Details

sample62.0ms

Algorithm

intervals

Results

30.0ms	98×	body	1280	valid
8.0ms	120×	body	80	valid
6.0ms	25×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite12.0ms

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` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
9.0ms	(- (atan (+ N 1.0)) (atan N))

series26.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify6.4s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
3	4357
2	506
1	139
0	66

prune152.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.0b	(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
2.2b	(- (+ N 1.0) N)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`prod-diff`
11×	`add-log-exp`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`expm1-log1p-u` `fma-neg` `associate-l` `log1p-expm1-u`
3×	`fma-def` `associate-r`
2×	`sum-log` `flip3-+` `diff-log` `associate-*l/` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `difference-of-squares` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

10.0ms	(+ 1 (* (+ N 1.0) N))
25.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
35.0ms	(- (+ N 1.0) N)

series86.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ 1 (* (+ N 1.0) N))
55.0ms	(* (+ N 1.0) N)
8.0ms	(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
2.0ms	(- (+ N 1.0) N)

simplify3.1s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1911
1	326
0	126

prune289.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ 1.0 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` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify1.7s

Counts

12 → 12

Iterations

Iter	Nodes
done	5001
8	1017
7	376
6	195
5	125
4	87
3	62
2	38
1	25
0	18

prune49.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ 1.0 N) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))) (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))))
15.6b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
15.6b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite15.0ms

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` `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 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
11.0ms	(* (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))) (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
3.0ms	(* (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))) (sqrt (atan2 1.0 (fma N (+ 1.0 N) 1))))
17.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify980.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	616
1	127
0	67

prune272.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample1.1s

Algorithm

intervals

Results

617.0ms	2776×	body	1280	valid
190.0ms	4138×	body	80	valid
87.0ms	626×	body	640	valid
34.0ms	313×	body	320	valid
11.0ms	147×	body	160	valid