Details

Time bar (total: 27.4s)

sample200.0ms

Algorithm
intervals
Results
77.0ms93×body1280valid
65.0ms29×body2560valid
21.0ms56×body640valid
6.0ms23×body320valid
6.0ms77×body80valid
4.0ms66×body80nan
2.0ms17×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune4.0ms

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: 48.1b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.3b
(pow (+ 1.0 (/ i n)) n)
8.5b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite81.0ms

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:
33.0ms
(* 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)
15.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series189.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
36.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms
(pow (+ 1.0 (/ i n)) n)
66.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012263285
150023166

prune2.9s

Filtered
293 candidates to 223 candidates (23.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New28310293
Fresh000
Picked101
Done000
Total28410294

Merged error: 21.7b

Counts
294 → 10

localize20.0ms

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)))
11.6b
(* (pow i 2) (log 1.0))
16.9b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite51.0ms

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))
13.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series63.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
21.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
16.0ms
(* (pow i 2) (log 1.0))
19.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify138.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09293610
147193341
250013341

prune2.0s

Filtered
198 candidates to 150 candidates (24.2%)
Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New18216198
Fresh099
Picked101
Done000
Total18325208

Merged error: 12.6b

Counts
208 → 25

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))
11.0b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b
(* (pow i 2) (log 1.0))

rewrite36.0ms

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 add-log-exp
8×prod-exp
6×log-prod cbrt-unprod
5×associate-*r*
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:
6.0ms
(+ (* 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))
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))

series57.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
21.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
16.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms
(* (pow i 2) (log 1.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
05401516
124651293
250011289

prune818.0ms

Filtered
110 candidates to 72 candidates (34.5%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New1082110
Fresh42024
Picked011
Done000
Total11223135

Merged error: 12.6b

Counts
135 → 23

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt i)
2.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n)))
7.7b
(* (/ (* (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))))
11.6b
(* (pow i 2) (log 1.0))

rewrite116.0ms

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)
21.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n)))
58.0ms
(* (/ (* (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))))
6.0ms
(* (pow i 2) (log 1.0))

series91.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(cbrt i)
25.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ (cbrt i) (cbrt n)))
31.0ms
(* (/ (* (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))))
12.0ms
(* (pow i 2) (log 1.0))

simplify143.0ms

Algorithm
egg-herbie
Counts
456 → 456
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0229612688
1500112255

prune13.0s

Filtered
456 candidates to 377 candidates (17.3%)
Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New4497456
Fresh71421
Picked101
Done011
Total45722479

Merged error: 12.6b

Counts
479 → 22

regimes763.0ms

Accuracy

68.1% (5.7b remaining)

Error of 17.1b against oracle of 11.4b and baseline of 29.2b

bsearch493.0ms

Steps
ItersRangePoint
10
6.262779125940342e+193
5.7865628163940424e+205
6.796660388732277e+201
9
1.5117428016084668e+134
3.065339794375008e+142
1.3389732962764689e+141
9
1.5972903132525599e-06
28.700163284045342
2.3801207475861577
6
-5.449012348541443
-0.4867936294477796
-1.6813941037862414

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09068
19068

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.3s2872×body1280valid
2.0s1000×body2560valid
677.0ms1778×body640valid
216.0ms908×body320valid
164.0ms2426×body80valid
88.0ms2190×body80nan
69.0ms479×body160valid
34.0ms9×body5120valid

Profiling

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