Details

Time bar (total: 3.6s)

sample45.0ms

Algorithm
intervals
Results
13.0ms52×body1280valid
8.0ms139×body80valid
7.0ms276×body80nan
4.0ms28×body640valid
3.0ms27×body320valid
1.0ms10×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: 26.8b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (log (+ N 1.0)) (log N))
3.2b
(log (+ N 1.0))

rewrite9.0ms

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:
6.0ms
(- (log (+ N 1.0)) (log N))
2.0ms
(log (+ N 1.0))

series134.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(- (log (+ N 1.0)) (log N))
42.0ms
(log (+ N 1.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0212281
1547264
21874250
35001247

prune98.0ms

Filtered
47 candidates to 33 candidates (70.2%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(log (log (+ N 1.0)))
0.7b
(exp (log (log (+ N 1.0))))
3.2b
(log (+ N 1.0))
22.5b
(- (exp (log (log (+ N 1.0)))) (log N))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
14×*-un-lft-identity
13×add-sqr-sqrt
10×pow1
9×add-cube-cbrt
6×add-exp-log log-pow
5×exp-sum add-log-exp
4×exp-prod add-cbrt-cube
3×associate--r+
2×log-div rem-log-exp distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+ rem-exp-log distribute-lft-out
Counts
4 → 63
Calls
4 calls:
1.0ms
(log (log (+ N 1.0)))
2.0ms
(exp (log (log (+ N 1.0))))
2.0ms
(log (+ N 1.0))
10.0ms
(- (exp (log (log (+ N 1.0)))) (log N))

series261.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(log (log (+ N 1.0)))
40.0ms
(exp (log (log (+ N 1.0))))
46.0ms
(log (+ N 1.0))
88.0ms
(- (exp (log (log (+ N 1.0)))) (log N))

simplify113.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0355529
11074481
24439443
35002427

prune161.0ms

Filtered
75 candidates to 52 candidates (69.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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))
0.4b
(/ 1 (pow N 2))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
57×times-frac
42×*-un-lft-identity
36×add-cube-cbrt
32×add-exp-log
28×associate-*l*
23×unpow-prod-down
12×div-exp
10×prod-exp add-cbrt-cube
9×unpow2 unswap-sqr sqr-pow
8×associate-/r*
6×pow-to-exp rec-exp 1-exp associate-*r* pow-exp
5×pow1 frac-add add-log-exp
4×distribute-rgt-in frac-times sub-neg associate-+l+ flip3-- distribute-lft-in associate-*r/ flip--
3×associate-/l*
2×cbrt-undiv associate-*l/ cbrt-unprod div-inv difference-of-squares
1×+-commutative pow-flip frac-2neg flip3-+ pow-prod-down clear-num sum-log *-commutative flip-+ distribute-lft-out-- inv-pow
Counts
3 → 150
Calls
3 calls:
17.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
44.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms
(/ 1 (pow N 2))

series122.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
72.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms
(/ 1 (pow N 2))

simplify72.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05831087
12726904
25001841

prune255.0ms

Filtered
159 candidates to 89 candidates (56.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 0.5 N) N)
0.1b
(* (/ 1 (pow N 2)) (/ 0.3333333333333333 N))
0.4b
(/ 1 (pow N 2))
15.0b
(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
157×times-frac
130×add-sqr-sqrt
93×*-un-lft-identity
85×add-cube-cbrt
68×add-exp-log
31×div-exp
28×associate-*l*
25×unpow-prod-down
23×add-cbrt-cube
20×prod-exp
18×unswap-sqr
16×associate-/l*
13×associate-*r*
12×frac-add
11×associate-/r* unpow2 sqr-pow
9×pow-to-exp rec-exp 1-exp pow-exp add-log-exp
8×cbrt-undiv div-inv
6×pow1
5×frac-times associate-*r/ associate-*l/
4×cbrt-unprod
3×flip3-- frac-sub flip-- sub-div
2×associate-+r+ frac-2neg clear-num sum-log
1×+-commutative associate-+r- sub-neg pow-flip flip3-+ diff-log pow-prod-down *-commutative flip-+ associate-/l/ inv-pow
Counts
4 → 249
Calls
4 calls:
5.0ms
(/ (/ 0.5 N) N)
22.0ms
(* (/ 1 (pow N 2)) (/ 0.3333333333333333 N))
4.0ms
(/ 1 (pow N 2))
105.0ms
(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

series112.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (/ 0.5 N) N)
34.0ms
(* (/ 1 (pow N 2)) (/ 0.3333333333333333 N))
15.0ms
(/ 1 (pow N 2))
34.0ms
(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))

simplify46.0ms

Algorithm
egg-herbie
Counts
261 → 261
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011841794
150011526

prune488.0ms

Filtered
261 candidates to 158 candidates (60.5%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.6b

bsearch36.0ms

Steps
ItersRangePoint
9
2.027436157277799
7103758.057079569
3926.442943372092

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
12915

end0.0ms

sample1.3s

Algorithm
intervals
Results
454.0ms1832×body1280valid
198.0ms1279×body640valid
184.0ms7781×body80nan
167.0ms3993×body80valid
62.0ms603×body320valid
18.0ms293×body160valid