Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample27.0ms

Algorithm

intervals

Results

13.0ms	88×	body	1280	valid
5.0ms	136×	body	80	valid
3.0ms	24×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune2.0ms

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: 12.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series4.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

simplify20.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5041	236

prune40.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	2	28

Merged error: 0.1b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.1b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

series6.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify59.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4980	272
1	4980	272

prune61.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Merged error: 0.1b

Counts

38 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))))))
16.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.0b	(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)))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
2.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5253	989

prune125.0ms

Filtered

47 candidates to 94 candidates (-100.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	7	99

Merged error: 0.1b

Counts

99 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (fabs (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))
16.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.6b	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.6b	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
10×	`cbrt-prod`
9×	`associate-r`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

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

series117.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (fabs (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))
8.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
34.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
33.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4914	1275
1	4914	1275

prune204.0ms

Filtered

51 candidates to 73 candidates (-43.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	73	7	80

Merged error: 0.1b

Counts

80 → 7

regimes85.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample795.0ms

Algorithm

intervals

Results

436.0ms	2855×	body	1280	valid
138.0ms	4056×	body	80	valid
82.0ms	648×	body	640	valid
29.0ms	304×	body	320	valid
9.0ms	137×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify3.0ms

prune2.0ms

localize6.0ms

rewrite4.0ms

series4.0ms

simplify20.0ms

prune40.0ms

localize6.0ms

rewrite7.0ms

series6.0ms

simplify59.0ms

prune61.0ms

localize8.0ms

rewrite11.0ms

series17.0ms

simplify46.0ms

prune125.0ms

localize16.0ms

rewrite10.0ms

series117.0ms

simplify58.0ms

prune204.0ms

regimes85.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample795.0ms

Profiling