Details

sample109.0ms

Algorithm

intervals

Results

44.0ms	65×	body	1280	valid
16.0ms	213×	body	80	nan
16.0ms	134×	body	80	valid
13.0ms	30×	body	640	valid
7.0ms	24×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize24.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (log (+ N 1)) (log N))
2.5b	(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))

series97.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(- (log (+ N 1)) (log N))
31.0ms	(log (+ N 1))

simplify791.0ms

Counts

49 → 49

Iterations

Iter	Nodes
done	2004
3	1329
2	452
1	200
0	97

prune657.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (cbrt (* (* (log (+ N 1)) (log (+ N 1))) (log (+ N 1)))) (log N))
2.5b	(log (+ N 1))
2.5b	(log (+ N 1))
2.5b	(log (+ N 1))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`log-prod`
10×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt`
7×	`add-exp-log`
6×	`log-div`
5×	`add-log-exp`
4×	`add-cbrt-cube` `log-pow` `insert-posit16`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out` `associate--r+`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

12.0ms	(- (cbrt (* (* (log (+ N 1)) (log (+ N 1))) (log (+ N 1)))) (log N))
3.0ms	(log (+ N 1))
4.0ms	(log (+ N 1))
9.0ms	(log (+ N 1))

series172.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (cbrt (* (* (log (+ N 1)) (log (+ N 1))) (log (+ N 1)))) (log N))
46.0ms	(log (+ N 1))
33.0ms	(log (+ N 1))
26.0ms	(log (+ N 1))

simplify892.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	2019
3	1419
2	458
1	198
0	97

prune358.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1/3 (* (* N N) N))
0.3b	(- (/ 1 N) (/ 1/2 (* N N)))
0.6b	(/ 1/2 (* N N))
12.4b	(+ (/ 1/3 (* (* N N) N)) (- (/ 1 N) (/ 1/2 (* N N))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cbrt-cube` `add-exp-log`
13×	`times-frac`
11×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-/l*` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `distribute-lft-out--`
3×	`frac-add` `distribute-lft-out`
2×	`associate-+r+` `clear-num` `associate-/r*` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `frac-sub` `flip--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 90

Calls

4 calls:

28.0ms	(/ 1/3 (* (* N N) N))
14.0ms	(- (/ 1 N) (/ 1/2 (* N N)))
6.0ms	(/ 1/2 (* N N))
70.0ms	(+ (/ 1/3 (* (* N N) N)) (- (/ 1 N) (/ 1/2 (* N N))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1/3 (* (* N N) N))
82.0ms	(- (/ 1 N) (/ 1/2 (* N N)))
37.0ms	(/ 1/2 (* N N))
33.0ms	(+ (/ 1/3 (* (* N N) N)) (- (/ 1 N) (/ 1/2 (* N N))))

simplify980.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	2036
2	1629
1	449
0	168

prune331.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1/2 (* N N))
12.4b	(+ (/ 1/3 (* (* N N) N)) (* (+ (sqrt (/ 1 N)) (sqrt (/ 1/2 (* N N)))) (- (sqrt (/ 1 N)) (sqrt (/ 1/2 (* N N))))))
29.8b	(sqrt (/ 1/2 (* N N)))
29.8b	(sqrt (/ 1/2 (* N N)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

19×	`frac-add`
18×	`sqrt-div`
14×	`add-sqr-sqrt` `sqrt-prod`
11×	`times-frac`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`frac-times` `add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`rem-sqrt-square` `associate-+r+` `flip3--` `frac-sub` `insert-posit16` `flip--`
3×	`associate-l/` `associate-r/` `div-inv` `associate-/l*`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `div-exp`
1×	`+-commutative` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

11.0ms	(/ 1/2 (* N N))
63.0ms	(+ (/ 1/3 (* (* N N) N)) (* (+ (sqrt (/ 1 N)) (sqrt (/ 1/2 (* N N)))) (- (sqrt (/ 1 N)) (sqrt (/ 1/2 (* N N))))))
5.0ms	(sqrt (/ 1/2 (* N N)))
5.0ms	(sqrt (/ 1/2 (* N N)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1/2 (* N N))
95.0ms	(+ (/ 1/3 (* (* N N) N)) (* (+ (sqrt (/ 1 N)) (sqrt (/ 1/2 (* N N)))) (- (sqrt (/ 1 N)) (sqrt (/ 1/2 (* N N))))))
74.0ms	(sqrt (/ 1/2 (* N N)))
67.0ms	(sqrt (/ 1/2 (* N N)))

simplify641.0ms

Counts

105 → 105

Iterations

Iter	Nodes
done	2000
1	668
0	218

prune474.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.3b

bsearch54.0ms

Steps

Iters	Range		Point
8	0.5242927222148749	9969.609054971397	5567.039381079165

simplify5.0ms

Iterations

Iter	Nodes
done	27
1	27
0	21

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	1780×	body	1280	valid
565.0ms	7964×	body	80	nan
481.0ms	1187×	body	640	valid
424.0ms	4113×	body	80	valid
218.0ms	628×	body	320	valid
52.0ms	292×	body	160	valid