Details

sample26.0ms

Algorithm

intervals

Results

12.0ms	93×	body	1280	valid
4.0ms	134×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	3×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.6b	(- (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))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify51.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (46.0ms)

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

prune64.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	2	45

Merged error: 0.5b

Counts

45 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.5b	(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))

simplify97.0ms

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

Filtered

12 candidates to 9 candidates (75.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	9	3	12
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	10	4	14

Merged error: 0.4b

Counts

14 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(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))))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite12.0ms

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)))

series26.0ms

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)))

simplify109.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (100.0ms)

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

prune142.0ms

Filtered

102 candidates to 54 candidates (52.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	100	6	106

Merged error: 0.4b

Counts

106 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.5b	(atan2 1.0 (fma N (+ N 1.0) 1))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

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

series26.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify175.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 6 (45.0ms)

Iter	Nodes	Cost
0	37	296
1	62	276
2	100	276
3	148	276
4	341	276
5	975	276
6	3911	274
7	5001	274

prune140.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	59	7	66

Merged error: 0.4b

Counts

66 → 7

regimes28.0ms

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

sample720.0ms

Algorithm

intervals

Results

391.0ms	2877×	body	1280	valid
124.0ms	4054×	body	80	valid
66.0ms	605×	body	640	valid
25.0ms	301×	body	320	valid
10.0ms	163×	body	160	valid