Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

sample27.0ms (1.6%)

Algorithm

1×

intervals

Results

14.0ms	89×	body	1280	valid
4.0ms	128×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	9×	body	160	valid

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune4.0ms (0.2%)

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 (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1.0))
1.6b	(-.f64 (atan.f64 (+.f64 N 1.0)) (atan.f64 N))

rewrite5.0ms (0.3%)

Algorithm

1×	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:

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

series4.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

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

simplify78.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5349	236

prune33.0ms (2%)

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 (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1.0))
0.2b	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

rewrite8.0ms (0.4%)

Algorithm

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

series9.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1.0))
3.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 N 1.0))))

simplify71.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune54.0ms (3.2%)

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

localize10.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))
0.7b	(.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))))))
13.3b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
13.3b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

rewrite12.0ms (0.7%)

Algorithm

1×	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:

6.0ms	(.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))))))
2.0ms	(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)))))
1.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))

series22.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
8.0ms	(sqrt.f64 (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))))))
3.0ms	(atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N))))

simplify49.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5253	989

prune139.0ms (8.1%)

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

localize11.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.7b	(.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))))))))
13.3b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
13.3b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
13.3b	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))

rewrite22.0ms (1.3%)

Algorithm

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

series30.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
8.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
8.0ms	(sqrt.f64 (atan2.f64 1.0 (+.f64 1 (*.f64 N (+.f64 1.0 N)))))
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))))))))

simplify61.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4775	929
1	4775	929

prune156.0ms (9.1%)

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

regimes71.0ms (4.1%)

Accuracy

Total 0.0b remaining (11.5%)

Threshold costs 0.0b (11.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms (0%)

sample808.0ms (47.4%)

Algorithm

1×

intervals

Results

458.0ms	2925×	body	1280	valid
137.0ms	4046×	body	80	valid
70.0ms	569×	body	640	valid
31.0ms	305×	body	320	valid
11.0ms	155×	body	160	valid

Details

analyze1.0ms (0.1%)

sample27.0ms (1.6%)

simplify7.0ms (0.4%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

rewrite5.0ms (0.3%)

series4.0ms (0.2%)

simplify78.0ms (4.6%)

prune33.0ms (2%)

localize6.0ms (0.3%)

rewrite8.0ms (0.4%)

series9.0ms (0.5%)

simplify71.0ms (4.1%)

prune54.0ms (3.2%)

localize10.0ms (0.6%)

rewrite12.0ms (0.7%)

series22.0ms (1.3%)

simplify49.0ms (2.9%)

prune139.0ms (8.1%)

localize11.0ms (0.7%)

rewrite22.0ms (1.3%)

series30.0ms (1.7%)

simplify61.0ms (3.6%)

prune156.0ms (9.1%)

regimes71.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample808.0ms (47.4%)

Profiling