Details

sample51.0ms

Algorithm

intervals

Results

30.0ms	92×	body	1280	valid
8.0ms	136×	body	80	valid
3.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

12.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize21.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (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`

Counts

2 → 40

Calls

2 calls:

Slowest

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

series22.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

19.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify1.6s

Counts

32 → 46

Calls

32 calls:

Slowest

220.0ms	(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
182.0ms	(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
173.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
129.0ms	(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
106.0ms	(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))

prune388.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(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)

series25.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

23.0ms	(fma N (+ N 1) 1)
2.0ms	(atan2 1 (fma N (+ N 1) 1))

simplify163.0ms

Counts

6 → 27

Calls

6 calls:

Slowest

32.0ms	(atan2 1 (fma N (+ N 1) 1))
30.0ms	(atan2 1 (fma N (+ N 1) 1))
28.0ms	(+ N (+ (pow N 2) 1))
27.0ms	(+ N (+ (pow N 2) 1))
26.0ms	(+ N (+ (pow N 2) 1))

prune187.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (fma N (+ N 1) 1))
14.5b	(cbrt (fma N (+ N 1) 1))
14.5b	(cbrt (fma N (+ N 1) 1))
0.2b	(* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1)))

rewrite21.0ms

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

15.0ms	(* (cbrt (fma N (+ N 1) 1)) (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))

series253.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

75.0ms	(cbrt (fma N (+ N 1) 1))
67.0ms	(cbrt (fma N (+ N 1) 1))
61.0ms	(* (cbrt (fma N (+ N 1) 1)) (cbrt (fma N (+ N 1) 1)))
49.0ms	(cbrt (fma N (+ N 1) 1))

simplify3.8s

Counts

65 → 97

Calls

65 calls:

Slowest

380.0ms	(+ (* 2/3 (pow N 1/3)) (+ (pow (/ 1 N) -4/3) (* 5/9 (pow (/ 1 (pow N 2)) 1/3))))
252.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
222.0ms	(* (fma N (+ N 1) 1) (fma N (+ N 1) 1))
209.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
197.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ 1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))

prune821.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (fma N (+ N 1) 1))
14.5b	(cbrt (fma N (+ N 1) 1))
14.5b	(cbrt (fma N (+ N 1) 1))
14.5b	(cbrt (fma N (+ N 1) 1))

rewrite3.0ms

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))

series246.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

74.0ms	(cbrt (fma N (+ N 1) 1))
69.0ms	(cbrt (fma N (+ N 1) 1))
54.0ms	(cbrt (fma N (+ N 1) 1))
49.0ms	(cbrt (fma N (+ N 1) 1))

simplify1.8s

Counts

24 → 68

Calls

24 calls:

Slowest

170.0ms	(+ (* 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))))
167.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ -1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))
166.0ms	(+ (* 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))))

prune732.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.1b

regimes61.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s	2921×	body	1280	valid
289.0ms	3993×	body	80	valid
209.0ms	615×	body	640	valid
52.0ms	302×	body	320	valid
21.0ms	169×	body	160	valid