Details

sample67.0ms

Algorithm

intervals

Results

26.0ms	71×	body	1280	valid
9.0ms	241×	body	80	nan
7.0ms	123×	body	80	valid
7.0ms	32×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 30.9b

localize7.0ms

Local error

Found 2 expressions with local error:

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

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:

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

series255.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(log (+ N 1.0))
177.0ms	(- (log (+ N 1.0)) (log N))

simplify3.0s

Counts

47 → 47

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	101	510
1	213	488
2	464	445
3	1067	443
4	2569	438
done	5000	426

prune155.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- 1.0 (/ 0.5 N)) N)
0.3b	(/ 0.3333333333333333 (pow N 3))
13.0b	(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

62×	`times-frac`
59×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
39×	`add-cube-cbrt`
15×	`associate-/r*`
12×	`unpow-prod-down` `cube-prod`
10×	`add-exp-log`
9×	`associate-/l*`
8×	`difference-of-squares`
7×	`add-cbrt-cube`
5×	`distribute-lft-out--` `add-log-exp`
4×	`cube-mult` `unpow3` `div-exp` `sqr-pow`
3×	`pow1` `distribute-lft-out`
2×	`cbrt-undiv` `frac-2neg` `div-sub` `clear-num` `div-inv` `associate-/l/`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `frac-add` `pow-exp` `sum-log` `flip--` `flip-+`

Counts

3 → 123

Calls

3 calls:

40.0ms	(/ (- 1.0 (/ 0.5 N)) N)
8.0ms	(/ 0.3333333333333333 (pow N 3))
141.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

series209.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(/ (- 1.0 (/ 0.5 N)) N)
59.0ms	(/ 0.3333333333333333 (pow N 3))
40.0ms	(+ (/ 0.3333333333333333 (pow N 3)) (/ (- 1.0 (/ 0.5 N)) N))

simplify977.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (313.0ms)

Iter	Nodes	Cost
0	203	1721
1	438	1521
2	1194	1426
done	5000	1426

prune427.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (log (cbrt (+ N 1.0))) (log N))
1.6b	(log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
1.6b	(log (cbrt (+ N 1.0)))
23.5b	(+ (log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))) (- (log (cbrt (+ N 1.0))) (log N)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

44×	`pow1`
41×	`*-un-lft-identity`
37×	`log-pow`
28×	`cbrt-div`
26×	`log-prod`
20×	`log-div`
18×	`distribute-lft-out`
16×	`distribute-lft-out--`
15×	`flip3-+` `flip-+`
14×	`associate--l+`
13×	`add-sqr-sqrt`
12×	`cbrt-prod`
11×	`add-cube-cbrt`
9×	`associate-+r+`
8×	`add-exp-log` `frac-times` `associate-+l-`
7×	`pow1/3` `pow-prod-down`
5×	`add-log-exp`
4×	`associate-r/` `associate-l/` `add-cbrt-cube`
3×	`rem-log-exp` `associate--r+`
2×	`associate--l-` `sub-neg` `diff-log` `sum-log` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+r-` `associate-+l+` `flip3--` `pow-plus` `prod-exp` `flip--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

28.0ms	(- (log (cbrt (+ N 1.0))) (log N))
34.0ms	(log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
11.0ms	(log (cbrt (+ N 1.0)))
201.0ms	(+ (log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))) (- (log (cbrt (+ N 1.0))) (log N)))

series1.0s

Counts

4 → 12

Calls

4 calls:

191.0ms	(- (log (cbrt (+ N 1.0))) (log N))
197.0ms	(log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))
193.0ms	(log (cbrt (+ N 1.0)))
450.0ms	(+ (log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))) (- (log (cbrt (+ N 1.0))) (log N)))

simplify3.1s

Counts

133 → 133

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	231	2242
1	536	2125
2	1261	1823
3	3979	1597
done	5001	1573

prune565.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes16.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.8b

bsearch40.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	10223.09734470724

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	36
1	25	36
done	25	36

end0.0ms

sample3.0s

Algorithm

intervals

Results

827.0ms	1180×	body	640	valid
760.0ms	1731×	body	1280	valid
570.0ms	8200×	body	80	nan
332.0ms	4111×	body	80	valid
127.0ms	679×	body	320	valid
35.0ms	299×	body	160	valid