Details

Time bar (total: 24.5s)

sample256.0ms

Algorithm
intervals
Results
109.0ms84×body1280valid
57.0ms23×body2560valid
49.0ms51×body640valid
10.0ms27×body320valid
9.0ms93×body80valid
6.0ms57×body80nan
4.0ms15×body160valid

simplify199.0ms

Calls
1 calls:
Slowest
199.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize19.0ms

Local error

Found 4 expressions with local error:

7.9b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
7.3b
(pow (+ 1 (/ i n)) n)
1.5b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite55.0ms

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))
15.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
9.0ms
(- (pow (+ 1 (/ i n)) n) 1)
2.0ms
(pow (+ 1 (/ i n)) n)

series611.0ms

Calls
4 calls:
Slowest
188.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
168.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
144.0ms
(- (pow (+ 1 (/ i n)) n) 1)
110.0ms
(pow (+ 1 (/ i n)) n)

simplify5.3s

Calls
97 calls:
Slowest
572.0ms
(/ (* n (- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)) i)
517.0ms
(/ (* (* (- (pow (+ 1 (/ i n)) n) 1) (- (pow (+ 1 (/ i n)) n) 1)) (- (pow (+ 1 (/ i n)) n) 1)) (* (* (/ i n) (/ i n)) (/ i n)))
347.0ms
(/ (* (- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1) n) i)
208.0ms
(* 100 (/ (* (- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1) n) i))
187.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.3b

localize19.0ms

Local error

Found 4 expressions with local error:

6.6b
(pow (* (/ 1 n) i) n)
3.5b
(- (pow (* (/ 1 n) i) n) 1)
0.2b
(* (/ 1 n) i)
0.1b
(* 100 (/ (* n (- (pow (* (/ 1 n) i) n) 1)) i))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×pow1 add-exp-log
4×add-cbrt-cube associate-*r* associate-*l* insert-posit16 add-log-exp
2×*-commutative div-inv
1×pow-to-exp sub-neg unpow-prod-down pow-pow flip3-- difference-of-sqr-1 associate-*l/ pow-exp associate-*r/ flip--
Calls
4 calls:
Slowest
4.0ms
(- (pow (* (/ 1 n) i) n) 1)
2.0ms
(pow (* (/ 1 n) i) n)
2.0ms
(* (/ 1 n) i)
1.0ms
(* 100 (/ (* n (- (pow (* (/ 1 n) i) n) 1)) i))

series215.0ms

Calls
4 calls:
Slowest
117.0ms
(* 100 (/ (* n (- (pow (* (/ 1 n) i) n) 1)) i))
61.0ms
(- (pow (* (/ 1 n) i) n) 1)
27.0ms
(pow (* (/ 1 n) i) n)
9.0ms
(* (/ 1 n) i)

simplify2.0s

Calls
23 calls:
Slowest
293.0ms
(/ (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n) i)
249.0ms
(- (+ (* 100/3 (/ (* (pow n 4) (* (pow (log n) 2) (log i))) i)) (+ (* 50/3 (/ (* (pow n 4) (* (log i) (pow (log n) 2))) i)) (+ (* 50/3 (/ (* (pow n 4) (pow (log i) 3)) i)) (+ (* 100 (/ (* (pow n 2) (log i)) i)) (+ (* 50 (/ (* (pow n 3) (pow (log i) 2)) i)) (* 50 (/ (* (pow n 3) (pow (log n) 2)) i))))))) (+ (* 50/3 (/ (* (pow n 4) (pow (log n) 3)) i)) (+ (* 50/3 (/ (* (pow n 4) (* (log n) (pow (log i) 2))) i)) (+ (* 50 (/ (* (pow n 3) (* (log n) (log i))) i)) (+ (* 100/3 (/ (* (pow n 4) (* (pow (log i) 2) (log n))) i)) (+ (* 100 (/ (* (pow n 2) (log n)) i)) (* 50 (/ (* (pow n 3) (* (log i) (log n))) i))))))))
204.0ms
(- (+ (* 1/2 (* (pow n 2) (pow (log i) 2))) (+ (* n (log i)) (+ (* 1/2 (* (pow n 2) (pow (log n) 2))) 1))) (+ (* 1/2 (* (pow n 2) (* (log i) (log n)))) (+ (* 1/2 (* (pow n 2) (* (log n) (log i)))) (* n (log n)))))
161.0ms
(- (+ (* 1/2 (* (pow n 2) (pow (log n) 2))) (+ (* 1/6 (* (pow n 3) (pow (log i) 3))) (+ (* n (log i)) (+ (* 1/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 1/6 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 1/2 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 1/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 1/2 (* (pow n 2) (* (log n) (log i)))) (+ (* 1/2 (* (pow n 2) (* (log i) (log n)))) (+ (* 1/6 (* (pow n 3) (pow (log n) 3))) (+ (* 1/6 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* n (log n))))))))
157.0ms
(/ (* (- (* 100 (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))) 100) n) i)

