Details

sample52.0ms

Algorithm

intervals

Results

27.0ms	88×	body	1280	valid
9.0ms	132×	body	80	valid
5.0ms	22×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify11.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

11.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize10.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (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))

series26.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

24.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify1.6s

Counts

32 → 46

Calls

32 calls:

Slowest

211.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
148.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
125.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
121.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
121.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))

prune359.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(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`

Counts

2 → 21

Calls

2 calls:

Slowest

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

series21.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

19.0ms	(fma N (+ N 1) 1)
2.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify168.0ms

Counts

6 → 27

Calls

6 calls:

Slowest

35.0ms	(+ N (+ (pow N 2) 1))
32.0ms	(+ N (+ (pow N 2) 1))
32.0ms	(+ N (+ (pow N 2) 1))
26.0ms	(atan2 1 (fma N (+ N 1) 1))
24.0ms	(atan2 1 (fma N (+ N 1) 1))

prune209.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

14.5b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.5b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.6b	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
0.4b	(atan2 1 (fma N (+ N 1) 1))

rewrite17.0ms

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`

Counts

4 → 94

Calls

4 calls:

Slowest

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

18.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
4.0ms	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
4.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify1.9s

Counts

82 → 106

Calls

82 calls:

Slowest

134.0ms	(* (* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))
133.0ms	(* (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
39.0ms	(* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))
38.0ms	(* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))
38.0ms	(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune841.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

14.5b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.5b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.5b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.6b	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-r` `*-commutative`

Counts

4 → 97

Calls

4 calls:

Slowest

36.0ms	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))
2.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

16.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
4.0ms	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))

simplify2.8s

Counts

87 → 109

Calls

87 calls:

Slowest

417.0ms	(* (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (* (* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))))
318.0ms	(* (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (* (* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))))
88.0ms	(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))
65.0ms	(* (atan2 1 (fma N (+ N 1) 1)) (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
64.0ms	(* (atan2 1 (fma N (+ N 1) 1)) (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))

prune898.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes59.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

777.0ms	2756×	body	1280	valid
748.0ms	4157×	body	80	valid
130.0ms	620×	body	640	valid
49.0ms	312×	body	320	valid
18.0ms	155×	body	160	valid