Details

Time bar (total: 52.8s)

sample350.0ms

Algorithm
intervals
Results
129.0ms37×body2560valid
126.0ms74×body1280valid
33.0ms44×body640valid
22.0ms98×body80valid
12.0ms24×body320valid
11.0ms83×body80nan
2.0ms7×body160valid

simplify307.0ms

Calls
1 calls:
Slowest
307.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize15.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
5.8b
(pow (+ 1 (/ i n)) n)
1.5b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
26×*-un-lft-identity add-cube-cbrt
25×associate-*r*
20×difference-of-sqr-1
13×unpow-prod-down div-inv
7×add-exp-log
6×add-cbrt-cube
5×pow1 associate-/l*
4×associate-/r* insert-posit16 add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp cbrt-undiv clear-num sub-neg pow-pow frac-2neg div-sub div-exp pow-exp associate-*r/ *-commutative
Calls
4 calls:
Slowest
26.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
19.0ms
(- (pow (+ 1 (/ i n)) n) 1)
11.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
3.0ms
(pow (+ 1 (/ i n)) n)

series675.0ms

Calls
4 calls:
Slowest
198.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
187.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
175.0ms
(- (pow (+ 1 (/ i n)) n) 1)
116.0ms
(pow (+ 1 (/ i n)) n)

simplify5.8s

Calls
97 calls:
Slowest
600.0ms
(/ (* (* (- (pow (+ 1 (/ i n)) n) 1) (- (pow (+ 1 (/ i n)) n) 1)) (- (pow (+ 1 (/ i n)) n) 1)) (* (* (/ i n) (/ i n)) (/ i n)))
332.0ms
(/ (* (- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1) n) i)
263.0ms
(/ (* n (- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)) i)
253.0ms
(* 100 (/ (* (- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1) n) i))
226.0ms
(exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.9b

localize22.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (/ i n))
5.8b
(pow (+ 1 (/ i n)) n)
5.8b
(pow (+ 1 (/ i n)) n)
1.5b
(- (sqrt (pow (+ 1 (/ i n)) n)) 1)

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-exp-log
9×add-cbrt-cube
8×*-un-lft-identity add-cube-cbrt associate-/l/
7×unpow-prod-down
6×pow1
4×frac-times associate-/r* times-frac flip3-- insert-posit16 flip-- add-log-exp
3×flip3-+ difference-of-sqr-1 flip-+ div-inv
2×pow-to-exp cbrt-undiv pow-pow div-exp associate-*l/ pow-exp associate-*r/ sqrt-prod
1×clear-num sub-neg frac-2neg prod-exp associate-/r/ cbrt-unprod associate-/l*
Calls
4 calls:
Slowest
54.0ms
(/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (/ i n))
12.0ms
(- (sqrt (pow (+ 1 (/ i n)) n)) 1)
4.0ms
(pow (+ 1 (/ i n)) n)
2.0ms
(pow (+ 1 (/ i n)) n)

series805.0ms

Calls
4 calls:
Slowest
333.0ms
(/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (/ i n))
201.0ms
(- (sqrt (pow (+ 1 (/ i n)) n)) 1)
143.0ms
(pow (+ 1 (/ i n)) n)
127.0ms
(pow (+ 1 (/ i n)) n)

simplify6.7s

Calls
50 calls:
Slowest
578.0ms
(* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)))
437.0ms
(/ (* (* (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1))) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1))) (* (* (/ i n) (/ i n)) (/ i n)))
429.0ms
(* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (* 1 1)))
427.0ms
(/ (* (* (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (+ (sqrt (pow (+ 1 (/ i n)) n)) 1)) (+ (sqrt (pow (+ 1 (/ i n)) n)) 1)) (* (* (- (sqrt (pow (+ 1 (/ i n)) n)) 1) (- (sqrt (pow (+ 1 (/ i n)) n)) 1)) (- (sqrt (pow (+ 1 (/ i n)) n)) 1))) (* (* (/ i n) (/ i n)) (/ i n)))
420.0ms
(* (- (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (* 1 1)) (- (sqrt (pow (+ 1 (/ i n)) n)) 1))

prune991.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.9b

localize32.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (/ i n))
5.8b
(pow (+ 1 (/ i n)) n)
5.8b
(pow (+ 1 (/ i n)) n)
5.8b
(pow (+ 1 (/ i n)) n)

