Details

sample78.0ms

Algorithm

intervals

Results

20.0ms	54×	body	1280	valid
11.0ms	11×	body	160	valid
11.0ms	209×	body	80	nan
10.0ms	36×	body	640	valid
10.0ms	137×	body	80	valid
3.0ms	18×	body	320	valid

simplify22.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize25.0ms

Local error

Found 2 expressions with local error:

3.0b	(- (log (+ N 1)) (log N))
2.4b	(log (+ N 1))

rewrite24.0ms

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:

Slowest

17.0ms	(- (log (+ N 1)) (log N))
6.0ms	(log (+ N 1))

series551.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

521.0ms	(- (log (+ N 1)) (log N))
30.0ms	(log (+ N 1))

simplify345.0ms

Counts: 57 → 49

prune387.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

3.1b	(log (/ (+ 1 N) N))
0.0b	(/ (+ 1 N) N)

rewrite17.0ms

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:

Slowest

13.0ms	(/ (+ 1 N) N)
3.0ms	(log (/ (+ 1 N) N))

series148.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

86.0ms	(/ (+ 1 N) N)
61.0ms	(log (/ (+ 1 N) N))

simplify503.0ms

Counts: 96 → 68

prune443.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (/ (+ 1 N) N))
3.1b	(log (/ (+ 1 N) N))
0.3b	(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
0.1b	(sqrt (log (/ (+ 1 N) N)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
32×	`log-prod`
30×	`sqrt-prod`
29×	`pow1` `add-cube-cbrt`
24×	`times-frac`
12×	`add-exp-log`
11×	`swap-sqr`
9×	`sqrt-pow1` `pow1/2` `log-pow`
7×	`associate-r` `associate-l`
6×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-up`
4×	`rem-log-exp` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`log-div` `div-exp` `div-inv`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

Slowest

12.0ms	(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
7.0ms	(log (/ (+ 1 N) N))
3.0ms	(log (/ (+ 1 N) N))
2.0ms	(sqrt (log (/ (+ 1 N) N)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(sqrt (log (/ (+ 1 N) N)))
65.0ms	(log (/ (+ 1 N) N))
55.0ms	(log (/ (+ 1 N) N))
53.0ms	(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))

simplify659.0ms

Counts: 182 → 138

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

13.6b	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 N) (* N N)))
0.4b	(/ 1/3 N)
0.4b	(/ -1/2 (* N N))
0.1b	(/ (/ 1/3 N) (* N N))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
35×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
19×	`associate-/l*`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
6×	`div-inv`
5×	`associate-/r*` `distribute-lft-out`
4×	`pow1` `frac-add` `insert-posit16`
3×	`clear-num` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `flip-+`
1×	`+-commutative` `associate-+l+` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

Slowest

112.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 N) (* N N)))
10.0ms	(/ (/ 1/3 N) (* N N))
7.0ms	(/ -1/2 (* N N))
4.0ms	(/ 1/3 N)

series153.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

48.0ms	(/ (/ 1/3 N) (* N N))
41.0ms	(+ (+ (/ 1 N) (/ -1/2 (* N N))) (/ (/ 1/3 N) (* N N)))
37.0ms	(/ -1/2 (* N N))
26.0ms	(/ 1/3 N)

simplify719.0ms

Counts: 161 → 129

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes59.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch48.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	7809×	body	80	nan
966.0ms	1684×	body	1280	valid
467.0ms	1275×	body	640	valid
456.0ms	4113×	body	80	valid
182.0ms	619×	body	320	valid
48.0ms	309×	body	160	valid