Details

Time bar (total: 26.8s)

sample91.0ms

Algorithm
intervals
Results
27.0ms53×body1280valid
15.0ms43×body640valid
15.0ms259×body80nan
13.0ms136×body80valid
4.0ms16×body320valid
1.0ms8×body160valid

simplify11.0ms

Counts
1 → 1
Iterations
IterNodes
done12
212
111
06

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize12.0ms

Local error

Found 2 expressions with local error:

2.1b
(- (log (+ N 1)) (log N))
3.3b
(log (+ N 1))

rewrite12.0ms

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:
8.0ms
(- (log (+ N 1)) (log N))
3.0ms
(log (+ N 1))

series93.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(- (log (+ N 1)) (log N))
30.0ms
(log (+ N 1))

simplify1.1s

Counts
49 → 49
Iterations
IterNodes
done2005
42005
31329
2452
1200
097

prune388.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1) N)
2.5b
(log (/ (+ N 1) N))

rewrite22.0ms

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×div-exp rem-log-exp insert-posit16 div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Counts
2 → 62
Calls
2 calls:
17.0ms
(/ (+ N 1) N)
4.0ms
(log (/ (+ N 1) N))

series149.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(/ (+ N 1) N)
73.0ms
(log (/ (+ N 1) N))

simplify903.0ms

Counts
68 → 68
Iterations
IterNodes
done2000
32000
2620
1233
0102

prune464.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* N N) N)
0.3b
(/ -1/2 (* N N))
0.5b
(/ 1/3 (* (* N N) N))
12.6b
(+ (/ 1/3 (* (* N N) N)) (+ (/ 1 N) (/ -1/2 (* N N))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1 add-cbrt-cube add-exp-log
16×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt add-log-exp
7×prod-exp cbrt-unprod
6×times-frac pow-plus pow-prod-up associate-/l*
5×cbrt-undiv div-exp distribute-lft-out
4×frac-add insert-posit16
3×sum-log associate-*r* pow-prod-down div-inv
2×pow2 clear-num associate-/r* frac-2neg flip3-+ pow-sqr flip-+
1×+-commutative associate-+r+ associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 95
Calls
4 calls:
15.0ms
(* (* N N) N)
11.0ms
(/ -1/2 (* N N))
27.0ms
(/ 1/3 (* (* N N) N))
98.0ms
(+ (/ 1/3 (* (* N N) N)) (+ (/ 1 N) (/ -1/2 (* N N))))

series216.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (* N N) N)
49.0ms
(/ -1/2 (* N N))
70.0ms
(/ 1/3 (* (* N N) N))
32.0ms
(+ (/ 1/3 (* (* N N) N)) (+ (/ 1 N) (/ -1/2 (* N N))))

simplify1.4s

Counts
107 → 107
Iterations
IterNodes
done2002
32002
21838
1455
0161

prune756.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1/3 (* (* N N) N))
0.5b
(/ 1/3 (* (* N N) N))
22.8b
(+ (* (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (+ (/ 1 N) (/ -1/2 (* N N)))) (/ (/ (/ 1/27 (* (* N N) N)) (* (* N N) N)) (* (* N N) N)))
45.5b
(/ (+ (* (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (+ (/ 1 N) (/ -1/2 (* N N)))) (/ (/ (/ 1/27 (* (* N N) N)) (* (* N N) N)) (* (* N N) N))) (+ (* (/ 1/3 (* (* N N) N)) (/ 1/3 (* (* N N) N))) (- (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (* (/ 1/3 (* (* N N) N)) (+ (/ 1 N) (/ -1/2 (* N N)))))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
831×frac-add
599×frac-times
369×flip3-+ flip-+
368×associate-*r/
341×associate-/r/
315×frac-sub
284×associate-*l/
65×associate-/l/
24×add-cbrt-cube add-exp-log
18×sub-div
16×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×times-frac
9×associate-/l*
7×cbrt-undiv div-exp
6×prod-exp cbrt-unprod add-log-exp
5×associate-/r*
4×pow1 insert-posit16
3×clear-num frac-2neg flip3-- div-inv flip--
2×associate-+l+
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
4 → 559
Calls
4 calls:
28.0ms
(/ 1/3 (* (* N N) N))
14.0ms
(/ 1/3 (* (* N N) N))
222.0ms
(+ (* (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (+ (/ 1 N) (/ -1/2 (* N N)))) (/ (/ (/ 1/27 (* (* N N) N)) (* (* N N) N)) (* (* N N) N)))
1.0s
(/ (+ (* (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (+ (/ 1 N) (/ -1/2 (* N N)))) (/ (/ (/ 1/27 (* (* N N) N)) (* (* N N) N)) (* (* N N) N))) (+ (* (/ 1/3 (* (* N N) N)) (/ 1/3 (* (* N N) N))) (- (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (* (/ 1/3 (* (* N N) N)) (+ (/ 1 N) (/ -1/2 (* N N)))))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 1/3 (* (* N N) N))
47.0ms
(/ 1/3 (* (* N N) N))
93.0ms
(+ (* (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (+ (/ 1 N) (/ -1/2 (* N N)))) (/ (/ (/ 1/27 (* (* N N) N)) (* (* N N) N)) (* (* N N) N)))
132.0ms
(/ (+ (* (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (+ (/ 1 N) (/ -1/2 (* N N)))) (/ (/ (/ 1/27 (* (* N N) N)) (* (* N N) N)) (* (* N N) N))) (+ (* (/ 1/3 (* (* N N) N)) (/ 1/3 (* (* N N) N))) (- (* (+ (/ 1 N) (/ -1/2 (* N N))) (+ (/ 1 N) (/ -1/2 (* N N)))) (* (/ 1/3 (* (* N N) N)) (+ (/ 1 N) (/ -1/2 (* N N)))))))

simplify3.0s

Counts
571 → 571
Iterations
IterNodes
done2076
02076

prune12.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch82.0ms

Steps
ItersRangePoint
10
1.8230705747381016e-09
318690.85562629136
8386.707428118045

simplify3.0ms

Iterations
IterNodes
done23
123
017

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.5s1773×body1280valid
578.0ms8060×body80nan
500.0ms1232×body640valid
489.0ms4056×body80valid
203.0ms634×body320valid
51.0ms305×body160valid