Details

sample70.0ms

Algorithm

intervals

Results

23.0ms	58×	body	1280	valid
13.0ms	277×	body	80	nan
10.0ms	39×	body	640	valid
10.0ms	134×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize17.0ms

Local error

Found 2 expressions with local error:

2.5b	(log (+ N 1))
2.8b	(- (log (+ N 1)) (log N))

rewrite15.0ms

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-+` `insert-posit16` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

3.0ms	(log (+ N 1))
11.0ms	(- (log (+ N 1)) (log N))

series114.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1))
75.0ms	(- (log (+ N 1)) (log N))

simplify1.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	2006
4	2006
3	1350
2	463
1	199
0	97

prune184.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1) N)
3.0b	(log (/ (+ N 1) N))

rewrite21.0ms

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` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `flip3-+` `log-pow` `flip-+`

Counts

2 → 62

Calls

2 calls:

15.0ms	(/ (+ N 1) N)
4.0ms	(log (/ (+ N 1) N))

series116.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (+ N 1) N)
54.0ms	(log (/ (+ N 1) N))

simplify813.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	2000
3	2000
2	620
1	233
0	102

prune221.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.3b	(/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))
3.0b	(+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (cbrt (+ N 1)) (sqrt N))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
56×	`log-prod`
54×	`times-frac`
46×	`associate-+r+`
40×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`cbrt-prod`
30×	`sqrt-prod`
16×	`cbrt-div`
12×	`distribute-lft-out`
10×	`associate-+l+`
9×	`flip3-+` `add-exp-log` `flip-+`
8×	`pow1` `associate-/l/`
7×	`add-cbrt-cube`
6×	`associate-/r*`
4×	`frac-times` `log-pow` `insert-posit16` `add-log-exp`
3×	`div-inv`
2×	`cbrt-undiv` `log-div` `pow1/3` `div-exp` `associate-l/` `associate-r/`
1×	`+-commutative` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `prod-exp` `associate-+l-` `cbrt-unprod` `associate-/l*`

Counts

4 → 140

Calls

4 calls:

5.0ms	(cbrt (+ N 1))
9.0ms	(cbrt (+ N 1))
29.0ms	(/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))
77.0ms	(+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (cbrt (+ N 1)) (sqrt N))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cbrt (+ N 1))
60.0ms	(cbrt (+ N 1))
139.0ms	(/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))
344.0ms	(+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (cbrt (+ N 1)) (sqrt N))))

simplify1.2s

Counts

152 → 152

Iterations

Iter	Nodes
done	2002
2	2002
1	759
0	314

prune768.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt N))
0.6b	(cbrt (sqrt N))
0.6b	(cbrt (sqrt N))
23.7b	(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1)))) (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (cbrt (+ N 1))) (cbrt (sqrt N)))))

rewrite527.0ms

Algorithm

rewrite-expression-head

Rules

177×	`cbrt-prod`
101×	`*-un-lft-identity`
94×	`associate-+r+` `log-prod`
90×	`times-frac`
68×	`add-sqr-sqrt` `add-cube-cbrt`
39×	`sqrt-prod`
27×	`distribute-lft-out`
17×	`pow1`
13×	`log-pow`
5×	`add-log-exp`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`log-div` `sum-log` `pow1/3` `associate-+l-`
2×	`associate-+r-`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+` `div-inv`

Counts

4 → 166

Calls

4 calls:

2.0ms	(cbrt (sqrt N))
2.0ms	(cbrt (sqrt N))
2.0ms	(cbrt (sqrt N))
514.0ms	(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1)))) (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (cbrt (+ N 1))) (cbrt (sqrt N)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (sqrt N))
238.0ms	(cbrt (sqrt N))
275.0ms	(cbrt (sqrt N))
536.0ms	(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ (* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1)))) (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (cbrt (+ N 1))) (cbrt (sqrt N)))))

simplify1.2s

Counts

178 → 178

Iterations

Iter	Nodes
done	2000
2	2000
1	944
0	371

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch32.0ms

Steps

Iters	Range		Point
6	3231.8276777318033	48819.349325626084	8810.738870329447

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

874.0ms	1701×	body	1280	valid
856.0ms	1268×	body	640	valid
573.0ms	8141×	body	80	nan
369.0ms	4106×	body	80	valid
177.0ms	627×	body	320	valid
41.0ms	298×	body	160	valid