Details

Time bar (total: 4.9s)

sample45.0ms

Algorithm
intervals
Results
13.0ms57×body1280valid
9.0ms43×body640valid
6.0ms245×body80nan
5.0ms121×body80valid
2.0ms26×body320valid
1.0ms9×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (log (+ N 1.0)) (log N))
4.0b
(log (+ N 1.0))

rewrite10.0ms

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:
7.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series135.0ms

Counts
2 → 6
Calls
2 calls:
93.0ms
(- (log (+ N 1.0)) (log N))
42.0ms
(log (+ N 1.0))

simplify57.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0212281
1547264
21874250
35001247

prune104.0ms

Filtered
47 candidates to 33 candidates (70.2%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.0b
(- (/ 0.3333333333333333 N) 0.5)
0.1b
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.7b
(/ 1 (pow N 2))

rewrite83.0ms

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:
19.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
10.0ms
(- (/ 0.3333333333333333 N) 0.5)
41.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
6.0ms
(/ 1 (pow N 2))

series157.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
34.0ms
(- (/ 0.3333333333333333 N) 0.5)
73.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms
(/ 1 (pow N 2))

simplify76.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05971169
12754978
25001915

prune307.0ms

Filtered
177 candidates to 101 candidates (57.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (pow N 2))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite57.0ms

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:
4.0ms
(/ 1 (pow N 2))
15.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
16.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
19.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (pow N 2))
159.0ms
(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)))
158.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify66.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05141549
120601446
250011388

prune374.0ms

Filtered
123 candidates to 82 candidates (66.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

4.2b
(exp (* 1/3 (+ (log 1.0) (log (/ 1 N)))))
13.5b
(- (+ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* 0.125 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (pow N 2)))) (+ (* 0.041666666666666664 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* (pow N 2) (pow 1.0 2)))) (* 0.16666666666666666 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) N))))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
18×add-log-exp
14×cbrt-div
12×frac-add
8×add-sqr-sqrt *-un-lft-identity associate-*r/
7×flip3-+ flip-+
6×cbrt-prod add-cube-cbrt frac-sub
5×flip3-- flip--
4×pow1 add-exp-log frac-times diff-log sum-log add-cbrt-cube
2×pow1/3 exp-sum associate-*l/
1×distribute-rgt-in sub-neg exp-prod exp-to-pow distribute-lft-in associate--l+ rem-exp-log associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 73
Calls
4 calls:
2.0ms
(exp (* 1/3 (+ (log 1.0) (log (/ 1 N)))))
55.0ms
(- (+ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* 0.125 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (pow N 2)))) (+ (* 0.041666666666666664 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* (pow N 2) (pow 1.0 2)))) (* 0.16666666666666666 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) N))))
18.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
16.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series797.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(exp (* 1/3 (+ (log 1.0) (log (/ 1 N)))))
186.0ms
(- (+ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* 0.125 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (pow N 2)))) (+ (* 0.041666666666666664 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* (pow N 2) (pow 1.0 2)))) (* 0.16666666666666666 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) N))))
156.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
156.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify102.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07953036
135492804
250012783

prune615.0ms

Filtered
85 candidates to 72 candidates (84.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch25.0ms

Steps
ItersRangePoint
7
481.02071266823316
19555.519105776155
8616.086423541381

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample1.2s

Algorithm
intervals
Results
414.0ms1753×body1280valid
182.0ms8037×body80nan
180.0ms1238×body640valid
168.0ms4084×body80valid
59.0ms625×body320valid
18.0ms300×body160valid