Details

sample48.0ms

Algorithm

intervals

Results

25.0ms	93×	body	1280	valid
8.0ms	126×	body	80	valid
4.0ms	21×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.6b	(- (atan (+ N 1)) (atan N))

rewrite13.0ms

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:

2.0ms	(atan (+ N 1))
10.0ms	(- (atan (+ N 1)) (atan N))

series22.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
20.0ms	(- (atan (+ N 1)) (atan N))

simplify1.3s

Counts

46 → 46

Iterations

Iter	Nodes
4	2081
3	752
2	286
1	138
0	67

prune361.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite0.0ms

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:

0.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify7.0s

Counts

13 → 13

Iterations

Iter	Nodes
10	7671
9	1595
8	509
7	227
6	133
5	94
4	72
3	55
2	35
1	23
0	18

prune97.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))))
15.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
15.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

rewrite13.0ms

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 (+ 1 N) 1))
9.0ms	(* (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)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(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))))
13.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
21.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

simplify789.0ms

Counts

106 → 106

Iterations

Iter	Nodes
4	2466
3	537
2	233
1	120
0	69

prune857.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

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))))
15.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
15.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
15.6b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

rewrite50.0ms

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:

45.0ms	(* (* (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:

2.0ms	(* (* (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))))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
16.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

simplify1.9s

Counts

115 → 115

Iterations

Iter	Nodes
5	2396
4	1269
3	799
2	417
1	185
0	89

prune787.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.1b

regimes73.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	6
1	6
0	5

end0.0ms

sample1.2s

Algorithm

intervals

Results

762.0ms	2859×	body	1280	valid
220.0ms	4083×	body	80	valid
104.0ms	609×	body	640	valid
40.0ms	299×	body	320	valid
16.0ms	150×	body	160	valid