Details

sample49.0ms

Algorithm

intervals

Results

24.0ms	84×	body	1280	valid
9.0ms	141×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize22.0ms

Local error

Found 1 expressions with local error:

0.8b	(- (atan (+ N 1)) (atan N))

rewrite11.0ms

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:

11.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify1.1s

Counts

33 → 33

Iterations

Iter	Nodes
done	2002
4	2002
3	777
2	288
1	136
0	62

prune100.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ N (fma N N 1))
0.2b	(atan2 1 (+ N (fma N N 1)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+r+` `sum-log` `flip3-+` `flip-+` `fma-udef` `distribute-lft-out`

Counts

2 → 29

Calls

2 calls:

4.0ms	(+ N (fma N N 1))
0.0ms	(atan2 1 (+ N (fma N N 1)))

series30.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(+ N (fma N N 1))
2.0ms	(atan2 1 (+ N (fma N N 1)))

simplify1.3s

Counts

35 → 35

Iterations

Iter	Nodes
done	2006
4	2006
3	1659
2	330
1	99
0	44

prune137.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1 (+ N (fma N N 1)))
0.6b	(* (sqrt (atan2 1 (+ N (fma N N 1)))) (sqrt (atan2 1 (+ N (fma N N 1)))))
15.7b	(sqrt (atan2 1 (+ N (fma N N 1))))
15.7b	(sqrt (atan2 1 (+ N (fma N N 1))))

rewrite25.0ms

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:

0.0ms	(atan2 1 (+ N (fma N N 1)))
18.0ms	(* (sqrt (atan2 1 (+ N (fma N N 1)))) (sqrt (atan2 1 (+ N (fma N N 1)))))
2.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))
2.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1 (+ N (fma N N 1)))
4.0ms	(* (sqrt (atan2 1 (+ N (fma N N 1)))) (sqrt (atan2 1 (+ N (fma N N 1)))))
22.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))
23.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))

simplify1.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	2001
4	2001
3	658
2	243
1	118
0	65

prune336.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1 (+ N (fma N N 1)))) (* (sqrt (sqrt (atan2 1 (+ N (fma N N 1))))) (sqrt (sqrt (atan2 1 (+ N (fma N N 1)))))))
15.7b	(sqrt (atan2 1 (+ N (fma N N 1))))
15.7b	(sqrt (atan2 1 (+ N (fma N N 1))))
15.7b	(sqrt (atan2 1 (+ N (fma N N 1))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
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-r` `*-commutative`

Counts

4 → 97

Calls

4 calls:

42.0ms	(* (sqrt (atan2 1 (+ N (fma N N 1)))) (* (sqrt (sqrt (atan2 1 (+ N (fma N N 1))))) (sqrt (sqrt (atan2 1 (+ N (fma N N 1)))))))
1.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))
1.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))
1.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (sqrt (atan2 1 (+ N (fma N N 1)))) (* (sqrt (sqrt (atan2 1 (+ N (fma N N 1))))) (sqrt (sqrt (atan2 1 (+ N (fma N N 1)))))))
22.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))
19.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))
17.0ms	(sqrt (atan2 1 (+ N (fma N N 1))))

simplify1.2s

Counts

109 → 109

Iterations

Iter	Nodes
done	2020
5	2020
4	1019
3	427
2	275
1	170
0	84

prune306.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes89.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	8
1	8
0	5

end0.0ms

sample1.9s

Algorithm

intervals

Results

966.0ms	2859×	body	1280	valid
405.0ms	300×	body	320	valid
241.0ms	4076×	body	80	valid
169.0ms	623×	body	640	valid
17.0ms	142×	body	160	valid