Details

sample68.0ms

Algorithm

intervals

Results

36.0ms	92×	body	1280	valid
11.0ms	126×	body	80	valid
7.0ms	22×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify10.0ms

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: 14.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.3b	(- (atan (+ N 1)) (atan N))

rewrite14.0ms

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:

3.0ms	(atan (+ N 1))
10.0ms	(- (atan (+ N 1)) (atan N))

series23.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
20.0ms	(- (atan (+ N 1)) (atan N))

simplify2.4s

Counts

46 → 46

Iterations

Iter	Nodes
done	5005
4	2140
3	773
2	288
1	140
0	67

prune141.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 1 expressions with local error:

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

1.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify4.1s

Counts

13 → 13

Iterations

Iter	Nodes
done	5051
10	4194
9	1412
8	774
7	530
6	355
5	221
4	134
3	58
2	32
1	21
0	15

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1 (fma N (+ N 1) 1))
0.6b	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
16.4b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.4b	(sqrt (atan2 1 (fma N (+ N 1) 1)))

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:

0.0ms	(atan2 1 (fma N (+ N 1) 1))
12.0ms	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
1.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
1.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
4	4102
3	670
2	254
1	118
0	65

prune234.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

16.4b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.4b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.4b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.4b	(sqrt (atan2 1 (fma N (+ N 1) 1)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

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

series57.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
18.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

simplify2.2s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
9	2063
8	947
7	579
6	386
5	247
4	145
3	68
2	43
1	31
0	23

prune225.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes26.0ms

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

sample1.5s

Algorithm

intervals

Results

667.0ms	2732×	body	1280	valid
484.0ms	4134×	body	80	valid
176.0ms	648×	body	640	valid
42.0ms	318×	body	320	valid
16.0ms	168×	body	160	valid