Details

sample50.0ms

Algorithm

intervals

Results

27.0ms	95×	body	1280	valid
8.0ms	127×	body	80	valid
4.0ms	16×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify12.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize16.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite6.0ms

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

5.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series26.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

24.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

simplify938.0ms

Counts: 46 → 46

prune381.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 1 expressions with local error:

0.1b	(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

1.0ms

(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)))

simplify6.0s

Counts: 13 → 13

prune88.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (atan2 1 (+ 1 (fma N N N))))
16.1b	(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)))))
0.1b	(atan2 1 (+ 1 (fma N N N)))

rewrite15.0ms

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

12.0ms	(* (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)))

series30.0ms

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))))
2.0ms	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
2.0ms	(atan2 1 (+ 1 (fma N N N)))

simplify2.1s

Counts: 106 → 106

prune731.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (atan2 1 (+ 1 (fma N N N))))
16.1b	(sqrt (atan2 1 (+ 1 (fma N N N))))
16.1b	(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)))))

rewrite36.0ms

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

31.0ms	(* (* (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))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

15.0ms	(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)))))

simplify1.6s

Counts: 115 → 115

prune833.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s	2820×	body	1280	valid
190.0ms	4113×	body	80	valid
131.0ms	589×	body	640	valid
42.0ms	313×	body	320	valid
16.0ms	165×	body	160	valid