Details

analyze945.0ms (8.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample82.0ms (0.8%)

Algorithm

1×

intervals

Results

21.0ms	70×	body	1024	valid
10.0ms	149×	body	128	valid
10.0ms	33×	body	1024	invalid
6.0ms	27×	body	512	invalid
5.0ms	24×	body	512	valid
2.0ms	17×	body	256	invalid
2.0ms	13×	body	256	valid
2.0ms	21×	body	128	invalid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`distribute-rgt-out_binary64` `associate-*r/_binary64`
6×	`associate-r_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	26	20
2	46	20
3	66	20
4	85	20
5	97	20
6	108	20
7	106	20
8	106	20

prune10.0ms (0.1%)

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

Error

0.4b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.5b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 92 to 63 computations (31.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite118.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
22×	`sqrt-prod_binary64` `associate-r_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`

Counts

2 → 83

Calls

2 calls:

12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 1855 to 696 computations (62.5% saved)

series151.0ms (1.4%)

Error

0.4b

Counts

2 → 30

Calls

2 calls:

90.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
43.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 1209 to 988 computations (18.3% saved)

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

701×	`cancel-sign-sub-inv_binary64`
353×	`sub-neg_binary64`
331×	`associate-/l*_binary64`
286×	`*-commutative_binary64`
281×	`unswap-sqr_binary64`

Counts

113 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	3045
1	412	2842
2	1416	2746
3	3969	2746
4	5319	2746

prune95.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Error

0.0b

Counts

108 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
	1.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 1989 to 907 computations (54.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
5.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite371.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

149×	`add-sqr-sqrt_binary64`
146×	`times-frac_binary64`
127×	`sqrt-prod_binary64`
90×	`cbrt-prod_binary64`
87×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 226

Calls

4 calls:

33.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 8394 to 3621 computations (56.9% saved)

series274.0ms (2.5%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

86.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
45.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
43.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
43.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4251 to 3247 computations (23.6% saved)

simplify295.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

840×	`times-frac_binary64`
421×	`associate-/r*_binary64`
205×	`cancel-sign-sub-inv_binary64`
204×	`associate-*r/_binary64`
203×	`associate-*l/_binary64`

Counts

286 → 264

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	11043
1	694	10029
2	2464	9533
3	4980	9533
4	4974	9533

prune231.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	264	8	272

Error

Counts

272 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
	1.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 6548 to 3160 computations (51.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.4b	(/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite511.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

187×	`times-frac_binary64`
171×	`add-sqr-sqrt_binary64`
130×	`cbrt-prod_binary64`
102×	`sqrt-prod_binary64`
90×	`add-exp-log_binary64`

Counts

4 → 240

Calls

4 calls:

54.0ms	(.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
17.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 12037 to 6691 computations (44.4% saved)

series315.0ms (2.9%)

Error

Counts

4 → 60

Calls

4 calls:

105.0ms	(/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
50.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
50.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
46.0ms	(.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))

Compiler

Compiled 4978 to 3976 computations (20.1% saved)

simplify392.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

410×	`associate-*l/_binary64`
350×	`associate-*r/_binary64`
253×	`associate-/l*_binary64`
240×	`cancel-sign-sub-inv_binary64`
228×	`associate-l_binary64`

Counts

300 → 274

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	365	18637
1	993	15326
2	3935	12371
3	4564	11862
4	4926	11862

prune243.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	275	7	282

Error

Counts

282 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
▶	0.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) 7))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
	1.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 6979 to 3887 computations (44.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite228.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

100×	`sqrt-prod_binary64`
96×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
40×	`associate-r_binary64`

Counts

4 → 170

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4836 to 1323 computations (72.6% saved)

series205.0ms (1.9%)

Error

Counts

4 → 60

Calls

4 calls:

51.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
44.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
36.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
34.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3137 to 2157 computations (31.2% saved)

simplify270.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

398×	`associate-*l/_binary64`
348×	`associate-/r*_binary64`
325×	`associate-*r/_binary64`
300×	`unswap-sqr_binary64`
267×	`associate-/l/_binary64`

Counts

230 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	5949
1	534	5776
2	1654	5615
3	3967	5615
4	4817	5615
5	4966	5615
6	4942	5615

prune122.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	169	7	176

Error

Counts

176 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))))
	0.6b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 1 (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) 7))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))
	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
	1.2b	(.f64 (.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (cbrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 3298 to 1242 computations (62.3% saved)

regimes3.2s (29.5%)

Accuracy

Total 0.3b remaining (81.6%)

Threshold costs 0.3b (81.6%)

Compiler

Compiled 56446 to 37143 computations (34.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	17	34
2	17	34

end10.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 75 to 39 computations (48% saved)

sample2.6s (24%)

Algorithm

1×

intervals

Results

563.0ms	1882×	body	1024	valid
475.0ms	1567×	body	1024	invalid
358.0ms	4828×	body	128	valid
193.0ms	884×	body	512	valid
178.0ms	809×	body	512	invalid
65.0ms	401×	body	256	valid
60.0ms	392×	body	256	invalid
55.0ms	684×	body	128	invalid
2.0ms	5×	body	2048	valid

Compiler

Compiled 275 to 181 computations (34.2% saved)

Details

analyze945.0ms (8.7%)

sample82.0ms (0.8%)

simplify10.0ms (0.1%)

prune10.0ms (0.1%)

localize10.0ms (0.1%)

rewrite118.0ms (1.1%)

series151.0ms (1.4%)

simplify116.0ms (1.1%)

prune95.0ms (0.9%)

localize18.0ms (0.2%)

rewrite371.0ms (3.4%)

series274.0ms (2.5%)

simplify295.0ms (2.7%)

prune231.0ms (2.1%)

localize20.0ms (0.2%)

rewrite511.0ms (4.7%)

series315.0ms (2.9%)

simplify392.0ms (3.6%)

prune243.0ms (2.2%)

localize13.0ms (0.1%)

rewrite228.0ms (2.1%)

series205.0ms (1.9%)

simplify270.0ms (2.5%)

prune122.0ms (1.1%)

regimes3.2s (29.5%)

simplify3.0ms (0%)

end10.0ms (0.1%)

sample2.6s (24%)

Profiling