Details

sample68.0ms

Algorithm

intervals

Results

39.0ms	105×	body	1280	valid
10.0ms	120×	body	80	valid
5.0ms	16×	body	640	valid
3.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify22.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

22.0ms

(- (atan (+ N 1)) (atan N))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize38.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

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:

Slowest

9.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series14.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

12.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify1.7s

Counts

32 → 46

Calls

32 calls:

Slowest

179.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
166.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
151.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
149.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
117.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune333.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 1 expressions with local error:

0.7b	(atan2 1 (fma N (+ N 1) 1))

rewrite1.0ms

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:

Slowest

1.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

3.0ms

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

simplify81.0ms

Counts

3 → 13

Calls

3 calls:

Slowest

37.0ms	(atan2 1 (fma N (+ N 1) 1))
26.0ms	(atan2 1 (fma N (+ N 1) 1))
17.0ms	(atan2 1 (fma N (+ N 1) 1))

prune132.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize20.0ms

Local error

Found 4 expressions with local error:

18.2b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
18.2b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.7b	(atan2 1 (fma N (+ N 1) 1))
0.7b	(atan2 1 (fma N (+ N 1) 1))

rewrite4.0ms

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:

Slowest

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

17.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms	(atan2 1 (fma N (+ N 1) 1))
2.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify612.0ms

Counts

22 → 64

Calls

22 calls:

Slowest

38.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
37.0ms	(atan2 1 (fma N (+ N 1) 1))
36.0ms	(atan2 1 (fma N (+ N 1) 1))
36.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
35.0ms	(atan2 1 (fma N (+ N 1) 1))

prune664.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize31.0ms

Local error

Found 4 expressions with local error:

18.2b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
18.2b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
18.2b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.7b	(atan2 1 (fma N (+ N 1) 1))

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:

Slowest

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

21.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
19.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
3.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify757.0ms

Counts

27 → 70

Calls

27 calls:

Slowest

41.0ms	(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
37.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
37.0ms	(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
36.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
35.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

prune939.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	2827×	body	1280	valid
369.0ms	4033×	body	80	valid
177.0ms	629×	body	640	valid
75.0ms	351×	body	320	valid
69.0ms	160×	body	160	valid