Details

sample57.0ms

Algorithm

intervals

Results

33.0ms	107×	body	1280	valid
9.0ms	121×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify21.0ms

Calls

1 calls:

Slowest

21.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize15.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1)) (atan N))

rewrite6.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

1 calls:

Slowest

5.0ms

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

series7.0ms

Calls

1 calls:

Slowest

7.0ms

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

simplify986.0ms

Calls

29 calls:

Slowest

82.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
71.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
71.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (sqrt (atan N)) (sqrt (atan N)))))
67.0ms	(fma 1 (atan (+ N 1)) (- (* (sqrt (atan N)) (sqrt (atan N)))))
66.0ms	(fma 1 (atan (+ N 1)) (- (* (atan N) 1)))

prune224.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(atan2 1 (fma N (+ N 1) 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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Calls

1 calls:

Slowest

0.0ms

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

series2.0ms

Calls

1 calls:

Slowest

2.0ms

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

simplify72.0ms

Calls

3 calls:

Slowest

33.0ms	(atan2 1 (fma N (+ N 1) 1))
22.0ms	(atan2 1 (fma N (+ N 1) 1))
16.0ms	(atan2 1 (fma N (+ N 1) 1))

prune156.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

17.8b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
17.8b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
17.8b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
0.2b	(atan2 1 (fma N (+ N 1) 1))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Calls

4 calls:

Slowest

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

series537.0ms

Calls

4 calls:

Slowest

188.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
185.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
161.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify566.0ms

Calls

21 calls:

Slowest

42.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
42.0ms	(cbrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
40.0ms	(cbrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
39.0ms	(cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
39.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)

prune564.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

17.8b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
17.8b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
17.1b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
17.1b	(sqrt (atan2 1 (fma N (+ N 1) 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

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

series352.0ms

Calls

4 calls:

Slowest

168.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
162.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
11.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
11.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

simplify564.0ms

Calls

26 calls:

Slowest

40.0ms	(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
36.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
34.0ms	(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
33.0ms	(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
31.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

prune685.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes29.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	2843×	body	1280	valid
248.0ms	4064×	body	80	valid
127.0ms	614×	body	640	valid
55.0ms	325×	body	320	valid
17.0ms	154×	body	160	valid