Details

sample60.0ms

Algorithm

intervals

Results

33.0ms	94×	body	1280	valid
10.0ms	134×	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))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite13.0ms

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`

Calls

2 calls:

Slowest

10.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

series24.0ms

Calls

2 calls:

Slowest

21.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify1.8s

Calls

32 calls:

Slowest

201.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
197.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
171.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
159.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
155.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune338.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(atan2 1 (fma N (+ N 1) 1))
0.0b	(fma N (+ N 1) 1)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`fma-udef`

Calls

2 calls:

Slowest

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

series20.0ms

Calls

2 calls:

Slowest

18.0ms	(fma N (+ N 1) 1)
2.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify228.0ms

Calls

6 calls:

Slowest

54.0ms	(+ N (+ (pow N 2) 1))
54.0ms	(+ N (+ (pow N 2) 1))
53.0ms	(+ N (+ (pow N 2) 1))
26.0ms	(atan2 1 (fma N (+ N 1) 1))
22.0ms	(atan2 1 (fma N (+ N 1) 1))

prune242.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 4 expressions with local error:

16.2b	(sqrt (fma N (+ N 1) 1))
16.2b	(sqrt (fma N (+ N 1) 1))
0.7b	(atan2 1 (* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1))))
0.0b	(* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1)))

rewrite19.0ms

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` `insert-posit16` `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`

Calls

4 calls:

Slowest

14.0ms	(* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1)))
1.0ms	(sqrt (fma N (+ N 1) 1))
1.0ms	(sqrt (fma N (+ N 1) 1))
0.0ms	(atan2 1 (* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1))))

series116.0ms

Calls

4 calls:

Slowest

41.0ms	(sqrt (fma N (+ N 1) 1))
39.0ms	(sqrt (fma N (+ N 1) 1))
32.0ms	(* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1)))
3.0ms	(atan2 1 (* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1))))

simplify3.0s

Calls

82 calls:

Slowest

224.0ms	(* (fma N (+ N 1) 1) (fma N (+ N 1) 1))
198.0ms	(* (fma N (+ N 1) 1) (fma N (+ N 1) 1))
194.0ms	(* (* (* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1))) (sqrt (fma N (+ N 1) 1))) (* (* (sqrt (fma N (+ N 1) 1)) (sqrt (fma N (+ N 1) 1))) (sqrt (fma N (+ N 1) 1))))
187.0ms	(* (fma N (+ N 1) 1) (fma N (+ N 1) 1))
128.0ms	(+ (* 1/2 N) (+ (* 3/8 (pow N 2)) 1))

prune920.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(atan2 1 (fma N (+ N 1) 1))
0.0b	(fma N (+ N 1) 1)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`fma-udef`

Calls

2 calls:

Slowest

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

series32.0ms

Calls

2 calls:

Slowest

29.0ms	(fma N (+ N 1) 1)
3.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify192.0ms

Calls

6 calls:

Slowest

44.0ms	(+ N (+ (pow N 2) 1))
37.0ms	(+ N (+ (pow N 2) 1))
35.0ms	(+ N (+ (pow N 2) 1))
31.0ms	(atan2 1 (fma N (+ N 1) 1))
22.0ms	(atan2 1 (fma N (+ N 1) 1))

prune187.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes51.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	2826×	body	1280	valid
287.0ms	4057×	body	80	valid
149.0ms	612×	body	640	valid
97.0ms	321×	body	320	valid
24.0ms	184×	body	160	valid