Details

sample39.0ms

Algorithm

intervals

Results

21.0ms	104×	body	1280	valid
6.0ms	116×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.2b	(- (atan (+ N 1)) (atan N))

rewrite10.0ms

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))
7.0ms	(- (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))

simplify981.0ms

Counts

46 → 46

Iterations

Iter	Nodes
4	2149
3	771
2	288
1	140
0	67

prune430.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1 (fma N N N))
0.6b	(atan2 1 (+ 1 (fma N N N)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`+-commutative` `associate-+r+` `sum-log` `flip3-+` `flip-+` `fma-udef` `distribute-lft-out`

Counts

2 → 29

Calls

2 calls:

4.0ms	(+ 1 (fma N N N))
0.0ms	(atan2 1 (+ 1 (fma N N N)))

series22.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ 1 (fma N N N))
2.0ms	(atan2 1 (+ 1 (fma N N N)))

simplify1.4s

Counts

35 → 35

Iterations

Iter	Nodes
4	3407
3	493
2	185
1	97
0	47

prune375.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1 (+ 1 (fma N N N)))
0.6b	(atan2 1 (+ 1 (fma N N N)))
17.5b	(sqrt (atan2 1 (+ 1 (fma N N N))))
17.5b	(sqrt (atan2 1 (+ 1 (fma N N N))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

0.0ms	(atan2 1 (+ 1 (fma N N N)))
0.0ms	(atan2 1 (+ 1 (fma N N N)))
3.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
3.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1 (+ 1 (fma N N N)))
4.0ms	(atan2 1 (+ 1 (fma N N N)))
19.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))
16.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))

simplify4.1s

Counts

64 → 64

Iterations

Iter	Nodes
8	6234
7	1474
6	594
5	243
4	131
3	90
2	63
1	44
0	33

prune723.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1 (+ 1 (fma N N N)))
17.5b	(sqrt (atan2 1 (+ 1 (fma N N N))))
17.5b	(sqrt (atan2 1 (+ 1 (fma N N N))))
17.5b	(sqrt (atan2 1 (+ 1 (fma N N N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`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×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify4.2s

Counts

70 → 70

Iterations

Iter	Nodes
8	6234
7	1474
6	594
5	243
4	131
3	90
2	63
1	44
0	33

prune854.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes123.0ms

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
2	8
1	8
0	5

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s	2856×	body	1280	valid
599.0ms	617×	body	640	valid
352.0ms	4043×	body	80	valid
59.0ms	310×	body	320	valid
23.0ms	174×	body	160	valid