Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	96×	body	1280	valid
4.0ms	116×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize6.0ms

Local error

Found 1 expressions with local error:

2.1b	(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 15

Calls

1 calls:

3.0ms

(- (atan (+ N 1.0)) (atan N))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(- (atan (+ N 1.0)) (atan N))

simplify73.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	72	123
1	142	114
2	286	112
3	678	111
4	2488	111
5	5001	111

prune34.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune59.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
17.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
6.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
18.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify104.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	110	649
1	391	565
2	2248	539
3	5001	520

prune136.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
17.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

14.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
4.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
2.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify83.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	193	630
1	469	496
2	1361	484
3	5001	484

prune151.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.4b

regimes55.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample765.0ms

Algorithm

intervals

Results

401.0ms	2844×	body	1280	valid
136.0ms	4009×	body	80	valid
74.0ms	649×	body	640	valid
30.0ms	332×	body	320	valid
11.0ms	166×	body	160	valid