Details

sample47.0ms

Algorithm

intervals

Results

13.0ms	57×	body	1280	valid
8.0ms	239×	body	80	nan
6.0ms	40×	body	640	valid
5.0ms	128×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(log (+ N 1.0))
3.3b	(- (log (+ N 1.0)) (log N))

rewrite21.0ms

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:

4.0ms	(log (+ N 1.0))
15.0ms	(- (log (+ N 1.0)) (log N))

series135.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(log (+ N 1.0))
91.0ms	(- (log (+ N 1.0)) (log N))

simplify121.0ms

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343
done	5001	343

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.5b	(log (/ (+ N 1.0) N))

rewrite28.0ms

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:

18.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series128.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ N 1.0) N)
77.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344
done	5001	344

prune119.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (sqrt (+ N 1.0)) N))
0.2b	(/ (sqrt (+ N 1.0)) N)
2.2b	(log (sqrt (+ N 1.0)))
3.2b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

81×	`*-un-lft-identity`
64×	`log-prod`
63×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-+r+`
16×	`distribute-lft-out`
13×	`pow1`
11×	`log-pow`
10×	`add-exp-log`
7×	`associate-+l+` `associate-/l*`
6×	`log-div` `fma-def` `sqrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp` `associate-/r*` `div-inv`
2×	`associate-+l-` `sqrt-pow1` `pow1/2` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 165

Calls

4 calls:

7.0ms	(log (/ (sqrt (+ N 1.0)) N))
15.0ms	(/ (sqrt (+ N 1.0)) N)
5.0ms	(log (sqrt (+ N 1.0)))
27.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(log (/ (sqrt (+ N 1.0)) N))
71.0ms	(/ (sqrt (+ N 1.0)) N)
80.0ms	(log (sqrt (+ N 1.0)))
229.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify48.0ms

Counts

177 → 177

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	528	1419
1	1596	1318
2	5002	1212
done	5002	1212

prune383.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (sqrt (+ N 1.0)))
3.2b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
3.2b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
3.2b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

103×	`log-prod`
95×	`*-un-lft-identity`
75×	`associate-+r+`
63×	`times-frac`
57×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`sqrt-prod`
25×	`distribute-lft-out`
24×	`pow1` `log-pow`
21×	`associate-+l+`
18×	`fma-def`
11×	`log-div`
8×	`sqrt-div`
7×	`flip3-+` `flip-+`
6×	`associate-+l-`
5×	`add-exp-log`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`+-commutative` `associate-+r-` `sum-log` `div-inv`
1×	`rem-log-exp`

Counts

4 → 196

Calls

4 calls:

6.0ms	(log (sqrt (+ N 1.0)))
26.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
23.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
27.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(log (sqrt (+ N 1.0)))
234.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
235.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
228.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify114.0ms

Counts

208 → 208

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	394	1878
1	1097	1715
2	4332	1476
3	5001	1447
done	5001	1447

prune637.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch29.0ms

Steps

Iters	Range		Point
9	51.26549425761527	15794870057.515802	9256.9590468846

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9
done	21	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

408.0ms	1730×	body	1280	valid
179.0ms	7837×	body	80	nan
174.0ms	1215×	body	640	valid
164.0ms	4129×	body	80	valid
60.0ms	614×	body	320	valid
18.0ms	312×	body	160	valid