Details

Time bar (total: 3.3s)

sample53.0ms

Algorithm
intervals
Results
17.0ms56×body1280valid
8.0ms252×body80nan
7.0ms38×body640valid
6.0ms121×body80valid
3.0ms23×body320valid
1.0ms18×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.9b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.0b
(log (+ N 1.0))
5.0b
(- (log (+ N 1.0)) (log N))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×pow1 add-sqr-sqrt prod-diff
14×add-cube-cbrt log-pow
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 65
Calls
2 calls:
3.0ms
(log (+ N 1.0))
7.0ms
(- (log (+ N 1.0)) (log N))

series139.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(log (+ N 1.0))
98.0ms
(- (log (+ N 1.0)) (log N))

simplify127.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (121.0ms)

IterNodesCost
0277598
1837444
23748347
35001343

prune119.0ms

Filtered
71 candidates to 43 candidates (60.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New69271
Fresh000
Picked101
Done000
Total70272

Merged error: 0.1b

Counts
72 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.3333333333333333 N) 0.5)
0.1b
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.5b
(/ 1 (pow N 2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
63×*-un-lft-identity
61×add-cube-cbrt times-frac
39×prod-diff
13×fma-neg
12×add-exp-log unpow-prod-down
8×associate-/r*
6×div-exp
5×add-cbrt-cube div-inv add-log-exp
4×unpow2 sqr-pow
3×pow1 expm1-log1p-u pow-to-exp rec-exp 1-exp pow-exp log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv sub-neg flip3-- pow-flip frac-2neg diff-log clear-num flip-- fma-udef distribute-lft-out-- inv-pow
Counts
3 → 138
Calls
3 calls:
8.0ms
(- (/ 0.3333333333333333 N) 0.5)
1.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
5.0ms
(/ 1 (pow N 2))

series87.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(- (/ 0.3333333333333333 N) 0.5)
33.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
20.0ms
(/ 1 (pow N 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04251067
11442713
25001631

prune175.0ms

Filtered
147 candidates to 67 candidates (45.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1452147
Fresh011
Picked011
Done000
Total1454149

Merged error: 0.0b

Counts
149 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (pow N 2))
0.5b
(/ 1 (pow N 2))
8.5b
(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
8.5b
(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt
40×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
16×associate-/r*
12×div-exp
8×add-cbrt-cube unpow2 sqr-pow
6×pow1 pow-to-exp rec-exp 1-exp pow-exp sqrt-prod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num div-inv inv-pow
Counts
4 → 148
Calls
4 calls:
8.0ms
(/ 1 (pow N 2))
5.0ms
(/ 1 (pow N 2))
1.0ms
(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
2.0ms
(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

series151.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (pow N 2))
16.0ms
(/ 1 (pow N 2))
62.0ms
(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
57.0ms
(sqrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

simplify47.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0237852
1849730
25002634

prune259.0ms

Filtered
160 candidates to 76 candidates (47.5%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1600160
Fresh022
Picked011
Done011
Total1604164

Merged error: 0.0b

Counts
164 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
5.3b
(log (/ (+ N 1.0) N))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×expm1-log1p-u div-exp rem-log-exp log1p-expm1-u div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 64
Calls
2 calls:
5.0ms
(/ (+ N 1.0) N)
4.0ms
(log (/ (+ N 1.0) N))

series131.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(/ (+ N 1.0) N)
85.0ms
(log (/ (+ N 1.0) N))

simplify110.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
0243383
1808358
23663347
35001344

prune97.0ms

Filtered
70 candidates to 50 candidates (71.4%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New69170
Fresh011
Picked011
Done022
Total69574

Merged error: 0.0b

Counts
74 → 5

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.9b

bsearch33.0ms

Steps
ItersRangePoint
8
1538.2388859235716
3249381.761613268
10531.413524966325

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219
1219

end0.0ms

sample1.6s

Algorithm
intervals
Results
535.0ms1728×body1280valid
257.0ms7954×body80nan
256.0ms1253×body640valid
220.0ms4117×body80valid
83.0ms615×body320valid
24.0ms287×body160valid

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