Details

sample93.0ms

Algorithm

intervals

Results

25.0ms	46×	body	640	valid
24.0ms	51×	body	1280	valid
13.0ms	248×	body	80	nan
11.0ms	132×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	7×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	6

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize13.0ms

Local error

Found 1 expressions with local error:

1.9b	(- (log1p N) (log N))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
5×	`pow1`
4×	`log-pow`
3×	`log-prod` `fma-neg` `associate--r+`
2×	`diff-log` `distribute-lft-out--` `add-log-exp`
1×	`expm1-log1p-u` `log1p-udef` `sub-neg` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `difference-of-squares`

Counts

1 → 37

Calls

1 calls:

9.0ms

(- (log1p N) (log N))

series91.0ms

Counts

1 → 3

Calls

1 calls:

91.0ms

(- (log1p N) (log N))

simplify2.8s

Counts

40 → 40

Iterations

Iter	Nodes
done	5000
4	4052
3	1137
2	403
1	185
0	83

prune109.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1 N) N)
1.9b	(log (/ (+ 1 N) N))

rewrite37.0ms

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` `insert-posit16` `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 → 66

Calls

2 calls:

29.0ms	(/ (+ 1 N) N)
6.0ms	(log (/ (+ 1 N) N))

series133.0ms

Counts

2 → 6

Calls

2 calls:

90.0ms	(/ (+ 1 N) N)
43.0ms	(log (/ (+ 1 N) N))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5052
3	2586
2	583
1	244
0	106

prune256.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 N))
0.1b	(/ (sqrt (+ 1 N)) N)
2.2b	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
2.7b	(log (sqrt (+ 1 N)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
42×	`times-frac`
40×	`add-cube-cbrt` `sqrt-prod`
39×	`log-prod`
25×	`associate-+r+`
14×	`distribute-lft-out`
13×	`pow1`
10×	`log-pow`
8×	`sqrt-div`
7×	`associate-+l+` `add-exp-log` `associate-/l*`
6×	`fma-def` `add-cbrt-cube`
5×	`log-div` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `sqrt-pow1` `pow1/2`
2×	`associate-+l-` `hypot-def` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `div-exp` `rem-log-exp` `hypot-1-def`

Counts

4 → 152

Calls

4 calls:

7.0ms	(sqrt (+ 1 N))
21.0ms	(/ (sqrt (+ 1 N)) N)
49.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
11.0ms	(log (sqrt (+ 1 N)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ 1 N))
75.0ms	(/ (sqrt (+ 1 N)) N)
242.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
73.0ms	(log (sqrt (+ 1 N)))

simplify3.0s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
3	4811
2	1236
1	478
0	223

prune567.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

2.2b	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
2.7b	(log (sqrt (+ 1 N)))
2.7b	(log (sqrt (+ 1 N)))
2.7b	(log (sqrt (+ 1 N)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

53×	`log-prod`
45×	`*-un-lft-identity`
28×	`sqrt-prod`
27×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-+r+`
21×	`times-frac`
16×	`pow1` `log-pow`
11×	`distribute-lft-out`
9×	`log-div`
8×	`sqrt-div`
7×	`associate-+l+` `add-exp-log`
6×	`fma-def`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`associate-+l-`
1×	`+-commutative` `associate-+r-` `sum-log` `div-inv`

Counts

4 → 128

Calls

4 calls:

50.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
10.0ms	(log (sqrt (+ 1 N)))
11.0ms	(log (sqrt (+ 1 N)))
11.0ms	(log (sqrt (+ 1 N)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(+ (log (sqrt (+ 1 N))) (log (/ (sqrt (+ 1 N)) N)))
84.0ms	(log (sqrt (+ 1 N)))
76.0ms	(log (sqrt (+ 1 N)))
71.0ms	(log (sqrt (+ 1 N)))

simplify3.2s

Counts

140 → 140

Iterations

Iter	Nodes
done	5004
3	3153
2	852
1	364
0	170

prune856.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.8b

bsearch27.0ms

Steps

Iters	Range		Point
8	29.100869698027953	73049.03827748532	8585.191610072276

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

877.0ms	1705×	body	1280	valid
556.0ms	8127×	body	80	nan
356.0ms	4166×	body	80	valid
356.0ms	1221×	body	640	valid
158.0ms	618×	body	320	valid
36.0ms	290×	body	160	valid