Details

sample76.0ms

Algorithm

intervals

Results

43.0ms	98×	body	1280	valid
10.0ms	117×	body	80	valid
7.0ms	21×	body	640	valid
3.0ms	10×	body	320	valid
2.0ms	10×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize22.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite8.0ms

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

7.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series14.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

12.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify823.0ms

Counts: 46 → 46

prune312.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 1 expressions with local error:

0.2b	(atan2 1 (fma N (+ 1 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:

Slowest

1.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

3.0ms

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

simplify4.9s

Counts: 13 → 13

prune83.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

14.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.6b	(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))))
0.2b	(atan2 1 (fma N (+ 1 N) 1))

rewrite16.0ms

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

9.0ms	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))
4.0ms	(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))

series29.0ms

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)))
2.0ms	(* (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: 106 → 106

prune940.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

14.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
0.6b	(* (* (sqrt (sqrt (atan2 1 (fma N (+ 1 N) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ 1 N) 1))))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

16.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
3.0ms	(* (* (sqrt (sqrt (atan2 1 (fma N (+ 1 N) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ 1 N) 1))))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))

simplify1.1s

Counts: 115 → 115

prune793.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes66.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

769.0ms	2951×	body	1280	valid
259.0ms	3960×	body	80	valid
110.0ms	616×	body	640	valid
42.0ms	312×	body	320	valid
16.0ms	161×	body	160	valid