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.2b

localize6.0ms

Local error

Found 4 expressions with local error:

6.6b
(pow (* (/ 1 n) i) n)
3.5b
(- (pow (* (/ 1 n) i) n) 1)
0.2b
(* (/ 1 n) i)
0.1b
(/ (* 100 (* n (- (pow (* (/ 1 n) i) n) 1))) i)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-exp-log add-cube-cbrt
4×add-cbrt-cube associate-*l* associate-*r/ insert-posit16 add-log-exp
2×flip3-- div-inv flip-- associate-/l/
1×pow-to-exp clear-num sub-neg unpow-prod-down pow-pow frac-2neg difference-of-sqr-1 associate-*l/ pow-exp *-commutative associate-/l*
Calls
4 calls:
Slowest
13.0ms
(/ (* 100 (* n (- (pow (* (/ 1 n) i) n) 1))) i)
4.0ms
(- (pow (* (/ 1 n) i) n) 1)
2.0ms
(* (/ 1 n) i)
2.0ms
(pow (* (/ 1 n) i) n)

series180.0ms

Calls
4 calls:
Slowest
98.0ms
(/ (* 100 (* n (- (pow (* (/ 1 n) i) n) 1))) i)
47.0ms
(- (pow (* (/ 1 n) i) n) 1)
29.0ms
(pow (* (/ 1 n) i) n)
6.0ms
(* (/ 1 n) i)

simplify2.3s

Calls
21 calls:
Slowest
282.0ms
(- (+ (* 100/3 (/ (* (pow n 4) (* (pow (log n) 2) (log i))) i)) (+ (* 50/3 (/ (* (pow n 4) (* (log i) (pow (log n) 2))) i)) (+ (* 50/3 (/ (* (pow n 4) (pow (log i) 3)) i)) (+ (* 100 (/ (* (pow n 2) (log i)) i)) (+ (* 50 (/ (* (pow n 3) (pow (log i) 2)) i)) (* 50 (/ (* (pow n 3) (pow (log n) 2)) i))))))) (+ (* 50/3 (/ (* (pow n 4) (pow (log n) 3)) i)) (+ (* 50/3 (/ (* (pow n 4) (* (log n) (pow (log i) 2))) i)) (+ (* 50 (/ (* (pow n 3) (* (log n) (log i))) i)) (+ (* 100/3 (/ (* (pow n 4) (* (pow (log i) 2) (log n))) i)) (+ (* 100 (/ (* (pow n 2) (log n)) i)) (* 50 (/ (* (pow n 3) (* (log i) (log n))) i))))))))
278.0ms
(- (+ (* 1/2 (* (pow n 2) (pow (log n) 2))) (+ (* 1/6 (* (pow n 3) (pow (log i) 3))) (+ (* n (log i)) (+ (* 1/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 1/6 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 1/2 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 1/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 1/2 (* (pow n 2) (* (log n) (log i)))) (+ (* 1/2 (* (pow n 2) (* (log i) (log n)))) (+ (* 1/6 (* (pow n 3) (pow (log n) 3))) (+ (* 1/6 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* n (log n))))))))
245.0ms
(exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))
241.0ms
(- (+ (* 1/2 (* (pow n 2) (pow (log i) 2))) (+ (* n (log i)) (+ (* 1/2 (* (pow n 2) (pow (log n) 2))) 1))) (+ (* 1/2 (* (pow n 2) (* (log i) (log n)))) (+ (* 1/2 (* (pow n 2) (* (log n) (log i)))) (* n (log n)))))
229.0ms
(exp (* (- (log (/ 1 n)) (log (/ 1 i))) n))

