Details

sample66.0ms

Algorithm

intervals

Results

25.0ms	66×	body	1280	valid
11.0ms	245×	body	80	nan
10.0ms	138×	body	80	valid
5.0ms	21×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	13
2	13
1	11
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(log1p N)
3.0b	(- (log1p N) (log N))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

0.0ms	(log1p N)
21.0ms	(- (log1p N) (log N))

series82.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(log1p N)
59.0ms	(- (log1p N) (log N))

simplify2.0s

Counts

55 → 55

Iterations

Iter	Nodes
done	5000
3	1878
2	605
1	231
0	101

prune225.0ms

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 N) N)
2.9b	(log (/ (+ 1 N) N))

rewrite39.0ms

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:

31.0ms	(/ (+ 1 N) N)
7.0ms	(log (/ (+ 1 N) N))

series113.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ 1 N) N)
64.0ms	(log (/ (+ 1 N) N))

simplify2.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5064
3	2729
2	602
1	244
0	106

prune249.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1 N))
0.1b	(/ (sqrt (+ 1 N)) N)
1.4b	(log (/ (sqrt (+ 1 N)) 1))
3.2b	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
84×	`times-frac`
75×	`log-prod`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
56×	`sqrt-prod`
25×	`associate-+l+` `associate-+r+`
18×	`distribute-lft-out`
11×	`pow1`
10×	`add-exp-log`
7×	`associate-/l*`
6×	`add-cbrt-cube` `log-pow`
4×	`expm1-log1p-u` `fma-def` `sqrt-div` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`log-div` `associate-/r*` `flip3-+` `div-exp` `rem-log-exp` `flip-+`
2×	`hypot-def` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `associate-+r-` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `hypot-1-def` `associate-+l-`

Counts

4 → 184

Calls

4 calls:

10.0ms	(sqrt (+ 1 N))
21.0ms	(/ (sqrt (+ 1 N)) N)
13.0ms	(log (/ (sqrt (+ 1 N)) 1))
25.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (+ 1 N))
80.0ms	(/ (sqrt (+ 1 N)) N)
75.0ms	(log (/ (sqrt (+ 1 N)) 1))
255.0ms	(+ (log (/ (sqrt (+ 1 N)) 1)) (log (/ (sqrt (+ 1 N)) N)))

simplify2.5s

Counts

196 → 196

Iterations

Iter	Nodes
done	5000
3	4636
2	1403
1	580
0	269

prune894.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ 1 N)) (sqrt N))
1.4b	(log (sqrt (+ 1 N)))
3.0b	(log (/ (sqrt (+ 1 N)) (sqrt N)))
3.0b	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
108×	`sqrt-prod`
84×	`times-frac`
82×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
66×	`log-prod`
51×	`log-pow`
39×	`pow1`
36×	`prod-diff`
16×	`sqrt-pow1` `pow1/2`
15×	`distribute-lft-out`
10×	`add-exp-log`
7×	`associate--l+` `associate-/l*`
6×	`associate-/r*` `add-cbrt-cube` `fma-neg` `sqrt-div` `associate--r+` `distribute-lft-out--`
5×	`log-div`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `rem-log-exp` `flip-+`
2×	`associate--l-` `div-exp` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 235

Calls

4 calls:

26.0ms	(/ (sqrt (+ 1 N)) (sqrt N))
7.0ms	(log (sqrt (+ 1 N)))
9.0ms	(log (/ (sqrt (+ 1 N)) (sqrt N)))
25.0ms	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (sqrt (+ 1 N)) (sqrt N))
87.0ms	(log (sqrt (+ 1 N)))
151.0ms	(log (/ (sqrt (+ 1 N)) (sqrt N)))
301.0ms	(- (log (sqrt (+ 1 N))) (log (sqrt N)))

simplify1.5s

Counts

247 → 247

Iterations

Iter	Nodes
done	5000
2	1599
1	691
0	326

prune981.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes61.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch32.0ms

Steps

Iters	Range		Point
6	2842.495256040047	21179.114160721674	5400.000739830978

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	1755×	body	1280	valid
821.0ms	4070×	body	80	valid
622.0ms	7851×	body	80	nan
487.0ms	1228×	body	640	valid
201.0ms	642×	body	320	valid
47.0ms	305×	body	160	valid