Details

sample82.0ms

Algorithm

intervals

Results

23.0ms	57×	body	1280	valid
13.0ms	298×	body	80	nan
10.0ms	135×	body	80	valid
8.0ms	33×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize9.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (log1p N) (log N))

rewrite7.0ms

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:

6.0ms

(- (log1p N) (log N))

series63.0ms

Counts

1 → 3

Calls

1 calls:

63.0ms

(- (log1p N) (log N))

simplify2.0s

Counts

40 → 40

Iterations

Iter	Nodes
4	2678
3	962
2	372
1	184
0	83

prune189.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (log1p N))
0.0b	(sqrt (log1p N))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

3 → 43

Calls

3 calls:

2.0ms	(sqrt (log1p N))
2.0ms	(sqrt (log1p N))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

series295.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(sqrt (log1p N))
50.0ms	(sqrt (log1p N))
188.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

simplify791.0ms

Counts

52 → 52

Iterations

Iter	Nodes
3	2015
2	635
1	228
0	100

prune444.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))) (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

8.0ms	(* (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))) (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

series698.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))) (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))))
162.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
158.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
167.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

simplify3.9s

Counts

88 → 88

Iterations

Iter	Nodes
3	4547
2	1334
1	395
0	156

prune904.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

13.5b	(log (exp (* (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))) (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))))))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
28.8b	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `log-pow` `fma-udef`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

4 → 50

Calls

4 calls:

6.0ms	(log (exp (* (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))) (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))))))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
0.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
1.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(log (exp (* (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))) (cbrt (fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))))))
174.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
153.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))
187.0ms	(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (log N)))

simplify3.0s

Counts

62 → 62

Iterations

Iter	Nodes
3	4044
2	1135
1	346
0	140

prune748.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.5b

bsearch55.0ms

Steps

Iters	Range		Point
7	1213.337773267216	20389.206216359467	5040.279255067729

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	18

end0.0ms

sample3.5s

Algorithm

intervals

Results

996.0ms	8131×	body	80	nan
982.0ms	1752×	body	1280	valid
535.0ms	1218×	body	640	valid
489.0ms	4137×	body	80	valid
214.0ms	606×	body	320	valid
46.0ms	287×	body	160	valid