Details

sample101.0ms

Algorithm

intervals

Results

33.0ms	61×	body	1280	valid
17.0ms	49×	body	640	valid
15.0ms	282×	body	80	nan
11.0ms	123×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	6×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize13.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (log (+ N 1.0)) (log N))
3.1b	(log (+ N 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`add-sqr-sqrt` `pow1`
5×	`log-pow` `add-cube-cbrt`
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:

35.0ms	(- (log (+ N 1.0)) (log N))
4.0ms	(log (+ N 1.0))

series221.0ms

Counts

2 → 6

Calls

2 calls:

145.0ms	(- (log (+ N 1.0)) (log N))
76.0ms	(log (+ N 1.0))

simplify1.4s

Counts

47 → 47

Iterations

Iter	Nodes
done	5000
3	2789
2	645
1	213
0	101

prune224.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
0.1b	(/ (/ 0.3333333333333333 N) (* N N))
0.4b	(/ 0.5 (* N N))
16.1b	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
39×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`add-cbrt-cube` `add-exp-log`
20×	`add-cube-cbrt`
16×	`associate-/l*`
11×	`add-log-exp`
8×	`cbrt-undiv` `div-exp` `difference-of-squares`
6×	`frac-sub` `div-inv`
5×	`distribute-lft-out--`
4×	`pow1` `diff-log`
3×	`sub-neg` `flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`clear-num` `associate-/r*` `frac-2neg` `associate--r+` `sub-div`
1×	`distribute-rgt-out--` `associate--r-` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

101.0ms	(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
11.0ms	(/ (/ 0.3333333333333333 N) (* N N))
7.0ms	(/ 0.5 (* N N))
58.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (/ 1.0 N) (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
62.0ms	(/ (/ 0.3333333333333333 N) (* N N))
56.0ms	(/ 0.5 (* N N))
136.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	3082
1	602
0	223

prune568.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 0.3333333333333333 N) (* N N))
0.4b	(/ 0.5 (* N N))
12.8b	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
24×	`*-un-lft-identity`
20×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/l*`
8×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`div-inv`
3×	`pow1` `frac-add` `prod-exp` `cbrt-unprod`
2×	`associate-+l+` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `distribute-lft-out`
1×	`+-commutative` `sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `associate-+l-` `flip-+` `flip--` `distribute-lft-out--` `associate-/l/`

Counts

3 → 87

Calls

3 calls:

11.0ms	(/ (/ 0.3333333333333333 N) (* N N))
6.0ms	(/ 0.5 (* N N))
168.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ (/ 0.3333333333333333 N) (* N N)))

series163.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (/ 0.3333333333333333 N) (* N N))
36.0ms	(/ 0.5 (* N N))
47.0ms	(+ (- (/ 1.0 N) (/ 0.5 (* N N))) (/ (/ 0.3333333333333333 N) (* N N)))

simplify2.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	3122
1	542
0	193

prune481.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

15.6b	(sqrt (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
15.6b	(sqrt (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
16.1b	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))
16.1b	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`times-frac`
24×	`sqrt-prod` `difference-of-squares`
22×	`*-un-lft-identity`
8×	`sqrt-div` `div-inv` `distribute-lft-out--` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `distribute-rgt-out--` `add-exp-log` `frac-sub` `flip--` `sub-div`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 98

Calls

4 calls:

60.0ms	(sqrt (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
63.0ms	(sqrt (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
56.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))
43.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(sqrt (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
90.0ms	(sqrt (- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N))))
135.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))
142.0ms	(- (/ 0.5 (* N N)) (/ (/ 0.3333333333333333 N) (* N N)))

simplify1.1s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1091
1	273
0	125

prune812.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch43.0ms

Steps

Iters	Range		Point
7	1126.7541422477805	58098.925141855936	8023.454188180856

simplify5.0ms

Iterations

Iter	Nodes
done	19
1	19
0	17

end0.0ms

sample2.9s

Algorithm

intervals

Results

935.0ms	7994×	body	80	nan
827.0ms	1747×	body	1280	valid
337.0ms	1272×	body	640	valid
332.0ms	4055×	body	80	valid
106.0ms	624×	body	320	valid
32.0ms	302×	body	160	valid