Details

sample30.0ms

Algorithm

intervals

Results

14.0ms	99×	body	1280	valid
4.0ms	123×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.0b

localize7.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

7.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify50.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	126	328
1	342	227
2	1471	217
3	5001	161

prune256.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify101.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	57
1	32	50
2	55	50
3	70	50
4	89	50
5	143	50
6	567	50
7	1779	50
8	5001	50

prune35.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
15.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite19.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
13.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify111.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	100	554
1	375	496
2	2244	476
3	5001	461

prune169.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.8b	(pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4)
15.8b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.8b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `unpow-prod-down`
6×	`pow1` `sqrt-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`sqrt-pow1`
1×	`pow-to-exp` `pow1/2` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

4 → 64

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
5.0ms	(pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4)
1.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series370.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
151.0ms	(pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4)
109.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
108.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify107.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	139	522
1	450	443
2	2162	410
3	5001	407

prune198.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.3b

regimes38.0ms

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	9	3
1	9	3

end0.0ms

sample870.0ms

Algorithm

intervals

Results

463.0ms	2971×	body	1280	valid
139.0ms	3953×	body	80	valid
75.0ms	597×	body	640	valid
30.0ms	307×	body	320	valid
12.0ms	172×	body	160	valid