Details

sample65.0ms

Algorithm

intervals

Results

35.0ms	98×	body	1280	valid
10.0ms	123×	body	80	valid
6.0ms	20×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.0b	(- (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))

series40.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
38.0ms	(- (atan (+ N 1)) (atan N))

simplify1.2s

Counts

46 → 46

Iterations

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

prune111.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 1 expressions with local error:

0.4b	(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))

simplify6.5s

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

prune41.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(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))))
16.1b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
16.1b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

rewrite12.0ms

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)))

series32.0ms

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

simplify661.0ms

Counts

106 → 106

Iterations

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

prune252.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
16.6b	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
16.6b	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
16.6b	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 52

Calls

4 calls:

1.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
5.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
5.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
5.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
110.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
115.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
110.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))

simplify4.5s

Counts

64 → 64

Iterations

Iter	Nodes
6	8148
5	1495
4	479
3	190
2	98
1	54
0	40

prune238.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes36.0ms

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
2	6
1	6
0	5

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s	2890×	body	1280	valid
234.0ms	3991×	body	80	valid
114.0ms	644×	body	640	valid
40.0ms	298×	body	320	valid
17.0ms	177×	body	160	valid