Details

sample50.0ms

Algorithm

intervals

Results

17.0ms	63×	body	1280	valid
7.0ms	42×	body	640	valid
6.0ms	198×	body	80	nan
6.0ms	121×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(log (+ N 1.0))
2.6b	(- (log (+ N 1.0)) (log N))

rewrite19.0ms

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:

5.0ms	(log (+ N 1.0))
13.0ms	(- (log (+ N 1.0)) (log N))

series175.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(log (+ N 1.0))
126.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Counts: 47 → 47

prune113.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.0b	(- (/ 0.3333333333333333 N) 0.5)
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.3b	(/ 1 (pow N 2))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

34.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
21.0ms	(- (/ 0.3333333333333333 N) 0.5)
74.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
9.0ms	(/ 1 (pow N 2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
47.0ms	(- (/ 0.3333333333333333 N) 0.5)
84.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
22.0ms	(/ 1 (pow N 2))

simplify75.0ms

Counts: 177 → 177

prune618.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(log (/ (+ N 1.0) N))

rewrite28.0ms

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:

19.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series156.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (+ N 1.0) N)
94.0ms	(log (/ (+ N 1.0) N))

simplify99.0ms

Counts: 66 → 66

prune114.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
1.6b	(log (+ N 1.0))
23.0b	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `associate--l+`
9×	`cbrt-prod`
6×	`pow1` `associate--r+` `add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`diff-log`
2×	`sub-neg` `log-div` `pow1/3` `log-pow` `distribute-lft-out` `distribute-lft-out--`
1×	`associate--l-` `flip3--` `flip3-+` `rem-log-exp` `flip--` `flip-+` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
5.0ms	(log (+ N 1.0))
53.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(cbrt N)
220.0ms	(cbrt N)
44.0ms	(log (+ N 1.0))
108.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

simplify140.0ms

Counts: 78 → 78

prune210.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.9b

bsearch33.0ms

Steps

Iters	Range		Point
9	5.295671684036253	137362616.0762091	9454.187458193412

simplify1.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

538.0ms	1810×	body	1280	valid
427.0ms	8006×	body	80	nan
230.0ms	3991×	body	80	valid
222.0ms	1244×	body	640	valid
110.0ms	648×	body	320	valid
24.0ms	307×	body	160	valid