Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	89×	body	1280	valid
8.0ms	130×	body	80	valid
5.0ms	22×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 1 expressions with local error:

1.5b	(- (atan (+ N 1.0)) (atan N))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

8.0ms

(- (atan (+ N 1.0)) (atan N))

series29.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(- (atan (+ N 1.0)) (atan N))

simplify6.4s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	4363
2	503
1	136
0	62

prune86.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 14.3b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

16.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
35.0ms	(- (+ N 1.0) N)

series53.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)))
1.0ms	(- (+ N 1.0) N)

simplify1.1s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
2	1237
1	252
0	106

prune215.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

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))

simplify1.4s

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

prune50.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

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))))
13.9b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
13.9b	(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))
10.0ms	(* (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)))

series31.0ms

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))))
13.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify963.0ms

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	616
1	127
0	67

prune274.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

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	9
1	9
0	6

end0.0ms

sample1.3s

Algorithm

intervals

Results

739.0ms	2873×	body	1280	valid
195.0ms	4029×	body	80	valid
96.0ms	589×	body	640	valid
50.0ms	165×	body	160	valid
45.0ms	344×	body	320	valid