Details

Time bar (total: 34.0s)

sample285.0ms

Algorithm
intervals
Results
107.0ms87×body1280valid
95.0ms30×body2560valid
31.0ms58×body640valid
8.0ms95×body80valid
7.0ms23×body320valid
4.0ms59×body80nan
2.0ms11×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5157815
done500015

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.4b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.8s

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:
649.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
382.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
34.0ms
(pow (+ 1.0 (/ i n)) n)
685.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.0s

Counts
4 → 12
Calls
4 calls:
649.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
422.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
366.0ms
(pow (+ 1.0 (/ i n)) n)
599.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.3s

Counts
333 → 333
Iterations

Useful iterations: done (1.3s)

IterNodesCost
04797415
115206929
done50016480

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
0.1b
(* 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)))
11.1b
(* (pow i 2) (log 1.0))
19.6b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite115.0ms

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:
0.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
55.0ms
(* 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)))
25.0ms
(* (pow i 2) (log 1.0))
26.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series982.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
306.0ms
(* 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)))
280.0ms
(* (pow i 2) (log 1.0))
323.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify783.0ms

Counts
201 → 201
Iterations

Useful iterations: done (772.0ms)

IterNodesCost
03296419
19506243
done50015768

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
0.1b
(* 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))
10.5b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b
(* (pow i 2) (log 1.0))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-exp-log
18×add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
11×associate-*l*
10×pow1
9×times-frac
8×prod-exp
6×log-prod cbrt-unprod
5×associate-*r*
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* associate-/l*
2×cbrt-undiv div-exp *-commutative associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ associate-*l/ pow-exp clear-num log-pow flip-- fma-udef div-inv
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
48.0ms
(* 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))
16.0ms
(/ (- (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))

series923.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
383.0ms
(* 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))
225.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
243.0ms
(* (pow i 2) (log 1.0))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02012728
14762658
222722275
done50012269

prune965.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt i)
7.1b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
8.4b
(* (/ 1 (pow (cbrt i) 2)) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
11.1b
(* (pow i 2) (log 1.0))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
386×times-frac
321×add-sqr-sqrt
188×*-un-lft-identity
168×add-cube-cbrt
104×add-exp-log
94×cbrt-prod
75×associate-*r*
51×div-exp
48×unswap-sqr
45×associate-*l*
38×unpow-prod-down
33×prod-exp
29×add-cbrt-cube
22×associate-/r*
13×unpow2 sqr-pow
12×cbrt-undiv
10×pow-to-exp pow-exp div-inv
9×rec-exp 1-exp
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative associate-/l/
1×frac-times flip3-- frac-2neg pow1/3 div-sub associate-*r/ pow-prod-down associate-*l/ clear-num log-pow flip--
Counts
4 → 362
Calls
4 calls:
2.0ms
(cbrt i)
45.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
178.0ms
(* (/ 1 (pow (cbrt i) 2)) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
30.0ms
(* (pow i 2) (log 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
312.0ms
(cbrt i)
355.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
411.0ms
(* (/ 1 (pow (cbrt i) 2)) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n)))
268.0ms
(* (pow i 2) (log 1.0))

simplify1.4s

Counts
374 → 374
Iterations

Useful iterations: done (1.3s)

IterNodesCost
057415287
1199114621
done500013535

prune2.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.4b

regimes606.0ms

Accuracy

47.8% (12.2b remaining)

Error of 23.4b against oracle of 11.2b and baseline of 34.6b

bsearch714.0ms

Steps
ItersRangePoint
7
1.2646612175373838e-175
6.651096339829762e-174
2.1282130468923694e-175
9
-5.259837781237774e-183
-5.703441385580287e-192
-5.8053964764311714e-192
8
-1.1067698676223754e+18
-1112375351328255.6
-5.024789071547713e+16
7
-8.687437031435021e+70
-1.5421164969392891e+69
-8.946323817142764e+69
6
-4.951685707263575e+118
-5.329286401239366e+117
-5.454213675553863e+117

simplify15.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
054166
165166
done65166

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.0s2476×body1280valid
2.9s994×body2560valid
1.4s1654×body640valid
789.0ms819×body320valid
241.0ms3091×body80valid
137.0ms2201×body80nan
77.0ms433×body160valid
23.0ms5×body5120valid