Details

Time bar (total: 14.7s)

sample65.0ms

Algorithm
intervals
Results
21.0ms60×body1280valid
10.0ms238×body80nan
9.0ms43×body640valid
7.0ms123×body80valid
3.0ms23×body320valid
1.0ms7×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize20.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (log (+ N 1.0)) (log N))
3.2b
(log (+ N 1.0))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×add-sqr-sqrt pow1
5×log-pow add-cube-cbrt
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:
19.0ms
(- (log (+ N 1.0)) (log N))
7.0ms
(log (+ N 1.0))

series228.0ms

Counts
2 → 6
Calls
2 calls:
131.0ms
(- (log (+ N 1.0)) (log N))
97.0ms
(log (+ N 1.0))

simplify1.6s

Counts
47 → 47
Iterations
IterNodes
done5000
32789
2645
1213
0101

prune204.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
0.1b
(/ (/ 0.3333333333333333 N) (* N N))
0.8b
(/ 0.5 (* N N))
13.6b
(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
46×times-frac
39×add-sqr-sqrt
29×*-un-lft-identity
21×add-cbrt-cube add-exp-log
20×add-cube-cbrt
16×associate-/l*
11×add-log-exp
8×cbrt-undiv div-exp difference-of-squares
6×frac-sub div-inv
5×distribute-lft-out--
4×pow1 diff-log
3×sub-neg flip3-- prod-exp cbrt-unprod flip--
2×clear-num associate-/r* frac-2neg associate--r+ sub-div
1×distribute-rgt-out-- associate--r- associate-/l/
Counts
4 → 114
Calls
4 calls:
126.0ms
(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
12.0ms
(/ (/ 0.3333333333333333 N) (* N N))
9.0ms
(/ 0.5 (* N N))
55.0ms
(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
55.0ms
(/ (/ 0.3333333333333333 N) (* N N))
41.0ms
(/ 0.5 (* N N))
152.0ms
(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

simplify2.3s

Counts
126 → 126
Iterations
IterNodes
done5000
23082
1602
0223

prune519.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 0.3333333333333333 N) (* N N))
0.8b
(/ 0.5 (* N N))
0.8b
(log (exp (/ 0.5 (* N N))))
15.8b
(- (log (exp (/ 0.5 (* N N)))) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
31×add-sqr-sqrt
27×*-un-lft-identity
24×add-cube-cbrt
21×add-cbrt-cube add-exp-log
16×associate-/l*
9×log-pow
8×cbrt-undiv div-exp
7×exp-prod
6×pow1 log-prod
5×div-inv add-log-exp
3×prod-exp associate--l+ cbrt-unprod difference-of-squares
2×clear-num associate-/r* frac-2neg distribute-lft-out--
1×sub-neg flip3-- diff-log rem-log-exp flip-- associate-/l/
Counts
4 → 106
Calls
4 calls:
20.0ms
(/ (/ 0.3333333333333333 N) (* N N))
6.0ms
(/ 0.5 (* N N))
9.0ms
(log (exp (/ 0.5 (* N N))))
98.0ms
(- (log (exp (/ 0.5 (* N N)))) (/ (/ 0.3333333333333333 N) (* N N)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (/ 0.3333333333333333 N) (* N N))
52.0ms
(/ 0.5 (* N N))
47.0ms
(log (exp (/ 0.5 (* N N))))
144.0ms
(- (log (exp (/ 0.5 (* N N)))) (/ (/ 0.3333333333333333 N) (* N N)))

simplify1.7s

Counts
118 → 118
Iterations
IterNodes
done5002
22694
1460
0191

prune559.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

13.6b
(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))
19.1b
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))
19.1b
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))
19.1b
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))

rewrite343.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
26×*-un-lft-identity
21×cbrt-prod
18×cbrt-div
16×frac-sub
14×times-frac
12×difference-of-squares
11×distribute-lft-out--
7×flip3-- add-cube-cbrt flip--
6×add-log-exp
4×pow1 add-cbrt-cube add-exp-log sub-div
3×pow1/3
2×div-inv
1×sub-neg distribute-rgt-out-- diff-log
Counts
4 → 86
Calls
4 calls:
31.0ms
(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))
126.0ms
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))
95.0ms
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))
89.0ms
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))

series796.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))
257.0ms
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))
209.0ms
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))
219.0ms
(cbrt (- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))))

simplify2.1s

Counts
98 → 98
Iterations
IterNodes
done5001
21930
1477
0188

prune656.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch44.0ms

Steps
ItersRangePoint
7
1875.4132169206714
53640.016154094046
7536.677708381749

simplify5.0ms

Iterations
IterNodes
done18
118
017

end0.0ms

sample2.4s

Algorithm
intervals
Results
899.0ms1807×body1280valid
405.0ms8087×body80nan
335.0ms1282×body640valid
320.0ms4016×body80valid
133.0ms603×body320valid
30.0ms292×body160valid