Details

Time bar (total: 15.7s)

sample52.0ms

Algorithm
intervals
Results
17.0ms60×body1280valid
8.0ms43×body640valid
7.0ms238×body80nan
6.0ms123×body80valid
3.0ms23×body320valid
1.0ms7×body160valid

simplify4.0ms

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

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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-+ log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 65
Calls
2 calls:
22.0ms
(- (log (+ N 1.0)) (log N))
4.0ms
(log (+ N 1.0))

series199.0ms

Counts
2 → 6
Calls
2 calls:
133.0ms
(- (log (+ N 1.0)) (log N))
65.0ms
(log (+ N 1.0))

simplify1.3s

Counts
71 → 71
Iterations
IterNodes
done5001
21090
1287
0127

prune268.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
0.1b
(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
0.1b
(/ (/ 1 N) N)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
201×times-frac
167×add-sqr-sqrt
152×*-un-lft-identity
149×add-cube-cbrt
78×prod-diff
43×associate-*l*
41×distribute-rgt-in distribute-lft-in
27×add-exp-log
17×add-cbrt-cube
16×div-inv
13×associate-/l*
12×div-exp
8×pow1
6×cbrt-undiv associate-*r*
5×prod-exp unswap-sqr
3×expm1-log1p-u associate-/r* cbrt-unprod log1p-expm1-u add-log-exp
2×frac-times rec-exp sub-neg flip3-- 1-exp associate-*r/ flip-- difference-of-squares pow-div
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative fma-udef pow-flip distribute-lft-out-- inv-pow associate-/l/
Counts
3 → 246
Calls
3 calls:
0.0ms
(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
76.0ms
(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
9.0ms
(/ (/ 1 N) N)

series234.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
153.0ms
(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
30.0ms
(/ (/ 1 N) N)

simplify1.3s

Counts
255 → 255
Iterations
IterNodes
done5001
11227
0416

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (log (exp (/ (/ 1 N) N))) (- (/ 0.3333333333333333 N) 0.5))
0.0b
(fma (/ 1 N) 1.0 (* (log (exp (/ (/ 1 N) N))) (- (/ 0.3333333333333333 N) 0.5)))
0.1b
(/ (/ 1 N) N)
0.8b
(log (exp (/ (/ 1 N) N)))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
262×times-frac
194×add-sqr-sqrt
189×*-un-lft-identity
187×add-cube-cbrt
88×log-pow
86×exp-prod
78×prod-diff
47×associate-*l*
41×distribute-rgt-in distribute-lft-in
19×div-inv
15×add-exp-log
13×associate-/l*
11×pow1 add-cbrt-cube
6×div-exp associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv log-prod associate-/r*
2×sub-neg associate-*r/ difference-of-squares pow-div
1×rec-exp clear-num frac-2neg flip3-- 1-exp rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef pow-flip flip-- distribute-lft-out-- inv-pow unswap-sqr associate-/l/
Counts
4 → 294
Calls
4 calls:
172.0ms
(* (log (exp (/ (/ 1 N) N))) (- (/ 0.3333333333333333 N) 0.5))
0.0ms
(fma (/ 1 N) 1.0 (* (log (exp (/ (/ 1 N) N))) (- (/ 0.3333333333333333 N) 0.5)))
26.0ms
(/ (/ 1 N) N)
33.0ms
(log (exp (/ (/ 1 N) N)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* (log (exp (/ (/ 1 N) N))) (- (/ 0.3333333333333333 N) 0.5))
44.0ms
(fma (/ 1 N) 1.0 (* (log (exp (/ (/ 1 N) N))) (- (/ 0.3333333333333333 N) 0.5)))
26.0ms
(/ (/ 1 N) N)
36.0ms
(log (exp (/ (/ 1 N) N)))

simplify2.3s

Counts
306 → 306
Iterations
IterNodes
done5000
24409
1959
0501

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))) (cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))))
19.1b
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))
19.1b
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))
19.1b
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
14.0ms
(* (cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))) (cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))))
1.0ms
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))
1.0ms
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))
2.0ms
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))

series966.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(* (cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))) (cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))))
275.0ms
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))
215.0ms
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))
232.0ms
(cbrt (fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
done5001
21475
1408
0160

prune637.0ms

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

bsearch24.0ms

Steps
ItersRangePoint
7
1875.4132169206714
53640.016154094046
7536.677708381749

simplify3.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample2.9s

Algorithm
intervals
Results
973.0ms1807×body1280valid
812.0ms8087×body80nan
393.0ms1282×body640valid
291.0ms4016×body80valid
108.0ms603×body320valid
32.0ms292×body160valid