Details

sample58.0ms

Algorithm

intervals

Results

17.0ms	55×	body	1280	valid
9.0ms	51×	body	640	valid
8.0ms	271×	body	80	nan
7.0ms	125×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	7×	body	160	valid

simplify1.0ms

Counts: 1 → 1

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize17.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (log (+ N 1.0)) (log N))
3.6b	(log (+ N 1.0))

rewrite26.0ms

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:

13.0ms	(- (log (+ N 1.0)) (log N))
12.0ms	(log (+ N 1.0))

series236.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(- (log (+ N 1.0)) (log N))
63.0ms	(log (+ N 1.0))

simplify91.0ms

Counts: 47 → 47

prune169.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.6b	(/ 1 (pow N 2))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 150

Calls

3 calls:

67.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
82.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
13.0ms	(/ 1 (pow N 2))

series197.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
127.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
34.0ms	(/ 1 (pow N 2))

simplify66.0ms

Counts: 159 → 159

prune565.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (pow N 2))
0.6b	(/ 1 (pow N 2))
8.3b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
8.3b	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
22×	`add-exp-log`
16×	`associate-/r*`
14×	`sqrt-div`
12×	`div-exp`
10×	`frac-add`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `sqrt-prod` `associate-/l*`
4×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*l/` `clear-num` `flip-+` `div-inv` `inv-pow`

Counts

4 → 154

Calls

4 calls:

20.0ms	(/ 1 (pow N 2))
17.0ms	(/ 1 (pow N 2))
82.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
102.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (pow N 2))
20.0ms	(/ 1 (pow N 2))
69.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
90.0ms	(sqrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify59.0ms

Counts: 166 → 166

prune713.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.1b	(log (/ (+ N 1.0) N))

rewrite33.0ms

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` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

25.0ms	(/ (+ N 1.0) N)
7.0ms	(log (/ (+ N 1.0) N))

series180.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (+ N 1.0) N)
114.0ms	(log (/ (+ N 1.0) N))

simplify49.0ms

Counts: 66 → 66

prune169.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch29.0ms

Steps

Iters	Range		Point
8	101.2523499030379	32504.544960343763	8716.005511358959

simplify185.0ms

end0.0ms

sample2.6s

Algorithm

intervals

Results

885.0ms	1715×	body	1280	valid
399.0ms	8052×	body	80	nan
375.0ms	1258×	body	640	valid
373.0ms	4027×	body	80	valid
117.0ms	683×	body	320	valid
34.0ms	317×	body	160	valid