Details

Time bar (total: 25.9s)

sample214.0ms

Algorithm
intervals
Results
71.0ms72×body1280valid
67.0ms26×body2560valid
24.0ms51×body640valid
15.0ms14×body160valid
7.0ms104×body80valid
7.0ms29×body320valid
4.0ms70×body80nan

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5157815
done500015

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.7b
(pow (+ 1.0 (/ i n)) n)
8.5b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative
Counts
4 → 321
Calls
4 calls:
471.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
305.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
23.0ms
(pow (+ 1.0 (/ i n)) n)
564.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.9s

Counts
4 → 12
Calls
4 calls:
588.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
379.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
326.0ms
(pow (+ 1.0 (/ i n)) n)
586.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.1s

Counts
333 → 333
Iterations

Useful iterations: done (1.0s)

IterNodesCost
04797415
115206929
done50016480

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.5 (pow i 2) (* (log 1.0) n))
0.1b
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
13.8b
(* (pow i 2) (log 1.0))
16.9b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 189
Calls
4 calls:
1.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
41.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
21.0ms
(* (pow i 2) (log 1.0))
46.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series822.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
280.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
189.0ms
(* (pow i 2) (log 1.0))
255.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify548.0ms

Counts
201 → 201
Iterations

Useful iterations: done (538.0ms)

IterNodesCost
03286373
19426200
done50005731

prune1.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.1b
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
13.0b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
13.8b
(* (pow i 2) (log 1.0))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*l/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-exp clear-num log-pow flip--
Counts
4 → 125
Calls
4 calls:
27.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
44.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
24.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
15.0ms
(* (pow i 2) (log 1.0))

series963.0ms

Counts
4 → 12
Calls
4 calls:
257.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
316.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
178.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
211.0ms
(* (pow i 2) (log 1.0))

simplify1.7s

Counts
137 → 137
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02203686
15433611
225573112
done50003100

prune733.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 12.0b

localize34.0ms

Local error

Found 4 expressions with local error:

13.8b
(* (pow i 2) (log 1.0))
13.8b
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
13.8b
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
13.8b
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
9×add-exp-log cbrt-prod
8×associate-*l*
6×cbrt-div log-prod add-cbrt-cube
5×pow1
4×expm1-log1p-u unpow-prod-down associate-*r* log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in flip3-- distribute-lft-in pow1/3 prod-exp flip--
2×unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
14.0ms
(* (pow i 2) (log 1.0))
3.0ms
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
3.0ms
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
6.0ms
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

series3.1s

Counts
4 → 12
Calls
4 calls:
210.0ms
(* (pow i 2) (log 1.0))
1.0s
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
986.0ms
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
928.0ms
(cbrt (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))

simplify820.0ms

Counts
93 → 93
Iterations

Useful iterations: done (815.0ms)

IterNodesCost
01512652
13332561
213292373
done50012280

prune481.0ms

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 12.0b

regimes241.0ms

Accuracy

49.6% (11.5b remaining)

Error of 22.3b against oracle of 10.8b and baseline of 33.6b

bsearch254.0ms

Steps
ItersRangePoint
12
0.1627416724571204
2.698896120127315e+48
187.33912381318797
3
-2.0664971820228305e-05
-1.4411493588155298e-05
-2.02211734635772e-05

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04391
15691
done5691

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.2s2508×body1280valid
2.2s999×body2560valid
856.0ms3053×body80valid
651.0ms1581×body640valid
246.0ms818×body320valid
142.0ms2243×body80nan
61.0ms445×body160valid
32.0ms9×body5120valid