Details

Time bar (total: 17.9s)

sample2.0s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 20.785522%

Guaranteed chance to sample good point: 72.739531%

Results
72.0ms32×body2560valid
69.0ms80×body1280valid
20.0ms53×body640valid
4.0ms63×body80valid
4.0ms18×body320valid
3.0ms4×body1280invalid
3.0ms9×body320invalid
1.0ms10×body160valid
1.0ms2×body640invalid
1.0ms11×body80invalid
1.0ms4×body160invalid
0.0ms8×body80nan

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.4b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b
(pow (+ 1.0 (/ i n)) n)
11.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
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 distribute-lft-out
Counts
4 → 281
Calls
4 calls:
35.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
16.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series196.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
35.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms
(pow (+ 1.0 (/ i n)) n)
67.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify65.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012263285
150023166

prune604.0ms

Filtered
223 candidates to 293 candidates (-31.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2858293
Fresh000
Picked101
Done000
Total2868294

Merged error: 20.5b

Counts
294 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
0.1b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.4b
(* (pow i 2) (log 1.0))
20.1b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
111×add-sqr-sqrt
90×add-cube-cbrt *-un-lft-identity
56×associate-*r*
28×add-exp-log
22×add-cbrt-cube
14×associate-*l*
13×associate-/r*
11×unswap-sqr
9×prod-exp div-inv
8×unpow-prod-down
7×pow1
6×cbrt-undiv log-prod div-exp
5×cbrt-unprod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num log-pow flip--
Counts
4 → 200
Calls
4 calls:
6.0ms
(* 0.5 (pow i 2))
19.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms
(* (pow i 2) (log 1.0))
14.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series57.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 0.5 (pow i 2))
22.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
13.0ms
(* (pow i 2) (log 1.0))
20.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify153.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09073537
148563275
250013275

prune785.0ms

Filtered
157 candidates to 212 candidates (-35.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2048212
Fresh077
Picked101
Done000
Total20515220

Merged error: 8.7b

Counts
220 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
0.1b
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
10.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b
(* (pow i 2) (log 1.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
14×associate-*l*
13×associate-*r*
11×prod-exp
10×pow1
9×times-frac
8×unpow-prod-down unswap-sqr
7×cbrt-unprod
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ associate-*l/ clear-num log-pow flip-- div-inv
Counts
4 → 112
Calls
4 calls:
6.0ms
(* 0.5 (pow i 2))
11.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms
(* (pow i 2) (log 1.0))

series55.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 0.5 (pow i 2))
22.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
15.0ms
(/ (- (+ (* 1.0 i) (+ (* 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))

simplify78.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05181449
124681227
250011223

prune526.0ms

Filtered
79 candidates to 124 candidates (-57.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1231124
Fresh11314
Picked011
Done000
Total12415139

Merged error: 8.7b

Counts
139 → 15

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt i)
2.6b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n)))
7.6b
(* (/ (* (cbrt n) (cbrt n)) (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n))))
11.4b
(* (pow i 2) (log 1.0))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
587×times-frac
391×add-sqr-sqrt
288×cbrt-prod
271×add-cube-cbrt *-un-lft-identity
129×associate-*r*
98×add-exp-log
42×div-exp
40×associate-/r* unswap-sqr
33×prod-exp add-cbrt-cube
23×associate-*l*
22×unpow-prod-down
18×cbrt-undiv
13×cbrt-unprod
10×div-inv
9×unpow2 sqr-pow
7×pow1 pow-to-exp pow-exp
6×log-prod
4×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 → 444
Calls
4 calls:
1.0ms
(cbrt i)
18.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n)))
63.0ms
(* (/ (* (cbrt n) (cbrt n)) (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n))))
7.0ms
(* (pow i 2) (log 1.0))

series90.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(cbrt i)
26.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n)))
26.0ms
(* (/ (* (cbrt n) (cbrt n)) (pow (cbrt i) 2)) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n))))
13.0ms
(* (pow i 2) (log 1.0))

simplify152.0ms

Algorithm
egg-herbie
Counts
456 → 456
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
0229612688
1500112255

prune3.8s

Filtered
377 candidates to 456 candidates (-21.0%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New4533456
Fresh01313
Picked101
Done011
Total45417471

Merged error: 8.7b

Counts
471 → 17

regimes624.0ms

Accuracy

65% (6.4b remaining)

Error of 17.4b against oracle of 11.0b and baseline of 29.3b

bsearch347.0ms

Steps
ItersRangePoint
9
3.9315449818453526e+221
3.8529189372622447e+230
7.470025160645056e+226
9
4.136920588370352e+119
3.261406201684019e+128
2.7103851344347878e+128
11
1.5182574466352638e-08
1.044198805660831e+16
0.029166621295560517
6
-9.621008612383004e-15
-1.2710526724847635e-15
-9.458751820935287e-15

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06650
16650

end0.0ms

sample7.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 20.785522%

Guaranteed chance to sample good point: 72.739531%

Results
2.4s2791×body1280valid
2.1s965×body2560valid
623.0ms1588×body640valid
167.0ms718×body320valid
113.0ms1602×body80valid
108.0ms223×body640invalid
89.0ms108×body1280invalid
59.0ms190×body320invalid
50.0ms333×body160valid
39.0ms416×body80invalid
21.0ms115×body160invalid
21.0ms10×body2560invalid
14.0ms3×body5120valid
8.0ms173×body80nan

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