Details

Time bar (total: 24.1s)

sample243.0ms

Algorithm
intervals
Results
85.0ms79×body1280valid
74.0ms29×body2560valid
29.0ms52×body640valid
24.0ms99×body80valid
9.0ms22×body320valid
7.0ms70×body80nan
4.0ms17×body160valid

simplify167.0ms

Calls
1 calls:
Slowest
167.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize19.0ms

Local error

Found 4 expressions with local error:

9.4b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
6.8b
(pow (+ 1 (/ i n)) n)
0.5b
(- (pow (+ 1 (/ i n)) n) 1)
0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite48.0ms

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
22.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
13.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
10.0ms
(- (pow (+ 1 (/ i n)) n) 1)
2.0ms
(pow (+ 1 (/ i n)) n)

series1.2s

Calls
4 calls:
Slowest
380.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
284.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
265.0ms
(- (pow (+ 1 (/ i n)) n) 1)
240.0ms
(pow (+ 1 (/ i n)) n)

simplify5.0s

Calls
97 calls:
Slowest
482.0ms
(/ (* (* (- (pow (+ 1 (/ i n)) n) 1) (- (pow (+ 1 (/ i n)) n) 1)) (- (pow (+ 1 (/ i n)) n) 1)) (* (* (/ i n) (/ i n)) (/ i n)))
289.0ms
(/ (* (- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1) n) i)
282.0ms
(/ (* n (- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)) i)
224.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)
204.0ms
(* 100 (/ (* (- (exp (* (- (log (/ 1 n)) (log (/ 1 i))) n)) 1) n) i))

prune886.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.1b

localize18.0ms

Local error

Found 4 expressions with local error:

6.6b
(pow (* (/ 1 n) i) n)
0.8b
(- (pow (* (/ 1 n) i) n) 1)
0.2b
(* (/ 1 n) i)
0.1b
(* 100 (/ (* n (- (pow (* (/ 1 n) i) n) 1)) i))

rewrite12.0ms

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
5.0ms
(- (pow (* (/ 1 n) i) n) 1)
3.0ms
(* (/ 1 n) i)
3.0ms
(pow (* (/ 1 n) i) n)
2.0ms
(* 100 (/ (* n (- (pow (* (/ 1 n) i) n) 1)) i))

series235.0ms

Calls
4 calls:
Slowest
127.0ms
(* 100 (/ (* n (- (pow (* (/ 1 n) i) n) 1)) i))
60.0ms
(- (pow (* (/ 1 n) i) n) 1)
37.0ms
(pow (* (/ 1 n) i) n)
11.0ms
(* (/ 1 n) i)

simplify1.8s

Calls
23 calls:
Slowest
244.0ms
(- (+ (* 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))))))))
198.0ms
(/ (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n) i)
182.0ms
(- (+ (* 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)))))
156.0ms
(- (+ (* 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))))))))
142.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)

prune488.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.9b

localize12.0ms

Local error

Found 4 expressions with local error:

6.6b
(pow (* (/ 1 n) i) n)
0.9b
(log (exp (- (pow (* (/ 1 n) i) n) 1)))
0.8b
(- (pow (* (/ 1 n) i) n) 1)
0.2b
(* (/ 1 n) i)

rewrite20.0ms

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
8.0ms
(log (exp (- (pow (* (/ 1 n) i) n) 1)))
7.0ms
(- (pow (* (/ 1 n) i) n) 1)
3.0ms
(* (/ 1 n) i)
2.0ms
(pow (* (/ 1 n) i) n)

series162.0ms

Calls
4 calls:
Slowest
60.0ms
(log (exp (- (pow (* (/ 1 n) i) n) 1)))
59.0ms
(- (pow (* (/ 1 n) i) n) 1)
32.0ms
(pow (* (/ 1 n) i) n)
10.0ms
(* (/ 1 n) i)

simplify1.6s

Calls
30 calls:
Slowest
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)))))
159.0ms
(- (+ (* 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))))))))
159.0ms
(- (+ (* 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))))))))
144.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)
142.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)

prune619.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.8b

localize6.0ms

Local error

Found 4 expressions with local error:

6.6b
(pow (* (/ 1 n) i) n)
0.8b
(- (pow (* (/ 1 n) i) n) 1)
0.2b
(* (/ 1 n) i)
0.1b
(/ (* 100 (* n (- (pow (* (/ 1 n) i) n) 1))) i)

rewrite27.0ms

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
17.0ms
(/ (* 100 (* n (- (pow (* (/ 1 n) i) n) 1))) i)
5.0ms
(- (pow (* (/ 1 n) i) n) 1)
3.0ms
(pow (* (/ 1 n) i) n)
3.0ms
(* (/ 1 n) i)

series232.0ms

Calls
4 calls:
Slowest
127.0ms
(/ (* 100 (* n (- (pow (* (/ 1 n) i) n) 1))) i)
62.0ms
(- (pow (* (/ 1 n) i) n) 1)
33.0ms
(pow (* (/ 1 n) i) n)
9.0ms
(* (/ 1 n) i)

simplify1.8s

Calls
21 calls:
Slowest
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))))))))
200.0ms
(/ (* (- (* 100 (exp (* n (- (log (/ -1 n)) (log (/ -1 i)))))) 100) n) i)
187.0ms
(- (+ (* 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)))))
159.0ms
(- (+ (* 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))))))))
149.0ms
(- (exp (* n (- (log (/ -1 n)) (log (/ -1 i))))) 1)

prune465.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 14.8b

regimes174.0ms

Accuracy

50% (13.6b remaining)

Error of 30.1b against oracle of 16.5b and baseline of 43.8b

bsearch778.0ms

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.1s2493×body1280valid
2.6s1001×body2560valid
1.2s1625×body640valid
359.0ms3019×body80valid
274.0ms811×body320valid
251.0ms2246×body80nan
100.0ms450×body160valid
27.0ms6×body5120valid