Details

sample39.0ms

Algorithm

intervals

Results

20.0ms	89×	body	1280	valid
6.0ms	134×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize19.0ms

Local error

Found 1 expressions with local error:

0.9b	(- (atan (+ N 1)) (atan N))

rewrite5.0ms

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

5.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

12.0ms

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

simplify904.0ms

Counts: 46 → 33

prune284.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b	(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

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

series32.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

30.0ms	(fma N (+ 1 N) 1)
2.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify3.6s

Counts: 27 → 27

prune162.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.6b	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))
0.4b	(atan2 1 (fma N (+ 1 N) 1))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 94

Calls

4 calls:

Slowest

8.0ms	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (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))

series32.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

13.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
6.0ms	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))
2.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify1.7s

Counts: 117 → 106

prune635.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.4b	(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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

17.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(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))

simplify564.0ms

Counts: 73 → 70

prune541.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.4b

regimes64.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

708.0ms	2839×	body	1280	valid
332.0ms	323×	body	320	valid
242.0ms	4066×	body	80	valid
107.0ms	627×	body	640	valid
13.0ms	145×	body	160	valid