Details

sample78.0ms

Algorithm

intervals

Results

23.0ms	56×	body	1280	valid
16.0ms	211×	body	80	nan
13.0ms	46×	body	640	valid
10.0ms	132×	body	80	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize23.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (log (+ N 1)) (log N))
3.4b	(log (+ N 1))

rewrite21.0ms

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:

13.0ms	(- (log (+ N 1)) (log N))
7.0ms	(log (+ N 1))

series97.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (log (+ N 1)) (log N))
40.0ms	(log (+ N 1))

simplify2.3s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
4	3749
3	1329
2	452
1	200
0	97

prune198.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
2.1b	(log (/ (+ N 1) N))

rewrite30.0ms

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:

18.0ms	(/ (+ N 1) N)
10.0ms	(log (/ (+ N 1) N))

series152.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(/ (+ N 1) N)
73.0ms	(log (/ (+ N 1) N))

simplify1.7s

Counts

68 → 68

Iterations

Iter	Nodes
done	5021
3	2563
2	620
1	233
0	102

prune267.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

2.1b	(log (+ (/ 1 N) 1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log-prod` `*-un-lft-identity`
2×	`add-sqr-sqrt` `pow1` `log-div` `add-exp-log` `add-cube-cbrt` `distribute-lft-out`
1×	`flip3-+` `add-cbrt-cube` `rem-log-exp` `log-pow` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

22.0ms

(log (+ (/ 1 N) 1))

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(log (+ (/ 1 N) 1))

simplify2.3s

Counts

20 → 20

Iterations

Iter	Nodes
done	5000
4	1949
3	645
2	271
1	107
0	50

prune80.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 N) (* (/ (/ 1 N) N) (- 1/2 (/ 1/3 N))))
0.1b	(* (/ (/ 1 N) N) (- 1/2 (/ 1/3 N)))
0.1b	(/ (/ 1 N) N)
0.4b	(/ 1/3 N)

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
93×	`*-un-lft-identity`
90×	`add-cube-cbrt`
43×	`associate-l`
30×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/l*`
13×	`div-exp`
11×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv`
6×	`associate-/r` `associate-r*` `add-log-exp`
5×	`sub-neg` `flip3--` `prod-exp` `frac-sub` `flip--` `unswap-sqr`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `insert-posit16` `associate--r+`
3×	`associate-*l/` `cbrt-unprod`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `difference-of-squares` `pow-div`
1×	`diff-log` `pow-prod-down` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow` `sub-div` `associate-/l/`

Counts

4 → 207

Calls

4 calls:

33.0ms	(- (/ 1 N) (* (/ (/ 1 N) N) (- 1/2 (/ 1/3 N))))
75.0ms	(* (/ (/ 1 N) N) (- 1/2 (/ 1/3 N)))
11.0ms	(/ (/ 1 N) N)
5.0ms	(/ 1/3 N)

series215.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ 1 N) (* (/ (/ 1 N) N) (- 1/2 (/ 1/3 N))))
130.0ms	(* (/ (/ 1 N) N) (- 1/2 (/ 1/3 N)))
20.0ms	(/ (/ 1 N) N)
23.0ms	(/ 1/3 N)

simplify1.9s

Counts

219 → 219

Iterations

Iter	Nodes
done	5003
2	2916
1	891
0	320

prune729.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

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

bsearch37.0ms

Steps

Iters	Range		Point
9	0.17679972651571432	94859.26993337883	7771.4619801305835

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample2.9s

Algorithm

intervals

Results

903.0ms	1742×	body	1280	valid
743.0ms	1273×	body	640	valid
458.0ms	7974×	body	80	nan
384.0ms	4057×	body	80	valid
116.0ms	606×	body	320	valid
39.0ms	322×	body	160	valid