Details

Time bar (total: 29.4s)

sample125.0ms

Algorithm
intervals
Results
46.0ms60×body1280valid
20.0ms267×body80nan
19.0ms42×body640valid
13.0ms115×body80valid
8.0ms27×body320valid
2.0ms12×body160valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
312
212
111
06

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 2 expressions with local error:

2.4b
(log (+ N 1))
3.4b
(- (log (+ N 1)) (log N))

rewrite25.0ms

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-+ insert-posit16 distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
7.0ms
(log (+ N 1))
17.0ms
(- (log (+ N 1)) (log N))

series122.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(log (+ N 1))
95.0ms
(- (log (+ N 1)) (log N))

simplify1.4s

Counts
49 → 49
Iterations
IterNodes
42935
31186
2414
1195
097

prune476.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1/3 N) (* N N))
0.3b
(/ 1/2 (* N N))
0.3b
(/ 1/3 N)
10.2b
(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
43×times-frac
35×*-un-lft-identity
28×add-sqr-sqrt add-cube-cbrt
23×add-cbrt-cube add-exp-log
19×associate-/l*
9×cbrt-undiv div-exp add-log-exp
6×div-inv
5×associate-/r*
4×pow1 insert-posit16
3×clear-num frac-2neg frac-add prod-exp cbrt-unprod distribute-lft-out
2×associate-+r+ sum-log distribute-lft-out--
1×+-commutative associate-+r- sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip-- associate-/l/
Counts
4 → 119
Calls
4 calls:
10.0ms
(/ (/ 1/3 N) (* N N))
12.0ms
(/ 1/2 (* N N))
7.0ms
(/ 1/3 N)
73.0ms
(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

series158.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (/ 1/3 N) (* N N))
40.0ms
(/ 1/2 (* N N))
22.0ms
(/ 1/3 N)
38.0ms
(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))

simplify11.0s

Counts
131 → 131
Iterations
IterNodes
310343
21958
1541
0200

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

10.2b
(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))
17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
18×cbrt-prod
15×cbrt-div
12×frac-add distribute-lft-out
9×add-log-exp
8×distribute-lft-out--
7×add-sqr-sqrt add-cube-cbrt
4×pow1 flip3-+ flip3-- add-cbrt-cube add-exp-log frac-sub flip-+ insert-posit16 div-inv flip--
3×pow1/3
2×associate-+r+ sum-log
1×+-commutative associate-+r- sub-neg diff-log
Counts
4 → 82
Calls
4 calls:
49.0ms
(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))
51.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
41.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
82.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N))))
69.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
77.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
93.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))

simplify5.2s

Counts
94 → 94
Iterations
IterNodes
36707
21575
1384
0138

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
17.4b
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
24×cbrt-prod
20×cbrt-div
12×frac-add distribute-lft-out
8×add-sqr-sqrt add-cube-cbrt distribute-lft-out--
4×pow1 flip3-+ flip3-- add-cbrt-cube pow1/3 add-exp-log frac-sub flip-+ insert-posit16 div-inv flip-- add-log-exp
Counts
4 → 80
Calls
4 calls:
60.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
48.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
56.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
49.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
74.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
101.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))
76.0ms
(cbrt (+ (/ (/ 1/3 N) (* N N)) (- (/ 1 N) (/ 1/2 (* N N)))))

simplify2.9s

Counts
92 → 92
Iterations
IterNodes
34738
21226
1336
0116

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch43.0ms

Steps
ItersRangePoint
8
9369.000823706243
5623247.098758675
9516.15297930401

simplify5.0ms

Iterations
IterNodes
221
121
017

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1817×body1280valid
877.0ms1222×body640valid
576.0ms8102×body80nan
400.0ms4055×body80valid
141.0ms609×body320valid
43.0ms297×body160valid