.3m

Counts
595 → 465
Calls
595 calls:
Slowest
949.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) 1))
632.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (cbrt n)))
618.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ i (sqrt n)))
614.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) (cbrt n)))
600.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (/ (sqrt i) (sqrt n)))

prune3.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.4b

localize42.0ms

Local error

Found 4 expressions with local error:

9.9b
(/ (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))
6.2b
(pow (+ (/ i n) 1) n)
6.2b
(pow (+ (/ i n) 1) n)
6.2b
(pow (+ (/ i n) 1) n)

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt unpow-prod-down add-cube-cbrt
9×pow-unpow
7×pow1
5×associate-/r/
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×pow-to-exp pow-pow times-frac pow-exp distribute-lft-out associate-/l* sqr-pow
2×frac-times flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ associate-/l/
1×clear-num associate-/r* frac-2neg flip3-- div-sub associate-*l/ div-inv flip--
Counts
4 → 89
Calls
4 calls:
Slowest
276.0ms
(/ (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))
12.0ms
(pow (+ (/ i n) 1) n)
12.0ms
(pow (+ (/ i n) 1) n)
11.0ms
(pow (+ (/ i n) 1) n)

series5.9s

Counts
4 → 12
Calls
4 calls:
Slowest
5.3s
(/ (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))
213.0ms
(pow (+ (/ i n) 1) n)
210.0ms
(pow (+ (/ i n) 1) n)
207.0ms
(pow (+ (/ i n) 1) n)

simplify8.6s

Counts
58 → 101
Calls
58 calls:
Slowest
1.1s
(/ (* (* (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)) (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)) (* (* (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))))
453.0ms
(- (pow (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 3) (pow 1 3))
439.0ms
(/ (* (cbrt (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)) (cbrt (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1))) (/ i n))
427.0ms
(/ (sqrt (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)) (/ i n))
345.0ms
(* (cbrt (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)) (cbrt (- (* (pow (+ (/ i n) 1) n) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.4b

localize52.0ms

Local error

Found 4 expressions with local error:

9.9b
(/ (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))
6.2b
(pow (+ (/ i n) 1) n)
6.2b
(pow (+ (/ i n) 1) n)
6.2b
(pow (+ (/ i n) 1) n)

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt unpow-prod-down add-cube-cbrt
9×pow-unpow
7×pow1
5×associate-/r/
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×pow-to-exp pow-pow times-frac pow-exp distribute-lft-out associate-/l* sqr-pow
2×frac-times flip3-+ prod-exp associate-*r/ cbrt-unprod flip-+ associate-/l/
1×clear-num associate-/r* frac-2neg flip3-- div-sub associate-*l/ div-inv flip--
Counts
4 → 89
Calls
4 calls:
Slowest
483.0ms
(/ (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))
12.0ms
(pow (+ (/ i n) 1) n)
11.0ms
(pow (+ (/ i n) 1) n)
11.0ms
(pow (+ (/ i n) 1) n)

series5.8s

Counts
4 → 12
Calls
4 calls:
Slowest
5.2s
(/ (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))
210.0ms
(pow (+ (/ i n) 1) n)
207.0ms
(pow (+ (/ i n) 1) n)
205.0ms
(pow (+ (/ i n) 1) n)

simplify7.0s

Counts
58 → 101
Calls
58 calls:
Slowest
369.0ms
(/ (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))
331.0ms
(- (log (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)) (+ (log (/ i n)) (log (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))))
315.0ms
(/ (* (- (pow (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 3) 1) n) (* (+ (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) (+ (pow (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 2) 1)) i))
314.0ms
(- (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))
309.0ms
(/ (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.3b

localize73.0ms

Local error

Found 4 expressions with local error:

9.2b
(/ (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))) (cbrt (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)))
6.2b
(pow (+ (/ i n) 1) n)
6.2b
(pow (+ (/ i n) 1) n)
6.2b
(pow (+ (/ i n) 1) n)

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
16×add-exp-log
14×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down
10×add-cbrt-cube
9×pow-unpow
7×pow1
6×cbrt-prod associate-/r* times-frac
5×associate-/l/
4×cbrt-undiv div-exp insert-posit16 add-log-exp
3×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
2×frac-times cbrt-div flip3-+ prod-exp associate-*r/ associate-/r/ cbrt-unprod flip-+
1×clear-num frac-2neg flip3-- associate-*l/ div-inv flip-- associate-/l*
Counts
4 → 94
Calls
4 calls:
Slowest
358.0ms
(/ (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))) (cbrt (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)))
12.0ms
(pow (+ (/ i n) 1) n)
11.0ms
(pow (+ (/ i n) 1) n)
11.0ms
(pow (+ (/ i n) 1) n)

series14.4s

Counts
4 → 12
Calls
4 calls:
Slowest
13.8s
(/ (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))) (cbrt (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1)))
219.0ms
(pow (+ (/ i n) 1) n)
209.0ms
(pow (+ (/ i n) 1) n)
209.0ms
(pow (+ (/ i n) 1) n)

simplify9.7s

Counts
68 → 106
Calls
68 calls:
Slowest
685.0ms
(/ (* (* (* (/ i n) (/ i n)) (/ i n)) (* (* (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))) (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1))
597.0ms
(/ (* (* (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1)))) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))) (* (/ i n) (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))) (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1))
422.0ms
(* i (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))
346.0ms
(- (+ (log (/ i n)) (log (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))) (log (cbrt (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1))))
291.0ms
(- (+ (- (log i) (log n)) (log (+ (* (pow (+ 1 (/ i n)) n) (pow (+ 1 (/ i n)) n)) (+ (* 1 1) (* (pow (+ 1 (/ i n)) n) 1))))) (log (cbrt (- (* (* (sqrt (pow (+ (/ i n) 1) n)) (sqrt (pow (+ (/ i n) 1) n))) (* (pow (+ (/ i n) 1) n) (pow (+ (/ i n) 1) n))) 1))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.3b

regimes179.0ms

Accuracy

52.8% (11.3b remaining)

Error of 30.2b against oracle of 18.8b and baseline of 42.8b

bsearch993.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.6s2561×body1280valid
2.2s961×body2560valid
828.0ms1644×body640valid
545.0ms2972×body80valid
326.0ms832×body320valid
229.0ms2310×body80nan
87.0ms467×body160valid
32.0ms8×body5120valid