Details

sample76.0ms

Algorithm

intervals

Results

24.0ms	56×	body	1280	valid
11.0ms	251×	body	80	nan
10.0ms	134×	body	80	valid
8.0ms	35×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize8.0ms

Local error

Found 2 expressions with local error:

3.4b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite42.0ms

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:

33.0ms	(- (log (+ N 1.0)) (log N))
7.0ms	(log (+ N 1.0))

series173.0ms

Counts

2 → 6

Calls

2 calls:

117.0ms	(- (log (+ N 1.0)) (log N))
55.0ms	(log (+ N 1.0))

simplify94.0ms

Counts: 47 → 47

prune151.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite73.0ms

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:

58.0ms	(/ (+ N 1.0) N)
11.0ms	(log (/ (+ N 1.0) N))

series215.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (+ N 1.0) N)
142.0ms	(log (/ (+ N 1.0) N))

simplify72.0ms

Counts: 66 → 66

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
0.2b	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
3.3b	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-prod`
114×	`*-un-lft-identity`
94×	`add-sqr-sqrt`
92×	`times-frac`
60×	`add-cube-cbrt`
37×	`pow1`
27×	`swap-sqr`
24×	`distribute-lft-out`
19×	`associate-r` `associate-l`
18×	`sqrt-pow1` `pow1/2`
14×	`log-pow`
10×	`sqrt-div` `pow-prod-up`
9×	`add-exp-log` `unswap-sqr`
6×	`pow-prod-down` `pow-sqr` `add-cbrt-cube` `div-inv`
4×	`rem-sqrt-square` `add-log-exp`
3×	`log-div`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `rem-log-exp` `associate-l/` `prod-exp`
1×	`log-prod` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 185

Calls

4 calls:

10.0ms	(sqrt (/ (+ N 1.0) N))
11.0ms	(sqrt (/ (+ N 1.0) N))
59.0ms	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
21.0ms	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (/ (+ N 1.0) N))
70.0ms	(sqrt (/ (+ N 1.0) N))
145.0ms	(* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)))
138.0ms	(log (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))))

simplify98.0ms

Counts: 197 → 197

prune584.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (log (+ N 1.0)) (log N)))
0.8b	(exp (log (- (log (+ N 1.0)) (log N))))
3.4b	(- (log (+ N 1.0)) (log N))
3.5b	(log (+ N 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
26×	`*-un-lft-identity`
19×	`pow1`
16×	`add-sqr-sqrt`
15×	`log-pow`
12×	`distribute-lft-out--`
10×	`add-cube-cbrt`
8×	`log-div` `exp-sum`
6×	`add-exp-log`
4×	`exp-prod` `associate--l+` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `flip--` `associate--r+` `difference-of-squares`
2×	`associate--l-` `flip3-+` `exp-diff` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`sub-neg` `diff-log` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

13.0ms	(log (- (log (+ N 1.0)) (log N)))
16.0ms	(exp (log (- (log (+ N 1.0)) (log N))))
12.0ms	(- (log (+ N 1.0)) (log N))
5.0ms	(log (+ N 1.0))

series604.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(log (- (log (+ N 1.0)) (log N)))
194.0ms	(exp (log (- (log (+ N 1.0)) (log N))))
133.0ms	(- (log (+ N 1.0)) (log N))
70.0ms	(log (+ N 1.0))

simplify79.0ms

Counts: 94 → 94

prune240.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.4b

bsearch5.0ms

simplify129.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	1770×	body	1280	valid
481.0ms	8028×	body	80	nan
346.0ms	1309×	body	640	valid
329.0ms	4092×	body	80	valid
97.0ms	563×	body	320	valid
28.0ms	266×	body	160	valid