Details

Time bar (total: 19.1s)

sample4.0s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 35.992432%

Guaranteed chance to sample good point: 69.071231%

Results
78.0ms96×body1280valid
74.0ms32×body2560valid
15.0ms40×body640valid
6.0ms26×body320valid
4.0ms50×body80valid
2.0ms5×body640invalid
2.0ms2×body1280invalid
2.0ms12×body160valid
0.0ms1×body320invalid
0.0ms5×body80nan
0.0ms1×body160invalid
0.0ms1×body80invalid

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: 48.1b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b
(pow (+ 1.0 (/ i n)) n)
9.9b
(/ (- (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:
31.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series191.0ms

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)
29.0ms
(pow (+ 1.0 (/ i n)) n)
60.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012263285
150023166

prune601.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2876293
Fresh000
Picked101
Done000
Total2886294

Merged error: 23.6b

Counts
294 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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)))
11.1b
(* (pow i 2) (log 1.0))
20.6b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite55.0ms

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 add-log-exp
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×unpow-prod-down cbrt-unprod
3×distribute-rgt-in distribute-lft-in sum-log associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 186
Calls
4 calls:
7.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
18.0ms
(* 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))
16.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series67.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
26.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
12.0ms
(* (pow i 2) (log 1.0))
21.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify146.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09293604
148183341
250013341

prune792.0ms

Filtered
150 candidates to 198 candidates (-32.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New18513198
Fresh055
Picked101
Done000
Total18618204

Merged error: 13.1b

Counts
204 → 18

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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)
10.6b
(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-exp-log
18×add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
10×pow1
9×times-frac associate-*l* add-log-exp
8×prod-exp
7×associate-*r*
6×log-prod cbrt-unprod
4×unpow-prod-down unswap-sqr
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* sum-log associate-/l*
2×cbrt-undiv div-exp *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ associate-*l/ pow-exp clear-num log-pow flip-- flip-+ div-inv
Counts
4 → 98
Calls
4 calls:
7.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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))

series59.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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)
18.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.0ms
(* (pow i 2) (log 1.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05471517
126191294
250011290

prune322.0ms

Filtered
72 candidates to 110 candidates (-52.8%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New1091110
Fresh11617
Picked011
Done000
Total11018128

Merged error: 13.1b

Counts
128 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt i)
9.3b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
10.6b
(* (/ 1 (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) n)))
11.1b
(* (pow i 2) (log 1.0))

rewrite101.0ms

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×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 → 354
Calls
4 calls:
1.0ms
(cbrt i)
15.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
58.0ms
(* (/ 1 (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) n)))
6.0ms
(* (pow i 2) (log 1.0))

series99.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(cbrt i)
35.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) n))
24.0ms
(* (/ 1 (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) n)))
18.0ms
(* (pow i 2) (log 1.0))

simplify115.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
018528881
150018431

prune1.6s

Filtered
270 candidates to 366 candidates (-35.6%)
Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New3588366
Fresh31316
Picked101
Done011
Total36222384

Merged error: 13.1b

Counts
384 → 22

regimes397.0ms

Accuracy

71.4% (5.8b remaining)

Error of 18.8b against oracle of 13.0b and baseline of 33.4b

bsearch572.0ms

Steps
ItersRangePoint
9
2.846971260289306e+151
1.0951419578678547e+158
1.3518573921420913e+154
11
1.1805954290403808e-06
3.834291256401624e+30
0.0002646648476336857
9
7.751283257276457e-214
6.089376719851176e-207
8.322109095952483e-208
7
-2.535162224106145
-0.02199654089169092
-0.11203948926345608

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09082
19082

end0.0ms

sample9.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 35.992432%

Guaranteed chance to sample good point: 69.071231%

Results
2.2s2639×body1280valid
1.8s841×body2560valid
605.0ms1600×body640valid
179.0ms749×body320valid
127.0ms1798×body80valid
72.0ms140×body640invalid
56.0ms368×body160valid
37.0ms40×body1280invalid
33.0ms99×body320invalid
24.0ms11×body2560invalid
23.0ms5×body5120valid
10.0ms209×body80nan
8.0ms43×body160invalid
4.0ms45×body80invalid

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