Details

sample65.0ms

Algorithm

intervals

Results

29.0ms	74×	body	1280	valid
11.0ms	137×	body	80	valid
9.0ms	28×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	3×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize22.0ms

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:

Slowest

10.0ms

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

series38.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

38.0ms

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

simplify1.0s

Counts: 33 → 33

prune279.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 2 expressions with local error:

0.8b	(atan2 1 (fma N (+ 1 N) 1))
0.0b	(fma N (+ 1 N) 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:

Slowest

1.0ms	(atan2 1 (fma N (+ 1 N) 1))
0.0ms	(fma N (+ 1 N) 1)

series32.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

28.0ms	(fma N (+ 1 N) 1)
3.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify4.2s

Counts: 27 → 27

prune253.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize33.0ms

Local error

Found 4 expressions with local error:

11.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
11.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.8b	(atan2 1 (fma N (+ 1 N) 1))
0.8b	(atan2 1 (fma N (+ 1 N) 1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`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`

Counts

4 → 52

Calls

4 calls:

Slowest

7.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
2.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.0ms	(atan2 1 (fma N (+ 1 N) 1))
0.0ms	(atan2 1 (fma N (+ 1 N) 1))

series36.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

20.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
2.0ms	(atan2 1 (fma N (+ 1 N) 1))
2.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify5.7s

Counts: 64 → 64

prune551.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

11.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
11.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
11.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.8b	(atan2 1 (fma N (+ 1 N) 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.0ms	(atan2 1 (fma N (+ 1 N) 1))

series60.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

21.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
19.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
18.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
2.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify4.8s

Counts: 70 → 70

prune576.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.7b

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	2868×	body	1280	valid
246.0ms	3992×	body	80	valid
122.0ms	656×	body	640	valid
78.0ms	323×	body	320	valid
27.0ms	161×	body	160	valid