Details

Time bar (total: 4.9s)

sample41.0ms

Algorithm
intervals
Results
12.0ms50×body1280valid
8.0ms52×body640valid
5.0ms227×body80nan
5.0ms122×body80valid
2.0ms26×body320valid
0.0ms6×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: 31.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b
(log (+ N 1.0))
2.5b
(- (log (+ N 1.0)) (log N))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×pow1 add-sqr-sqrt
5×add-cube-cbrt log-pow
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
3.0ms
(log (+ N 1.0))
7.0ms
(- (log (+ N 1.0)) (log N))

series140.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(log (+ N 1.0))
99.0ms
(- (log (+ N 1.0)) (log N))

simplify53.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0212281
1547264
21875250
35001247

prune105.0ms

Filtered
47 candidates to 33 candidates (70.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New44347
Fresh000
Picked101
Done000
Total45348

Merged error: 0.0b

Counts
48 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.3333333333333333 N) 0.5)
0.0b
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.8b
(/ 1 (pow N 2))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
58×times-frac
45×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
28×associate-*l*
23×unpow-prod-down
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×associate-/r* add-log-exp
6×pow1 pow-to-exp rec-exp 1-exp associate-*r* pow-exp
5×sub-neg flip3-- frac-add flip--
4×distribute-rgt-in frac-times associate-+l+ distribute-lft-in associate-*r/ difference-of-squares
3×associate-/l*
2×cbrt-undiv associate-*l/ cbrt-unprod div-inv distribute-lft-out--
1×+-commutative pow-flip frac-2neg flip3-+ diff-log pow-prod-down clear-num sum-log *-commutative flip-+ inv-pow
Counts
4 → 165
Calls
4 calls:
7.0ms
(- (/ 0.3333333333333333 N) 0.5)
18.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
17.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms
(/ 1 (pow N 2))

series164.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (/ 0.3333333333333333 N) 0.5)
30.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
78.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
17.0ms
(/ 1 (pow N 2))

simplify73.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05971169
12754978
25001915

prune292.0ms

Filtered
177 candidates to 101 candidates (57.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1761177
Fresh022
Picked011
Done000
Total1764180

Merged error: 0.0b

Counts
180 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (pow N 2))
17.6b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
17.6b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
17.6b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
21×cbrt-div
15×frac-add
13×add-exp-log
12×unpow-prod-down
9×cbrt-prod
8×associate-/r*
6×frac-times flip3-- associate-*r/ div-exp add-cbrt-cube flip--
4×pow1 unpow2 add-log-exp sqr-pow
3×pow-to-exp rec-exp flip3-+ pow1/3 1-exp associate-*l/ pow-exp flip-+ associate-/l*
1×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
Counts
4 → 111
Calls
4 calls:
5.0ms
(/ 1 (pow N 2))
15.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
15.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
15.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series497.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ 1 (pow N 2))
159.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
159.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
161.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify65.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05141549
120601446
250011388

prune359.0ms

Filtered
123 candidates to 82 candidates (66.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1221123
Fresh022
Picked101
Done011
Total1234127

Merged error: 0.0b

Counts
127 → 4

localize34.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)))
15.1b
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)
17.6b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
17.6b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
106×associate-*l/
80×frac-add
56×cbrt-div
36×add-exp-log
32×frac-times associate-*r/
23×flip3-+ flip-+
22×flip3-- flip--
21×prod-exp
13×add-cbrt-cube
9×pow1 cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×div-exp
5×cbrt-unprod
4×add-log-exp
3×pow-to-exp rec-exp pow1/3 1-exp associate-*r* pow-prod-down pow-exp
1×cbrt-undiv associate-*l* *-commutative
Counts
4 → 122
Calls
4 calls:
36.0ms
(cbrt (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)))
36.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)
15.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
15.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series600.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(cbrt (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)))
115.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)
161.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
157.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify79.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015944781
150014653

prune878.0ms

Filtered
134 candidates to 106 candidates (79.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1331134
Fresh022
Picked101
Done011
Total1344138

Merged error: 0b

Counts
138 → 4

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.3b

bsearch38.0ms

Steps
ItersRangePoint
9
0.3235305135594418
61404.87568264329
3345.380548053578

simplify6.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03820
13820

end0.0ms

sample1.2s

Algorithm
intervals
Results
401.0ms1670×body1280valid
182.0ms1246×body640valid
180.0ms8087×body80nan
167.0ms4159×body80valid
60.0ms631×body320valid
21.0ms294×body160valid