Details

sample88.0ms

Algorithm

intervals

Results

27.0ms	55×	body	1280	valid
14.0ms	43×	body	640	valid
13.0ms	255×	body	80	nan
11.0ms	134×	body	80	valid
3.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify14.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize8.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1.0)) (log N))
3.6b	(log (+ N 1.0))

rewrite35.0ms

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:

24.0ms	(- (log (+ N 1.0)) (log N))
9.0ms	(log (+ N 1.0))

series244.0ms

Counts

2 → 6

Calls

2 calls:

172.0ms	(- (log (+ N 1.0)) (log N))
73.0ms	(log (+ N 1.0))

simplify804.0ms

Counts: 47 → 47

prune207.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.3b	(log (/ (+ N 1.0) N))

rewrite49.0ms

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:

35.0ms	(/ (+ N 1.0) N)
12.0ms	(log (/ (+ N 1.0) N))

series220.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(/ (+ N 1.0) N)
144.0ms	(log (/ (+ N 1.0) N))

simplify1.1s

Counts: 66 → 66

prune198.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (log (+ N 1.0)) (log N))
3.6b	(log (+ N 1.0))

rewrite43.0ms

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:

31.0ms	(- (log (+ N 1.0)) (log N))
9.0ms	(log (+ N 1.0))

series237.0ms

Counts

2 → 6

Calls

2 calls:

161.0ms	(- (log (+ N 1.0)) (log N))
76.0ms	(log (+ N 1.0))

simplify772.0ms

Counts: 47 → 47

prune128.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ N 1.0)) N)
0.2b	(log (/ (sqrt (+ N 1.0)) N))
2.7b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
3.4b	(log (sqrt (+ N 1.0)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

80×	`*-un-lft-identity`
64×	`log-prod`
63×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-+r+`
16×	`distribute-lft-out`
11×	`pow1`
10×	`add-exp-log`
8×	`log-pow`
7×	`associate-+l+` `associate-/l*`
6×	`log-div` `sqrt-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-log-exp` `associate-/r*` `div-inv`
2×	`associate-+l-` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log`

Counts

4 → 151

Calls

4 calls:

32.0ms	(/ (sqrt (+ N 1.0)) N)
22.0ms	(log (/ (sqrt (+ N 1.0)) N))
46.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
11.0ms	(log (sqrt (+ N 1.0)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sqrt (+ N 1.0)) N)
223.0ms	(log (/ (sqrt (+ N 1.0)) N))
328.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
100.0ms	(log (sqrt (+ N 1.0)))

simplify817.0ms

Counts: 163 → 163

prune568.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

100% (0.0b remaining)

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

bsearch80.0ms

Steps

Iters	Range		Point
9	555.6593536559827	1008309312.7880352	8226.710483527566

simplify703.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

799.0ms	1784×	body	1280	valid
471.0ms	7985×	body	80	nan
328.0ms	4114×	body	80	valid
317.0ms	1224×	body	640	valid
147.0ms	606×	body	320	valid
29.0ms	272×	body	160	valid