Details

sample37.0ms

Algorithm

intervals

Results

19.0ms	87×	body	1280	valid
6.0ms	133×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify4.0ms

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: 15.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

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))
6.0ms	(- (atan (+ N 1)) (atan N))

series17.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
15.0ms	(- (atan (+ N 1)) (atan N))

simplify676.0ms

Counts

46 → 46

Iterations

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

prune346.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1 (+ 1 (fma N N N)))

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 (+ 1 (fma N N N)))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify4.8s

Counts

13 → 13

Iterations

Iter	Nodes
10	7757
9	1615
8	521
7	243
6	138
5	83
4	59
3	43
2	30
1	22
0	17

prune84.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1 (+ 1 (fma N N N)))
0.6b	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
13.9b	(sqrt (atan2 1 (+ 1 (fma N N N))))
13.9b	(sqrt (atan2 1 (+ 1 (fma N N N))))

rewrite16.0ms

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.0s

Counts

106 → 106

Iterations

Iter	Nodes
5	2615
4	731
3	397
2	231
1	118
0	68

prune667.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (* (sqrt (sqrt (atan2 1 (+ 1 (fma N N N))))) (sqrt (sqrt (atan2 1 (+ 1 (fma N N N)))))))
13.9b	(sqrt (atan2 1 (+ 1 (fma N N N))))
13.9b	(sqrt (atan2 1 (+ 1 (fma N N N))))
13.9b	(sqrt (atan2 1 (+ 1 (fma N N N))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
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-r` `*-commutative`

Counts

4 → 97

Calls

4 calls:

32.0ms	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (* (sqrt (sqrt (atan2 1 (+ 1 (fma N N N))))) (sqrt (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))))
1.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (* (sqrt (sqrt (atan2 1 (+ 1 (fma N N N))))) (sqrt (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))))
13.0ms	(sqrt (atan2 1 (+ 1 (fma N N N))))

simplify1.2s

Counts

109 → 109

Iterations

Iter	Nodes
5	2391
4	876
3	382
2	260
1	172
0	87

prune742.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes38.0ms

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	8
1	8
0	5

end0.0ms

sample1.5s

Algorithm

intervals

Results

845.0ms	2890×	body	1280	valid
275.0ms	3977×	body	80	valid
133.0ms	653×	body	640	valid
52.0ms	327×	body	320	valid
44.0ms	153×	body	160	valid