Details

sample69.0ms

Algorithm

intervals

Results

38.0ms	98×	body	1280	valid
11.0ms	123×	body	80	valid
6.0ms	20×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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))
9.0ms	(- (atan (+ N 1)) (atan N))

series19.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
17.0ms	(- (atan (+ N 1)) (atan N))

simplify1.3s

Counts

46 → 46

Iterations

Iter	Nodes
done	2004
4	2004
3	773
2	288
1	140
0	67

prune345.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 1 expressions with local error:

0.4b	(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:

1.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify1.8s

Counts

13 → 13

Iterations

Iter	Nodes
done	2004
10	2004
9	1660
8	834
7	554
6	378
5	223
4	133
3	62
2	37
1	25
0	18

prune148.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize29.0ms

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)))

rewrite22.0ms

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1 (fma N (+ 1 N) 1))
4.0ms	(* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1))))
17.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
18.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

simplify1.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	2011
4	2011
3	679
2	259
1	123
0	69

prune681.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

localize33.0ms

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)))))

rewrite17.0ms

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)))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
112.0ms	(cbrt (* (sqrt (atan2 1 (fma N (+ 1 N) 1))) (sqrt (atan2 1 (fma N (+ 1 N) 1)))))
111.0ms	(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)))))

simplify912.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	2000
6	2000
5	1707
4	607
3	206
2	100
1	56
0	40

prune548.0ms

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
done	8
1	8
0	5

end0.0ms

sample1.3s

Algorithm

intervals

Results

757.0ms	2890×	body	1280	valid
252.0ms	3991×	body	80	valid
116.0ms	644×	body	640	valid
71.0ms	298×	body	320	valid
17.0ms	177×	body	160	valid