Details

Time bar (total: 1.9m)

sample23.7s

Algorithm
intervals
Results
95.0ms112×body1280valid
71.0ms34×body2560valid
27.0ms59×body640valid
9.0ms32×body320valid
7.0ms154×body80nan
6.0ms76×body80valid
5.0ms1×body5120valid
2.0ms9×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.6b

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)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.5b
(pow (+ 1.0 (/ i n)) n)
13.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite83.0ms

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:
30.0ms
(* 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))

series185.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms
(pow (+ 1.0 (/ i n)) n)
58.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012263285
150023166

prune601.0ms

Filtered
293 candidates to 223 candidates (23.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2858293
Fresh000
Picked101
Done000
Total2868294

Merged error: 23.2b

Counts
294 → 8

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)))
9.1b
(* (pow i 2) (log 1.0))
18.5b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite54.0ms

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:
6.0ms
(+ (* 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))
15.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series62.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
23.0ms
(* 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))
20.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify149.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09293604
148183341
250013341

prune794.0ms

Filtered
198 candidates to 150 candidates (24.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New18711198
Fresh077
Picked101
Done000
Total18818206

Merged error: 9.6b

Counts
206 → 18

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 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))
8.6b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.1b
(* (pow i 2) (log 1.0))

rewrite42.0ms

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×unpow-prod-down pow-prod-down 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 → 117
Calls
4 calls:
11.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) 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))
10.0ms
(/ (- (+ (* 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))

series69.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
23.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
14.0ms
(/ (- (+ (* 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))

simplify79.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05291979
124351684
250011679

prune395.0ms

Filtered
129 candidates to 87 candidates (32.6%)
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New1272129
Fresh11617
Picked011
Done000
Total12819147

Merged error: 9.6b

Counts
147 → 19

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)) n)
2.5b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
9.1b
(* (pow i 2) (log 1.0))
9.7b
(* (/ 1 (* (cbrt i) (cbrt i))) (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)) n))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
94×add-exp-log
54×add-sqr-sqrt
49×prod-exp
41×times-frac
40×add-cube-cbrt *-un-lft-identity
38×add-cbrt-cube
37×associate-*l*
22×cbrt-prod
21×div-exp cbrt-unprod
12×pow1
11×cbrt-undiv
8×associate-*r*
7×unswap-sqr
6×rec-exp log-prod 1-exp associate-/r*
4×unpow-prod-down pow-prod-down associate-*l/ add-log-exp
3×distribute-rgt-in distribute-lft-in *-commutative div-inv associate-/l*
2×associate-/l/ unpow2 sqr-pow
1×frac-times pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-exp clear-num log-pow flip--
Counts
4 → 169
Calls
4 calls:
12.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)) n)
11.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
6.0ms
(* (pow i 2) (log 1.0))
18.0ms
(* (/ 1 (* (cbrt i) (cbrt i))) (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)) n))

series97.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)) n)
26.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
12.0ms
(* (pow i 2) (log 1.0))
23.0ms
(* (/ 1 (* (cbrt i) (cbrt i))) (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)) n))

simplify133.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
09813673
142193061
250022987

prune502.0ms

Filtered
181 candidates to 114 candidates (37.0%)
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New1774181
Fresh31417
Picked101
Done011
Total18119200

Merged error: 9.6b

Counts
200 → 19

regimes414.0ms

Accuracy

61.6% (4.5b remaining)

Error of 13.4b against oracle of 8.9b and baseline of 20.7b

bsearch55.6s

Steps
ItersRangePoint
4
0.1851646928076403
0.27320132762925337
0.18755331690160862
7
-3.129616319816678
-0.12675029390091438
-0.4168061934748711

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04729
14729

end0.0ms

sample28.1s

Algorithm
intervals
Results
2.8s3433×body1280valid
2.5s1237×body2560valid
812.0ms1908×body640valid
220.0ms850×body320valid
185.0ms4574×body80nan
180.0ms2367×body80valid
64.0ms394×body160valid
27.0ms7×body5120valid

Profiling

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