Details

sample96.0ms

Algorithm

intervals

Results

33.0ms	62×	body	1280	valid
16.0ms	42×	body	640	valid
15.0ms	243×	body	80	nan
11.0ms	123×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize44.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (log (+ N 1)) (log N))
3.7b	(log (+ N 1))

rewrite20.0ms

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:

11.0ms	(- (log (+ N 1)) (log N))
8.0ms	(log (+ N 1))

series136.0ms

Counts

2 → 6

Calls

2 calls:

102.0ms	(- (log (+ N 1)) (log N))
34.0ms	(log (+ N 1))

simplify1.3s

Counts

49 → 49

Iterations

Iter	Nodes
4	2935
3	1181
2	416
1	194
0	97

prune473.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* N (* N N))
0.2b	(/ -1/2 (* N N))
0.6b	(/ 1/3 (* N (* N N)))
11.6b	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-cbrt-cube` `add-exp-log`
18×	`pow1`
16×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`times-frac` `associate-/l*`
5×	`cbrt-undiv` `div-exp` `pow-prod-up` `distribute-lft-out`
4×	`frac-add` `insert-posit16`
3×	`sum-log` `associate-l` `pow-prod-down` `div-inv`
2×	`clear-num` `associate-/r*` `frac-2neg` `flip3-+` `flip-+`
1×	`pow2` `+-commutative` `associate-+l+` `pow-plus` `cube-unmult` `associate-r` `pow-sqr` `*-commutative` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

27.0ms	(* N (* N N))
13.0ms	(/ -1/2 (* N N))
24.0ms	(/ 1/3 (* N (* N N)))
120.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N))))

series213.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* N (* N N))
50.0ms	(/ -1/2 (* N N))
72.0ms	(/ 1/3 (* N (* N N)))
46.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N))))

simplify5.5s

Counts

103 → 103

Iterations

Iter	Nodes
3	7916
2	1481
1	416
0	161

prune811.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

11.6b	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N))))
19.2b	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))
19.2b	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))
19.2b	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
20×	`distribute-lft-out`
18×	`cbrt-prod`
16×	`frac-add`
15×	`cbrt-div`
9×	`add-log-exp`
8×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `div-inv`
3×	`sum-log` `pow1/3`
1×	`+-commutative` `associate-+l+`

Counts

4 → 80

Calls

4 calls:

107.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N))))
64.0ms	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))
97.0ms	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))
66.0ms	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N))))
79.0ms	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))
83.0ms	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))
65.0ms	(cbrt (+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ 1/3 (* N (* N N)))))

simplify7.0s

Counts

92 → 92

Iterations

Iter	Nodes
3	8424
2	1399
1	345
0	138

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
2.4b	(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:

18.0ms	(/ (+ N 1) N)
4.0ms	(log (/ (+ N 1) N))

series157.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(/ (+ N 1) N)
63.0ms	(log (/ (+ N 1) N))

simplify3.3s

Counts

68 → 68

Iterations

Iter	Nodes
4	5391
3	1555
2	508
1	225
0	102

prune495.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.8b

bsearch56.0ms

Steps

Iters	Range		Point
9	3862.7483140020904	25612678030.77693	6613.323166361232

simplify3.0ms

Iterations

Iter	Nodes
2	23
1	23
0	19

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	1779×	body	1280	valid
588.0ms	7976×	body	80	nan
567.0ms	1289×	body	640	valid
383.0ms	4061×	body	80	valid
172.0ms	573×	body	320	valid
47.0ms	298×	body	160	valid