Details

sample70.0ms

Algorithm

intervals

Results

38.0ms	91×	body	1280	valid
13.0ms	141×	body	80	valid
4.0ms	11×	body	640	valid
3.0ms	12×	body	320	valid
0.0ms	1×	body	160	valid

simplify29.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

29.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (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))

series19.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

16.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify1.7s

Counts

32 → 46

Calls

32 calls:

Slowest

249.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
187.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
151.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (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)))))
137.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))

prune338.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 1 expressions with local error:

0.1b	(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))

series4.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

4.0ms

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

simplify94.0ms

Counts

3 → 13

Calls

3 calls:

Slowest

33.0ms	(atan2 1 (fma N (+ N 1) 1))
30.0ms	(atan2 1 (fma N (+ N 1) 1))
30.0ms	(atan2 1 (fma N (+ N 1) 1))

prune132.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
0.2b	(* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

16.0ms	(* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (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)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1))))
163.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
137.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
133.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))

simplify3.4s

Counts

65 → 97

Calls

65 calls:

Slowest

377.0ms	(pow (pow (atan2 1 (fma N (+ N 1) 1)) 2) 1/3)
343.0ms	(pow (pow (atan2 1 (fma N (+ N 1) 1)) 2) 1/3)
341.0ms	(pow (pow (atan2 1 (fma N (+ N 1) 1)) 2) 1/3)
115.0ms	(* (* (cbrt (cbrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (cbrt (atan2 1 (fma N (+ N 1) 1))))) (* (cbrt (cbrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (cbrt (atan2 1 (fma N (+ N 1) 1))))))
106.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize61.0ms

Local error

Found 4 expressions with local error:

15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))
15.1b	(cbrt (atan2 1 (fma N (+ N 1) 1)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

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

series652.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

180.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
168.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
155.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))
148.0ms	(cbrt (atan2 1 (fma N (+ N 1) 1)))

simplify1.3s

Counts

24 → 68

Calls

24 calls:

Slowest

108.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
106.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
103.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
102.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
96.0ms	(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)

prune954.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

812.0ms	2839×	body	1280	valid
325.0ms	4079×	body	80	valid
148.0ms	564×	body	640	valid
64.0ms	349×	body	320	valid
18.0ms	169×	body	160	valid