Details

Time bar (total: 13.3s)

sample89.0ms

Algorithm
intervals
Results
32.0ms68×body1280valid
15.0ms45×body640valid
15.0ms258×body80nan
10.0ms117×body80valid
3.0ms13×body320valid
2.0ms13×body160valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done13
213
111
06

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize23.0ms

Local error

Found 2 expressions with local error:

3.1b
(log (+ N 1))
3.4b
(- (log (+ N 1)) (log N))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×add-sqr-sqrt pow1 prod-diff
14×log-pow add-cube-cbrt
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 67
Calls
2 calls:
6.0ms
(log (+ N 1))
44.0ms
(- (log (+ N 1)) (log N))

series99.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(log (+ N 1))
70.0ms
(- (log (+ N 1)) (log N))

simplify1.4s

Counts
73 → 73
Iterations
IterNodes
done2009
42009
31955
2622
1268
0123

prune581.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 N) (/ 1/2 (* N N)))
0.8b
(/ 1/2 (* N N))
0.9b
(/ 1/3 (* N N))
13.4b
(fma (/ 1/3 (* N N)) (/ 1 N) (- (/ 1 N) (/ 1/2 (* N N))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
124×times-frac
104×add-sqr-sqrt
95×*-un-lft-identity
91×prod-diff
90×add-cube-cbrt
24×div-inv
14×add-cbrt-cube add-exp-log
13×fma-neg
6×associate-/l* add-log-exp difference-of-squares
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
2×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub fma-udef flip--
Counts
4 → 187
Calls
4 calls:
26.0ms
(- (/ 1 N) (/ 1/2 (* N N)))
10.0ms
(/ 1/2 (* N N))
6.0ms
(/ 1/3 (* N N))
0.0ms
(fma (/ 1/3 (* N N)) (/ 1 N) (- (/ 1 N) (/ 1/2 (* N N))))

series168.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (/ 1 N) (/ 1/2 (* N N)))
31.0ms
(/ 1/2 (* N N))
45.0ms
(/ 1/3 (* N N))
32.0ms
(fma (/ 1/3 (* N N)) (/ 1 N) (- (/ 1 N) (/ 1/2 (* N N))))

simplify1.1s

Counts
199 → 199
Iterations
IterNodes
done2001
32001
21570
1621
0274

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt 1/2) N)
0.9b
(/ 1/3 (* N N))
13.4b
(fma (/ 1/3 (* N N)) (/ 1 N) (+ (- (* (/ 1 (sqrt N)) (/ 1 (sqrt N))) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N))) (fma (- (/ (sqrt 1/2) N)) (/ (sqrt 1/2) N) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N)))))
43.6b
(fma (- (/ (sqrt 1/2) N)) (/ (sqrt 1/2) N) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
12×sqrt-prod
11×add-cbrt-cube add-exp-log
9×associate-/l*
4×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×clear-num frac-2neg fma-udef div-inv
1×prod-exp cbrt-unprod
Counts
4 → 88
Calls
4 calls:
17.0ms
(/ (sqrt 1/2) N)
13.0ms
(/ 1/3 (* N N))
0.0ms
(fma (/ 1/3 (* N N)) (/ 1 N) (+ (- (* (/ 1 (sqrt N)) (/ 1 (sqrt N))) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N))) (fma (- (/ (sqrt 1/2) N)) (/ (sqrt 1/2) N) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N)))))
1.0ms
(fma (- (/ (sqrt 1/2) N)) (/ (sqrt 1/2) N) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N)))

series495.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (sqrt 1/2) N)
40.0ms
(/ 1/3 (* N N))
194.0ms
(fma (/ 1/3 (* N N)) (/ 1 N) (+ (- (* (/ 1 (sqrt N)) (/ 1 (sqrt N))) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N))) (fma (- (/ (sqrt 1/2) N)) (/ (sqrt 1/2) N) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N)))))
176.0ms
(fma (- (/ (sqrt 1/2) N)) (/ (sqrt 1/2) N) (* (/ (sqrt 1/2) N) (/ (sqrt 1/2) N)))

simplify1.0s

Counts
100 → 100
Iterations
IterNodes
done2001
32001
2984
1310
0156

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1) N)
3.2b
(log (/ (+ N 1) N))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×expm1-log1p-u div-exp rem-log-exp insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Counts
2 → 66
Calls
2 calls:
28.0ms
(/ (+ N 1) N)
8.0ms
(log (/ (+ N 1) N))

series135.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(/ (+ N 1) N)
66.0ms
(log (/ (+ N 1) N))

simplify882.0ms

Counts
72 → 72
Iterations
IterNodes
done2001
32001
2665
1242
0106

prune509.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.4b

bsearch15.0ms

Steps
ItersRangePoint
4
5124.349206015988
8718.24681470488
7726.51655081009

simplify2.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample3.5s

Algorithm
intervals
Results
966.0ms1718×body1280valid
887.0ms4146×body80valid
606.0ms8102×body80nan
530.0ms1248×body640valid
191.0ms605×body320valid
83.0ms283×body160valid