Details

sample66.0ms

Algorithm

intervals

Results

33.0ms	104×	body	1280	valid
8.0ms	113×	body	80	valid
6.0ms	22×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.8b	(- (atan (+ N 1.0)) (atan N))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
15.0ms	(- (atan (+ N 1.0)) (atan N))

series25.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
22.0ms	(- (atan (+ N 1.0)) (atan N))

simplify6.2s

Counts

44 → 44

Iterations

Iter	Nodes
done	5001
4	2122
3	725
2	286
1	139
0	66

prune251.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 1 expressions with local error:

0.5b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify5.7s

Counts

12 → 12

Iterations

Iter	Nodes
done	5001
9	1339
8	422
7	194
6	127
5	97
4	77
3	56
2	32
1	21
0	15

prune93.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
13.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
22.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
3.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
24.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
25.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify9.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
4	4053
3	650
2	239
1	117
0	63

prune575.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize104.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))))
13.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
4×	`expm1-log1p-u` `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 → 93

Calls

4 calls:

103.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
4.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))))
28.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
30.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
27.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify7.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	5007
5	3281
4	1003
3	430
2	280
1	167
0	83

prune560.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

regimes147.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2872×	body	1280	valid
871.0ms	4010×	body	80	valid
179.0ms	631×	body	640	valid
65.0ms	332×	body	320	valid
22.0ms	155×	body	160	valid