Details

Time bar (total: 3.8m)

sample351.0ms

Algorithm
intervals
Results
144.0ms93×body1280valid
117.0ms29×body2560valid
34.0ms48×body640valid
14.0ms32×body320valid
12.0ms86×body80valid
8.0ms64×body80nan
5.0ms15×body160valid

simplify181.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
181.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize27.0ms

Local error

Found 4 expressions with local error:

10.4b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
4.4b
(pow (+ 1 (/ i n)) n)
1.6b
(- (pow (+ 1 (/ i n)) n) 1)
0.1b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))

rewrite582.0ms

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
250.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
203.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
98.0ms
(- (pow (+ 1 (/ i n)) n) 1)
9.0ms
(pow (+ 1 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
382.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))
374.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
329.0ms
(pow (+ 1 (/ i n)) n)
295.0ms
(- (pow (+ 1 (/ i n)) n) 1)

simplify2.9m

Counts
595 → 465
Calls
595 calls:
Slowest
966.0ms
(/ (sqrt (- (pow (+ 1 (/ i n)) n) 1)) (sqrt (/ i n)))
803.0ms
(/ (- (pow (sqrt (+ 1 (/ i n))) n) 1) (/ (cbrt i) (cbrt n)))
690.0ms
(/ (+ (pow (+ 1 (/ i n)) (/ n 2)) (sqrt 1)) (/ 1 (sqrt n)))
677.0ms
(/ (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (/ (sqrt i) n))
666.0ms
(/ (* (cbrt (- (pow (+ 1 (/ i n)) n) 1)) (cbrt (- (pow (+ 1 (/ i n)) n) 1))) (/ (sqrt i) 1))

prune3.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.0b

localize21.0ms

Local error

Found 4 expressions with local error:

16.8b
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
0.3b
(* 1/6 i)
0.1b
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
0.0b
(* (* i i) (+ (* 1/6 i) 1/2))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
97×add-sqr-sqrt
85×*-un-lft-identity add-cube-cbrt
50×associate-*r*
25×add-cbrt-cube add-exp-log
13×pow1 associate-/r*
9×div-inv
7×associate-*l* prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow-prod-down unswap-sqr
4×insert-posit16 add-log-exp
3×associate-*r/ *-commutative associate-/l*
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in
Counts
4 → 183
Calls
4 calls:
Slowest
35.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
29.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
17.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
5.0ms
(* 1/6 i)

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))
72.0ms
(/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n))
69.0ms
(* (* i i) (+ (* 1/6 i) 1/2))
15.0ms
(* 1/6 i)

simplify26.6s

Counts
194 → 195
Calls
194 calls:
Slowest
518.0ms
(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n))))
448.0ms
(+ (log 100) (- (log (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (- (log i) (log n))))
442.0ms
(* (* (* 100 100) 100) (/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (* (* (/ i n) (/ i n)) (/ i n))))
310.0ms
(/ (* (* (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (+ i (* (* i i) (+ (* 1/6 i) 1/2)))) (/ (* (* i i) i) (* (* n n) n)))
282.0ms
(* 100 (/ (+ i (* (* i i) (+ (* 1/6 i) 1/2))) (/ i n)))

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 9.1b

localize14.0ms

Local error

Found 3 expressions with local error:

1.9b
(* n (+ 100 (* i (+ (* 50/3 i) 50))))
0.5b
(* 50/3 i)
0.1b
(* i (+ (* 50/3 i) 50))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
4×associate-*r/
3×pow-prod-down prod-exp *-commutative cbrt-unprod insert-posit16 add-log-exp unswap-sqr
2×distribute-rgt-in distribute-lft-in flip3-+ flip-+
Counts
3 → 65
Calls
3 calls:
Slowest
18.0ms
(* i (+ (* 50/3 i) 50))
11.0ms
(* n (+ 100 (* i (+ (* 50/3 i) 50))))
5.0ms
(* 50/3 i)

series135.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
66.0ms
(* i (+ (* 50/3 i) 50))
54.0ms
(* n (+ 100 (* i (+ (* 50/3 i) 50))))
15.0ms
(* 50/3 i)

simplify2.3s

Counts
46 → 74
Calls
46 calls:
Slowest
234.0ms
(* (* (* n n) n) (* (* (+ 100 (* i (+ (* 50/3 i) 50))) (+ 100 (* i (+ (* 50/3 i) 50)))) (+ 100 (* i (+ (* 50/3 i) 50)))))
198.0ms
(+ (* (* 50/3 i) (* 50/3 i)) (- (* 50 50) (* (* 50/3 i) 50)))
175.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
173.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))
172.0ms
(+ (* 50/3 (* (pow i 2) n)) (+ (* 100 n) (* 50 (* i n))))

prune475.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.1b

localize29.0ms

Local error

Found 4 expressions with local error:

10.8b
(/ (* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))))) (- 100 (* i (+ (* 50/3 i) 50))))
1.0b
(* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))))
0.5b
(* 50/3 i)
0.5b
(* 50/3 i)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
12×*-un-lft-identity add-cube-cbrt
10×pow1 associate-*r*
9×associate-*l*
4×prod-exp associate-*r/ cbrt-unprod insert-posit16 add-log-exp
3×associate-/r* times-frac flip3-- pow-prod-down *-commutative flip-- unswap-sqr
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in div-exp associate-/r/ associate-/l/
1×clear-num frac-2neg div-inv associate-/l* difference-of-squares
Counts
4 → 90
Calls
4 calls:
Slowest
21.0ms
(/ (* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))))) (- 100 (* i (+ (* 50/3 i) 50))))
21.0ms
(* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))))
7.0ms
(* 50/3 i)
5.0ms
(* 50/3 i)

series270.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(/ (* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))))) (- 100 (* i (+ (* 50/3 i) 50))))
84.0ms
(* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))))
18.0ms
(* 50/3 i)
15.0ms
(* 50/3 i)

simplify6.8s

Counts
64 → 102
Calls
64 calls:
Slowest
558.0ms
(/ (* (* (* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))))) (* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))))) (* n (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))))) (* (* (- 100 (* i (+ (* 50/3 i) 50))) (- 100 (* i (+ (* 50/3 i) 50)))) (- 100 (* i (+ (* 50/3 i) 50)))))
484.0ms
(/ (* (* (* n n) n) (* (* (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))) (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))))) (- (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))))) (* (* (- 100 (* i (+ (* 50/3 i) 50))) (- 100 (* i (+ (* 50/3 i) 50)))) (- 100 (* i (+ (* 50/3 i) 50)))))
407.0ms
(+ (* (* 100 100) (* 100 100)) (+ (* (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50)))) (* (* 100 100) (* (* i (+ (* 50/3 i) 50)) (* i (+ (* 50/3 i) 50))))))
404.0ms
(* (* (* 50/3 50/3) 50/3) (* (* i i) i))
295.0ms
(- (+ (* 5000/3 (* (pow i 3) n)) (+ (* 2500 (* (pow i 2) n)) (* 2500/9 (* (pow i 4) n)))))

prune668.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.1b

regimes333.0ms

Accuracy

38.5% (10.9b remaining)

Error of 19.3b against oracle of 8.4b and baseline of 26.1b

bsearch271.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
2.7s2564×body1280valid
2.5s999×body2560valid
834.0ms1607×body640valid
322.0ms800×body320valid
307.0ms2999×body80valid
216.0ms2270×body80nan
134.0ms465×body160valid
30.0ms8×body5120valid