Details

sample64.0ms

Algorithm

intervals

Results

33.0ms	84×	body	1280	valid
12.0ms	142×	body	80	valid
6.0ms	19×	body	640	valid
2.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify20.0ms

Calls

1 calls:

Slowest

20.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize21.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite29.0ms

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

18.0ms	(atan (+ N 1))
10.0ms	(- (atan (+ N 1)) (atan N))

series22.0ms

Calls

2 calls:

Slowest

20.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify1.7s

Calls

32 calls:

Slowest

212.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
196.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
173.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
150.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
124.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune335.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(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

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

series24.0ms

Calls

2 calls:

Slowest

20.0ms	(fma N (+ N 1) 1)
4.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify189.0ms

Calls

6 calls:

Slowest

43.0ms	(+ N (+ (pow N 2) 1))
41.0ms	(+ N (+ (pow N 2) 1))
35.0ms	(+ N (+ (pow N 2) 1))
27.0ms	(atan2 1 (fma N (+ N 1) 1))
25.0ms	(atan2 1 (fma N (+ N 1) 1))

prune201.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

14.6b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.6b	(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))))
0.3b	(atan2 1 (fma N (+ N 1) 1))

rewrite25.0ms

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

18.0ms	(* (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)))
2.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.0ms	(atan2 1 (fma N (+ N 1) 1))

series38.0ms

Calls

4 calls:

Slowest

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

simplify2.2s

Calls

82 calls:

Slowest

123.0ms	(* (* (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))))))
122.0ms	(* (* (* (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)))))
44.0ms	(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
41.0ms	(* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))
41.0ms	(* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

19.2b	(cbrt (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
14.6b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.6b	(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.6b	(sqrt (atan2 1 (fma N (+ N 1) 1)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
62×	`cbrt-prod`
57×	`sqrt-prod`
35×	`associate-l`
34×	`unswap-sqr`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr`
12×	`associate-r`
7×	`pow1`
5×	`*-commutative`
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`
2×	`pow3` `rem-cbrt-cube`
1×	`pow1/3`

Calls

4 calls:

Slowest

50.0ms	(cbrt (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (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)))
1.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

series85.0ms

Calls

4 calls:

Slowest

22.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms	(cbrt (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
21.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms	(sqrt (atan2 1 (fma N (+ N 1) 1)))

simplify3.9s

Calls

91 calls:

Slowest

128.0ms	(cbrt (* (* (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))))))
120.0ms	(cbrt (* (* (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)))))))
119.0ms	(cbrt (* (* (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))))))
110.0ms	(cbrt (* (* (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))))))
108.0ms	(cbrt (* (* (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))))))

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

999.0ms	2965×	body	1280	valid
325.0ms	3943×	body	80	valid
151.0ms	636×	body	640	valid
84.0ms	302×	body	320	valid
20.0ms	154×	body	160	valid