Details

sample87.0ms

Algorithm

intervals

Results

27.0ms	55×	body	1280	valid
12.0ms	225×	body	80	nan
11.0ms	133×	body	80	valid
11.0ms	34×	body	640	valid
5.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.0ms

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: 28.6b

localize17.0ms

Local error

Found 2 expressions with local error:

1.8b	(log (+ N 1.0))
2.8b	(- (log (+ N 1.0)) (log N))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `pow1` `prod-diff`
14×	`log-pow` `add-cube-cbrt`
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:

8.0ms	(log (+ N 1.0))
30.0ms	(- (log (+ N 1.0)) (log N))

series224.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(log (+ N 1.0))
170.0ms	(- (log (+ N 1.0)) (log N))

simplify2.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
3	2040
2	708
1	286
0	127

prune303.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 N) N)
3.4b	(log (/ (+ 1.0 N) N))

rewrite41.0ms

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

Counts

2 → 64

Calls

2 calls:

28.0ms	(/ (+ 1.0 N) N)
9.0ms	(log (/ (+ 1.0 N) N))

series176.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (+ 1.0 N) N)
117.0ms	(log (/ (+ 1.0 N) N))

simplify1.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	2267
2	632
1	249
0	111

prune344.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (sqrt N))
0.4b	(/ (+ 1.0 N) (sqrt N))
3.0b	(+ (- (log (sqrt N))) (log (/ (+ 1.0 N) (sqrt N))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
48×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`log-prod`
33×	`sqrt-prod`
28×	`associate-+r+`
19×	`distribute-lft-out`
16×	`fma-def`
14×	`pow1` `log-pow`
10×	`distribute-rgt-neg-in`
6×	`distribute-lft-neg-in` `associate-+l+` `distribute-neg-in` `associate-/r*` `add-exp-log`
5×	`add-cbrt-cube`
4×	`associate-/l*` `add-log-exp`
3×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `log1p-expm1-u`
2×	`sum-log` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `log-div` `clear-num` `associate-+r-` `neg-mul-1` `frac-2neg` `div-exp` `rem-log-exp` `neg-log` `associate-+l-`

Counts

3 → 141

Calls

3 calls:

2.0ms	(log (sqrt N))
26.0ms	(/ (+ 1.0 N) (sqrt N))
37.0ms	(+ (- (log (sqrt N))) (log (/ (+ 1.0 N) (sqrt N))))

series400.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(log (sqrt N))
70.0ms	(/ (+ 1.0 N) (sqrt N))
243.0ms	(+ (- (log (sqrt N))) (log (/ (+ 1.0 N) (sqrt N))))

simplify1.3s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1369
1	487
0	205

prune777.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (+ 1.0 N) (sqrt N)))
0.5b	(cbrt (/ (+ 1.0 N) (sqrt N)))
0.5b	(* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N))))
3.0b	(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N)))) (cbrt (/ (+ 1.0 N) (sqrt N))))))

rewrite460.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
240×	`cbrt-prod`
208×	`times-frac`
187×	`add-sqr-sqrt`
115×	`add-cube-cbrt`
107×	`sqrt-prod`
68×	`distribute-lft-out`
55×	`swap-sqr`
37×	`pow1`
31×	`associate-r` `associate-l`
19×	`log-pow`
18×	`cbrt-div`
16×	`fma-def` `unswap-sqr`
14×	`distribute-rgt-neg-in`
11×	`pow-prod-down`
8×	`pow1/3`
7×	`log-div` `log-prod` `associate-+r-`
6×	`distribute-lft-neg-in` `frac-times` `associate-+l+` `distribute-neg-in` `associate-*l/` `add-exp-log` `div-inv`
5×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `associate-*r/` `log1p-expm1-u`
2×	`sum-log` `sqrt-pow1` `pow1/2` `pow-sqr` `pow-prod-up`
1×	`pow2` `neg-sub0` `+-commutative` `associate-+r+` `neg-mul-1` `flip3-+` `pow-plus` `neg-log` `prod-exp` `*-commutative` `associate-+l-` `cbrt-unprod` `flip-+`

Counts

4 → 291

Calls

4 calls:

6.0ms	(cbrt (/ (+ 1.0 N) (sqrt N)))
6.0ms	(cbrt (/ (+ 1.0 N) (sqrt N)))
79.0ms	(* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N))))
346.0ms	(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N)))) (cbrt (/ (+ 1.0 N) (sqrt N))))))

series846.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (/ (+ 1.0 N) (sqrt N)))
174.0ms	(cbrt (/ (+ 1.0 N) (sqrt N)))
203.0ms	(* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N))))
284.0ms	(+ (- (log (sqrt N))) (log (* (* (cbrt (/ (+ 1.0 N) (sqrt N))) (cbrt (/ (+ 1.0 N) (sqrt N)))) (cbrt (/ (+ 1.0 N) (sqrt N))))))

simplify1.9s

Counts

303 → 303

Iterations

Iter	Nodes
done	5001
2	1845
1	733
0	337

prune1.6s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes84.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch47.0ms

Steps

Iters	Range		Point
7	44.35744796693956	8445.545519380286	7951.823313362933

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample2.8s

Algorithm

intervals

Results

848.0ms	1761×	body	1280	valid
755.0ms	7962×	body	80	nan
374.0ms	1264×	body	640	valid
321.0ms	4041×	body	80	valid
145.0ms	624×	body	320	valid
35.0ms	310×	body	160	valid