Details

Time bar (total: 12.0s)

sample62.0ms

Algorithm
intervals
Results
19.0ms61×body1280valid
9.0ms276×body80nan
9.0ms44×body640valid
6.0ms119×body80valid
3.0ms22×body320valid
1.0ms10×body160valid

simplify20.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize8.0ms

Local error

Found 2 expressions with local error:

2.5b
(- (log (+ N 1.0)) (log N))
2.9b
(log (+ N 1.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×pow1 add-sqr-sqrt
5×add-cube-cbrt log-pow
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:
46.0ms
(- (log (+ N 1.0)) (log N))
6.0ms
(log (+ N 1.0))

series262.0ms

Counts
2 → 6
Calls
2 calls:
179.0ms
(- (log (+ N 1.0)) (log N))
83.0ms
(log (+ N 1.0))

simplify819.0ms

Counts
47 → 47

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
0.1b
(* (/ 1 N) (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))
0.4b
(/ 0.3333333333333333 (pow N 2))

rewrite390.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
35×add-sqr-sqrt times-frac
28×add-cube-cbrt
17×add-exp-log
13×associate-*l*
12×unpow-prod-down
10×add-cbrt-cube
8×associate-/r* add-log-exp
6×frac-add
5×pow1 div-exp associate-*r*
4×frac-times associate-*r/ prod-exp distribute-lft-out unpow2 sqr-pow
3×flip3-- flip3-+ flip-- flip-+ associate-/l* unswap-sqr
2×cbrt-undiv associate-+r+ sum-log cbrt-unprod div-inv distribute-lft-out--
1×+-commutative distribute-rgt-in pow-to-exp associate-+r- sub-neg rec-exp frac-2neg distribute-lft-in diff-log 1-exp pow-prod-down associate-*l/ pow-exp clear-num *-commutative
Counts
3 → 115
Calls
3 calls:
102.0ms
(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
266.0ms
(* (/ 1 N) (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))
15.0ms
(/ 0.3333333333333333 (pow N 2))

series159.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
75.0ms
(* (/ 1 N) (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))
47.0ms
(/ 0.3333333333333333 (pow N 2))

simplify1.4s

Counts
124 → 124

prune436.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
0.0b
(/ (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))) N)
0.4b
(/ 0.3333333333333333 (pow N 2))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
39×times-frac
30×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down
11×associate-/r*
10×add-exp-log distribute-lft-out
8×associate-/l* add-log-exp
7×add-cbrt-cube
5×distribute-lft-out--
4×div-exp frac-add associate-/l/ unpow2 sqr-pow
3×pow1
2×cbrt-undiv associate-+r- associate-+r+ flip3-- frac-2neg flip3-+ clear-num sum-log flip-- flip-+ div-inv
1×+-commutative pow-to-exp sub-neg diff-log div-sub pow-exp
Counts
3 → 108
Calls
3 calls:
64.0ms
(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
257.0ms
(/ (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))) N)
13.0ms
(/ 0.3333333333333333 (pow N 2))

series132.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
71.0ms
(/ (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))) N)
34.0ms
(/ 0.3333333333333333 (pow N 2))

simplify672.0ms

Counts
117 → 117

prune341.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 0.3333333333333333 (pow N 2))
0.4b
(/ 0.3333333333333333 (pow N 2))
12.8b
(- (* (/ 0.3333333333333333 (pow N 2)) (/ 0.3333333333333333 (pow N 2))) (* (- 1.0 (/ 0.5 N)) (- 1.0 (/ 0.5 N))))
16.1b
(/ (/ (- (* (/ 0.3333333333333333 (pow N 2)) (/ 0.3333333333333333 (pow N 2))) (* (- 1.0 (/ 0.5 N)) (- 1.0 (/ 0.5 N)))) N) (- (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))

rewrite348.0ms

Algorithm
rewrite-expression-head
Rules
408×times-frac
347×add-sqr-sqrt
228×*-un-lft-identity
143×add-cube-cbrt
119×difference-of-squares
51×distribute-lft-out--
41×unpow-prod-down
26×associate-/r* frac-sub
25×unpow2 sqr-pow
22×associate-/l*
21×flip3-- flip--
20×frac-times
19×add-exp-log
14×associate-*r/ associate-*l/ div-inv
13×add-cbrt-cube
9×div-exp
6×add-log-exp
5×cbrt-undiv
4×pow1 associate-/r/ associate--r+
3×sub-neg frac-2neg clear-num
2×distribute-rgt-in pow-to-exp distribute-lft-in div-sub pow-exp
1×diff-log associate-/l/
Counts
4 → 345
Calls
4 calls:
8.0ms
(/ 0.3333333333333333 (pow N 2))
14.0ms
(/ 0.3333333333333333 (pow N 2))
43.0ms
(- (* (/ 0.3333333333333333 (pow N 2)) (/ 0.3333333333333333 (pow N 2))) (* (- 1.0 (/ 0.5 N)) (- 1.0 (/ 0.5 N))))
258.0ms
(/ (/ (- (* (/ 0.3333333333333333 (pow N 2)) (/ 0.3333333333333333 (pow N 2))) (* (- 1.0 (/ 0.5 N)) (- 1.0 (/ 0.5 N)))) N) (- (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 0.3333333333333333 (pow N 2))
43.0ms
(/ 0.3333333333333333 (pow N 2))
75.0ms
(- (* (/ 0.3333333333333333 (pow N 2)) (/ 0.3333333333333333 (pow N 2))) (* (- 1.0 (/ 0.5 N)) (- 1.0 (/ 0.5 N))))
159.0ms
(/ (/ (- (* (/ 0.3333333333333333 (pow N 2)) (/ 0.3333333333333333 (pow N 2))) (* (- 1.0 (/ 0.5 N)) (- 1.0 (/ 0.5 N)))) N) (- (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))

simplify992.0ms

Counts
357 → 357

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.2b

bsearch1.0ms

simplify1.2s

end0.0ms

sample2.5s

Algorithm
intervals
Results
777.0ms1844×body1280valid
458.0ms8109×body80nan
399.0ms1220×body640valid
315.0ms4040×body80valid
103.0ms616×body320valid
72.0ms280×body160valid