prune583.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

Local error

Found 4 expressions with local error:

6.6b
(pow (* (/ 1 n) i) n)
3.5b
(log (exp (- (pow (* (/ 1 n) i) n) 1)))
3.5b
(- (pow (* (/ 1 n) i) n) 1)
0.2b
(* (/ 1 n) i)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1
5×log-prod add-exp-log log-pow
4×exp-prod add-cbrt-cube associate-*l* insert-posit16 add-log-exp
2×sub-neg difference-of-sqr-1 exp-sum
1×pow-to-exp log-div unpow-prod-down pow-pow flip3-- exp-diff rem-log-exp associate-*l/ pow-exp *-commutative div-inv flip--
Calls
4 calls:
Slowest
7.0ms
(log (exp (- (pow (* (/ 1 n) i) n) 1)))
4.0ms
(- (pow (* (/ 1 n) i) n) 1)
2.0ms
(pow (* (/ 1 n) i) n)
2.0ms
(* (/ 1 n) i)

series127.0ms

Calls
4 calls:
Slowest
49.0ms
(log (exp (- (pow (* (/ 1 n) i) n) 1)))
46.0ms
(- (pow (* (/ 1 n) i) n) 1)
27.0ms
(pow (* (/ 1 n) i) n)
6.0ms
(* (/ 1 n) i)

simplify1.8s

Calls
30 calls:
Slowest
203.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)
194.0ms
(exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))
186.0ms
(- (+ (* 1/2 (* (pow n 2) (pow (log n) 2))) (+ (* 1/6 (* (pow n 3) (pow (log i) 3))) (+ (* n (log i)) (+ (* 1/3 (* (pow n 3) (* (pow (log n) 2) (log i)))) (+ (* 1/6 (* (pow n 3) (* (log i) (pow (log n) 2)))) (* 1/2 (* (pow n 2) (pow (log i) 2)))))))) (+ (* 1/3 (* (pow n 3) (* (pow (log i) 2) (log n)))) (+ (* 1/2 (* (pow n 2) (* (log n) (log i)))) (+ (* 1/2 (* (pow n 2) (* (log i) (log n)))) (+ (* 1/6 (* (pow n 3) (pow (log n) 3))) (+ (* 1/6 (* (pow n 3) (* (log n) (pow (log i) 2)))) (* n (log n))))))))
186.0ms
(- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1)
185.0ms
(- (+ (* 1/2 (* (pow n 2) (pow (log i) 2))) (+ (* n (log i)) (+ (* 1/2 (* (pow n 2) (pow (log n) 2))) 1))) (+ (* 1/2 (* (pow n 2) (* (log i) (log n)))) (+ (* 1/2 (* (pow n 2) (* (log n) (log i)))) (* n (log n)))))

prune693.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

regimes271.0ms

Accuracy

51.4% (13.0b remaining)

Error of 29.4b against oracle of 16.4b and baseline of 43.1b

bsearch308.0ms

end0.0ms

sample8.0s

Algorithm
intervals
Results
2.8s2452×body1280valid
2.6s1010×body2560valid
1.3s1604×body640valid
365.0ms3079×body80valid
341.0ms844×body320valid
250.0ms2323×body80nan
115.0ms414×body160valid
24.0ms5×body5120valid