Details

sample47.0ms

Algorithm

intervals

Results

15.0ms	60×	body	1280	valid
7.0ms	286×	body	80	nan
6.0ms	40×	body	640	valid
5.0ms	123×	body	80	valid
2.0ms	22×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.0b	(log (+ N 1.0))
3.3b	(- (log (+ N 1.0)) (log N))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

2.0ms	(log (+ N 1.0))
8.0ms	(- (log (+ N 1.0)) (log N))

series146.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
102.0ms	(- (log (+ N 1.0)) (log N))

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (439.0ms)

Iter	Nodes	Cost
0	127	1052
1	273	855
2	710	705
3	2289	614
done	5001	614

prune148.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
0.2b	(/ 0.5 (* N N))
0.5b	(/ 0.3333333333333333 (pow N 3))
12.0b	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

115×	`*-un-lft-identity`
82×	`times-frac`
60×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
35×	`prod-diff`
19×	`distribute-lft-out`
14×	`add-exp-log`
13×	`fma-def` `associate-/r*`
12×	`unpow-prod-down` `cube-prod`
11×	`add-cbrt-cube` `add-log-exp`
8×	`div-inv`
6×	`associate-/l*`
5×	`fma-neg` `div-exp`
4×	`pow1` `expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `sqr-pow`
3×	`cbrt-undiv` `frac-sub`
2×	`frac-2neg` `flip3-+` `diff-log` `frac-add` `clear-num` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `prod-exp` `associate--l+` `flip--` `cbrt-unprod`

Counts

4 → 182

Calls

4 calls:

34.0ms	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
3.0ms	(/ 0.5 (* N N))
4.0ms	(/ 0.3333333333333333 (pow N 3))
364.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series195.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
31.0ms	(/ 0.5 (* N N))
39.0ms	(/ 0.3333333333333333 (pow N 3))
34.0ms	(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify973.0ms

Counts

194 → 194

Iterations

Useful iterations: 2 (441.0ms)

Iter	Nodes	Cost
0	264	3729
1	606	3122
2	2136	2772
done	5000	2772

prune357.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.1b	(log (/ (+ N 1.0) N))

rewrite13.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series142.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ N 1.0) N)
92.0ms	(log (/ (+ N 1.0) N))

simplify1.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (416.0ms)

Iter	Nodes	Cost
0	112	749
1	240	708
2	618	660
3	1864	647
done	5000	647

prune277.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

2.0b	(log (+ N 1.0))
2.0b	(log (+ 1.0 N))
2.0b	(log (+ 1.0 N))
3.3b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

196×	`prod-diff`
140×	`unpow-prod-down` `cube-prod`
118×	`add-sqr-sqrt` `*-un-lft-identity`
94×	`add-cube-cbrt`
81×	`pow1`
77×	`log-pow`
37×	`sqr-pow`
29×	`cube-mult` `unpow3`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`log-prod`
7×	`add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 309

Calls

4 calls:

2.0ms	(log (+ N 1.0))
2.0ms	(log (+ 1.0 N))
3.0ms	(log (+ 1.0 N))
28.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

series350.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(log (+ N 1.0))
50.0ms	(log (+ 1.0 N))
44.0ms	(log (+ 1.0 N))
211.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

simplify898.0ms

Counts

321 → 321

Iterations

Useful iterations: 2 (322.0ms)

Iter	Nodes	Cost
0	349	11205
1	740	6382
2	2496	4930
done	5000	4930

prune422.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.5b

bsearch33.0ms

Steps

Iters	Range		Point
9	4368.076441928604	4102759194.3132896	7622.504121247211

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	25
1	20	25
done	20	25

end0.0ms

sample1.3s

Algorithm

intervals

Results

449.0ms	1747×	body	1280	valid
203.0ms	8031×	body	80	nan
200.0ms	1234×	body	640	valid
179.0ms	4072×	body	80	valid
64.0ms	612×	body	320	valid
22.0ms	335×	body	160	valid