Details

sample27.0ms

Algorithm

intervals

Results

14.0ms	99×	body	1280	valid
4.0ms	124×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	8×	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: 13.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.6b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
4.0ms	(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify48.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	129	365
1	345	264
2	1480	254
3	5001	198

prune70.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

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:

1.0ms

(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))

simplify96.0ms

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

prune28.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.5b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
17.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

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×	`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:

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

series27.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(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)))

simplify113.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (101.0ms)

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

prune168.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
17.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 99

Calls

4 calls:

15.0ms	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (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)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (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)))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify189.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	197	608
1	590	481
2	3838	465
3	5001	465

prune179.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes26.0ms

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

sample759.0ms

Algorithm

intervals

Results

399.0ms	2829×	body	1280	valid
135.0ms	4035×	body	80	valid
75.0ms	649×	body	640	valid
31.0ms	315×	body	320	valid
11.0ms	172×	body	160	valid