Details

sample56.0ms

Algorithm

intervals

Results

28.0ms	87×	body	1280	valid
10.0ms	137×	body	80	valid
3.0ms	12×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize18.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (atan (+ N 1)) (atan N))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `diff-atan` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 30

Calls

1 calls:

9.0ms

(- (atan (+ N 1)) (atan N))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(- (atan (+ N 1)) (atan N))

simplify2.5s

Counts

33 → 33

Iterations

Iter	Nodes
done	5000
4	2265
3	830
2	306
1	136
0	62

prune111.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ N 1) 1)
0.3b	(atan2 1 (fma N (+ N 1) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

2 → 21

Calls

2 calls:

0.0ms	(fma N (+ N 1) 1)
0.0ms	(atan2 1 (fma N (+ N 1) 1))

series26.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma N (+ N 1) 1)
2.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify1.2s

Counts

27 → 27

Iterations

Iter	Nodes
done	5001
4	1246
3	274
2	84
1	49
0	30

prune134.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1 (+ (fma N N N) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(atan2 1 (+ (fma N N N) 1))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(atan2 1 (+ (fma N N N) 1))

simplify2.3s

Counts

13 → 13

Iterations

Iter	Nodes
done	5011
9	2331
8	820
7	378
6	213
5	113
4	58
3	42
2	29
1	21
0	15

prune83.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1 (* (* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1))) (cbrt (fma N (+ N 1) 1))))
14.7b	(cbrt (fma N (+ N 1) 1))
14.7b	(cbrt (fma N (+ N 1) 1))
14.7b	(cbrt (fma N (+ N 1) 1))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 52

Calls

4 calls:

0.0ms	(atan2 1 (* (* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1))) (cbrt (fma N (+ N 1) 1))))
2.0ms	(cbrt (fma N (+ N 1) 1))
1.0ms	(cbrt (fma N (+ N 1) 1))
1.0ms	(cbrt (fma N (+ N 1) 1))

series155.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1 (* (* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1))) (cbrt (fma N (+ N 1) 1))))
53.0ms	(cbrt (fma N (+ N 1) 1))
50.0ms	(cbrt (fma N (+ N 1) 1))
47.0ms	(cbrt (fma N (+ N 1) 1))

simplify2.1s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
5	4288
4	1519
3	549
2	203
1	104
0	56

prune337.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes34.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
1	8
0	5

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	2934×	body	1280	valid
314.0ms	4006×	body	80	valid
154.0ms	596×	body	640	valid
82.0ms	293×	body	320	valid
19.0ms	171×	body	160	valid