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
13×add-cbrt-cube
9×add-sqr-sqrt unpow-prod-down *-un-lft-identity add-cube-cbrt
7×pow1
5×associate-/l/
4×cbrt-undiv associate-/r* times-frac div-exp insert-posit16 add-log-exp
3×pow-to-exp pow-pow pow-exp div-inv
2×frac-times flip3-+ associate-*l/ prod-exp cbrt-unprod flip-+
1×clear-num frac-2neg associate-*r/ associate-/r/ associate-/l*
Calls
4 calls:
Slowest
58.0ms
(/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (/ i n))
2.0ms
(pow (+ 1 (/ i n)) n)
2.0ms
(pow (+ 1 (/ i n)) n)
2.0ms
(pow (+ 1 (/ i n)) n)

series6.6s

Calls
4 calls:
Slowest
6.3s
(/ (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (/ i n))
113.0ms
(pow (+ 1 (/ i n)) n)
108.0ms
(pow (+ 1 (/ i n)) n)
105.0ms
(pow (+ 1 (/ i n)) n)

simplify6.0s

Calls
51 calls:
Slowest
883.0ms
(/ (* (* (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (+ (sqrt (pow (+ 1 (/ i n)) n)) 1)) (+ (sqrt (pow (+ 1 (/ i n)) n)) 1)) (* (* (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))) (* (* (/ i n) (/ i n)) (/ i n)))
629.0ms
(/ (* (* (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))) (* (* (/ i n) (/ i n)) (/ i n)))
348.0ms
(/ (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))) (cbrt (/ i n)))
279.0ms
(* (+ (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)))
278.0ms
(/ (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))) (sqrt (/ i n)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.9b

localize14.0ms

Local error

Found 4 expressions with local error:

10.7b
(/ (/ i n) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))))
5.8b
(pow (+ 1 (/ i n)) n)
5.8b
(pow (+ 1 (/ i n)) n)
5.8b
(pow (+ 1 (/ i n)) n)

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
16×add-exp-log
13×add-cbrt-cube
9×add-sqr-sqrt unpow-prod-down *-un-lft-identity add-cube-cbrt
7×pow1
5×associate-/r/
4×cbrt-undiv times-frac div-exp insert-posit16 associate-/l* add-log-exp
3×pow-to-exp pow-pow pow-exp div-inv
2×frac-times flip3-+ associate-*l/ prod-exp cbrt-unprod flip-+
1×clear-num associate-/r* frac-2neg associate-*r/ associate-/l/
Calls
4 calls:
Slowest
52.0ms
(/ (/ i n) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))))
2.0ms
(pow (+ 1 (/ i n)) n)
2.0ms
(pow (+ 1 (/ i n)) n)
2.0ms
(pow (+ 1 (/ i n)) n)

series9.6s

Calls
4 calls:
Slowest
9.3s
(/ (/ i n) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))))
86.0ms
(pow (+ 1 (/ i n)) n)
86.0ms
(pow (+ 1 (/ i n)) n)
86.0ms
(pow (+ 1 (/ i n)) n)

simplify4.6s

Calls
49 calls:
Slowest
557.0ms
(/ (* (* (/ i n) (/ i n)) (/ i n)) (* (* (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))) (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))))
534.0ms
(/ (* (* (/ i n) (/ i n)) (/ i n)) (* (* (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (+ (sqrt (pow (+ 1 (/ i n)) n)) 1)) (+ (sqrt (pow (+ 1 (/ i n)) n)) 1)) (* (* (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))))
296.0ms
(* (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (- (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1))))
212.0ms
(/ (* i (+ (sqrt (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) (+ (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1))) (* (- (+ (pow (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 2) (sqrt (pow (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 3))) (+ (sqrt (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 1)) n))
194.0ms
(- (log (/ i n)) (log (* (+ (sqrt (pow (+ 1 (/ i n)) n)) 1) (/ (- (pow (sqrt (pow (+ 1 (/ i n)) n)) 3) (pow 1 3)) (+ (* (sqrt (pow (+ 1 (/ i n)) n)) (sqrt (pow (+ 1 (/ i n)) n))) (+ (* 1 1) (* (sqrt (pow (+ 1 (/ i n)) n)) 1)))))))

prune923.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

regimes140.0ms

Accuracy

40.3% (7.4b remaining)

Error of 15.0b against oracle of 7.6b and baseline of 20.0b

bsearch13.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.4s967×body2560valid
2.3s2474×body1280valid
1.1s1650×body640valid
323.0ms3049×body80valid
231.0ms812×body320valid
225.0ms2185×body80nan
81.0ms436×body160valid
42.0ms11×body5120valid