Details

sample45.0ms

Algorithm

intervals

Results

26.0ms	108×	body	1280	valid
6.0ms	118×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	9×	body	160	valid
1.0ms	4×	body	320	valid

simplify11.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize21.0ms

Local error

Found 2 expressions with local error:

2.7b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

Slowest

9.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

series20.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

19.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify929.0ms

Counts: 46 → 46

prune351.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 1 expressions with local error:

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

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:

Slowest

0.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

4.0ms

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

simplify11.3s

Counts: 13 → 13

prune104.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

17.7b	(sqrt (atan2 1 (+ 1 (fma N N N))))
17.7b	(sqrt (atan2 1 (+ 1 (fma N N N))))
0.6b	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
0.3b	(atan2 1 (+ 1 (fma N N N)))

rewrite18.0ms

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

14.0ms	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
0.0ms	(atan2 1 (+ 1 (fma N N N)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

13.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
12.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
3.0ms	(atan2 1 (+ 1 (fma N N N)))
2.0ms	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))

simplify2.2s

Counts: 106 → 106

prune639.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

17.7b	(sqrt (atan2 1 (+ 1 (fma N N N))))
17.7b	(sqrt (atan2 1 (+ 1 (fma N N N))))
17.7b	(sqrt (atan2 1 (+ 1 (fma N N N))))
0.6b	(* (* (sqrt (sqrt (atan2 1 (+ 1 (fma N N N))))) (sqrt (sqrt (atan2 1 (+ 1 (fma N N N)))))) (sqrt (atan2 1 (+ 1 (fma N N N)))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 103

Calls

4 calls:

Slowest

35.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (fma N N N))))) (sqrt (sqrt (atan2 1 (+ 1 (fma N N N)))))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

13.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
13.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
12.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
3.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (fma N N N))))) (sqrt (sqrt (atan2 1 (+ 1 (fma N N N)))))) (sqrt (atan2 1 (+ 1 (fma N N N)))))

simplify1.0s

Counts: 115 → 115

prune751.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

701.0ms	2874×	body	1280	valid
216.0ms	4061×	body	80	valid
139.0ms	625×	body	640	valid
68.0ms	285×	body	320	valid
14.0ms	155×	body	160	valid