Details

analyze1.0ms

Algorithm

Search

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

sample29.0ms

Algorithm

intervals

Results

14.0ms	89×	body	1280	valid
5.0ms	128×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	9×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	70	7
1	70	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: 16.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-atan_binary64`

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series4.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify63.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4923	236
1	4923	236

prune27.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.2b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`add-log-exp_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
2.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify58.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5066	260

prune44.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	32	6	38

Merged error: 0.2b

Counts

38 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
0.7b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
13.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
8×	`swap-sqr_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
6.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series22.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))
3.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))
9.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
7.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5258	989

prune79.0ms

Filtered

46 candidates to 94 candidates (-104.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	93	7	100

Merged error: 0.1b

Counts

100 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
13.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
13.3b	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1_binary64`
45×	`pow1_binary64`
30×	`pow1/2_binary64` `pow-prod-up_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow-prod-down_binary64`
6×	`associate-l_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64`
3×	`cbrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64`
2×	`swap-sqr_binary64` `sqrt-unprod_binary64` `unswap-sqr_binary64`
1×	`associate-r_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

15.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
1.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
2.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (.f64 N (+.f64 1 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N))))))))
7.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
7.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))
7.0ms	(sqrt.f64 (atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 1 N)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4780	929
1	4780	929

prune82.0ms

Filtered

49 candidates to 97 candidates (-98.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Merged error: 0.1b

Counts

104 → 7

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	9
1	10	9

end0.0ms

sample832.0ms

Algorithm

intervals

Results

465.0ms	2925×	body	1280	valid
145.0ms	4046×	body	80	valid
76.0ms	569×	body	640	valid
31.0ms	305×	body	320	valid
11.0ms	155×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify8.0ms

prune2.0ms

localize5.0ms

rewrite5.0ms

series4.0ms

simplify63.0ms

prune27.0ms

localize6.0ms

rewrite8.0ms

series9.0ms

simplify58.0ms

prune44.0ms

localize8.0ms

rewrite12.0ms

series22.0ms

simplify47.0ms

prune79.0ms

localize13.0ms

rewrite22.0ms

series25.0ms

simplify61.0ms

prune82.0ms

regimes74.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample832.0ms

Profiling