Details

analyze1.0ms

Algorithm

Search

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

sample28.0ms

Algorithm

intervals

Results

14.0ms	96×	body	1280	valid
4.0ms	127×	body	80	valid
1.0ms	12×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 15.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1.0))
2.2b	(-.f64 (atan.f64 (+.f64 N 1.0)) (atan.f64 N))

rewrite6.0ms

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

series7.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1.0))
6.0ms	(-.f64 (atan.f64 (+.f64 N 1.0)) (atan.f64 N))

simplify88.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5349	236

prune28.0ms

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: 0.3b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1.0))
0.3b	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

rewrite9.0ms

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:

7.0ms	(*.f64 N (+.f64 N 1.0))
1.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

series13.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(*.f64 N (+.f64 N 1.0))
3.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

simplify78.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune42.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

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

Merged error: 0.3b

Counts

38 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
0.6b	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))
14.9b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
14.9b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

rewrite14.0ms

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 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
7.0ms	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))
1.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
2.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

series26.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
3.0ms	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))
10.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
10.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5253	989

prune74.0ms

Filtered

47 candidates to 94 candidates (-100.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Merged error: 0.3b

Counts

99 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))))
14.9b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
14.9b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
14.9b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

rewrite26.0ms

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:

17.0ms	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))))
2.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
2.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
2.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N))))) (.f64 (sqrt.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (.f64 N (+.f64 1.0 N)))))) (sqrt.f64 (sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))))))
9.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
9.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
12.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4775	929
1	4775	929

prune86.0ms

Filtered

49 candidates to 97 candidates (-98.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	97	5	102

Merged error: 0.2b

Counts

102 → 5

regimes64.0ms

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	11	9
1	11	9

end0.0ms

sample773.0ms

Algorithm

intervals

Results

419.0ms	2826×	body	1280	valid
134.0ms	4078×	body	80	valid
80.0ms	631×	body	640	valid
29.0ms	310×	body	320	valid
11.0ms	155×	body	160	valid

Details

analyze1.0ms

sample28.0ms

simplify8.0ms

prune2.0ms

localize6.0ms

rewrite6.0ms

series7.0ms

simplify88.0ms

prune28.0ms

localize6.0ms

rewrite9.0ms

series13.0ms

simplify78.0ms

prune42.0ms

localize9.0ms

rewrite14.0ms

series26.0ms

simplify46.0ms

prune74.0ms

localize12.0ms

rewrite26.0ms

series35.0ms

simplify65.0ms

prune86.0ms

regimes64.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample773.0ms

Profiling