Details

sample62.0ms

Algorithm

intervals

Results

33.0ms	91×	body	1280	valid
10.0ms	130×	body	80	valid
6.0ms	22×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	8×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize10.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite7.0ms

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

5.0ms	(- (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))
3.0ms	(atan (+ N 1))

simplify1.7s

Counts

32 → 46

Calls

32 calls:

Slowest

201.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
193.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
136.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
132.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
123.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune363.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize20.0ms

Local error

Found 1 expressions with local error:

0.9b	(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))

series3.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

3.0ms

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

simplify96.0ms

Counts

3 → 13

Calls

3 calls:

Slowest

38.0ms	(atan2 1 (fma N (+ N 1) 1))
34.0ms	(atan2 1 (fma N (+ N 1) 1))
23.0ms	(atan2 1 (fma N (+ N 1) 1))

prune138.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.3b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.9b	(atan2 1 (fma N (+ N 1) 1))
0.9b	(atan2 1 (fma N (+ N 1) 1))

rewrite6.0ms

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

3.0ms	(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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

21.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
15.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
3.0ms	(atan2 1 (fma N (+ N 1) 1))
3.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify862.0ms

Counts

22 → 64

Calls

22 calls:

Slowest

75.0ms	(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
72.0ms	(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
70.0ms	(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
67.0ms	(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
51.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

prune590.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.9b

localize62.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
14.7b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
14.7b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
14.3b	(sqrt (atan2 1 (fma N (+ N 1) 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

2.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
1.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
1.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
154.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
149.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

simplify1.6s

Counts

26 → 70

Calls

26 calls:

Slowest

147.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
132.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
124.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
118.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
106.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)

prune869.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes106.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	2849×	body	1280	valid
350.0ms	4051×	body	80	valid
157.0ms	632×	body	640	valid
62.0ms	312×	body	320	valid
21.0ms	156×	body	160	valid