Details

sample61.0ms

Algorithm

intervals

Results

36.0ms	96×	body	1280	valid
9.0ms	131×	body	80	valid
5.0ms	19×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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`

Counts

1 → 30

Calls

1 calls:

Slowest

6.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

19.0ms

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

simplify1.6s

Counts

29 → 33

Calls

29 calls:

Slowest

205.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
178.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
140.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
130.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
120.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune287.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b	(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)

series33.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

30.0ms	(fma N (+ N 1) 1)
3.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify208.0ms

Counts

6 → 27

Calls

6 calls:

Slowest

49.0ms	(+ N (+ (pow N 2) 1))
43.0ms	(+ N (+ (pow N 2) 1))
37.0ms	(atan2 1 (fma N (+ N 1) 1))
31.0ms	(atan2 1 (fma N (+ N 1) 1))
30.0ms	(+ N (+ (pow N 2) 1))

prune257.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 4 expressions with local error:

16.2b	(cbrt (fma N (+ N 1) 1))
16.2b	(cbrt (fma N (+ N 1) 1))
16.2b	(cbrt (fma N (+ N 1) 1))
0.5b	(atan2 1 (* (* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1))) (cbrt (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`

Counts

4 → 52

Calls

4 calls:

Slowest

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

series202.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(cbrt (fma N (+ N 1) 1))
68.0ms	(cbrt (fma N (+ N 1) 1))
61.0ms	(cbrt (fma N (+ N 1) 1))
2.0ms	(atan2 1 (* (* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1))) (cbrt (fma N (+ N 1) 1))))

simplify1.6s

Counts

21 → 64

Calls

21 calls:

Slowest

213.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
204.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
186.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ 1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
169.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
159.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ 1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))

prune555.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize43.0ms

Local error

Found 4 expressions with local error:

16.2b	(cbrt (fma N (+ N 1) 1))
16.2b	(cbrt (fma N (+ N 1) 1))
16.2b	(cbrt (fma N (+ N 1) 1))
16.2b	(cbrt (fma N (+ N 1) 1))

rewrite4.0ms

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

series222.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

66.0ms	(cbrt (fma N (+ N 1) 1))
62.0ms	(cbrt (fma N (+ N 1) 1))
47.0ms	(cbrt (fma N (+ N 1) 1))
47.0ms	(cbrt (fma N (+ N 1) 1))

simplify1.8s

Counts

24 → 68

Calls

24 calls:

Slowest

179.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
179.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
171.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
156.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ 1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
152.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))

prune818.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.5b

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	2783×	body	1280	valid
314.0ms	4111×	body	80	valid
147.0ms	629×	body	640	valid
58.0ms	322×	body	320	valid
20.0ms	155×	body	160	valid