Details

analyze759.0ms (3.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
25%	25%	74.9%	0.1%	0%	0%	0%	6
25%	25%	74.9%	0.1%	0%	0%	0%	7
25%	25%	74.9%	0.1%	0%	0%	0%	8
25%	25%	74.9%	0.1%	0%	0%	0%	9
28.1%	25%	64%	0.1%	10.9%	0%	0%	10
36.4%	31.2%	54.6%	0.1%	14%	0%	0%	11
46.9%	39%	44.1%	0.1%	16.8%	0%	0%	12

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample7.7s (32.1%)

Results

2.1s	1872×	body	1024	valid
1.9s	5476×	body	256	valid
1.8s	1667×	body	1024	infinite
605.0ms	1598×	body	256	infinite
537.0ms	901×	body	512	valid
497.0ms	828×	body	512	infinite
8.0ms	7×	body	2048	valid

Bogosity

preprocess128.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1184×	`rational.json-simplify-64`
1138×	`rational.json-simplify-45`
978×	`rational.json-simplify-1`
940×	`rational.json-simplify-42`
872×	`rational.json-simplify-44`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	236
1	65	156
2	124	156
3	192	156
4	282	156
5	454	156
6	1057	156
7	3714	156
8	7668	156
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 th (.f64 th (/.f64 (cos.f64 a1) (sqrt.f64 2)))) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 a1) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 th th)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))
(+.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 a2) (sqrt.f64 2))) (.f64 th (.f64 th (/.f64 (cos.f64 a2) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 th th) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 th th)))

Symmetry

(sort a1 a2)

Compiler

Compiled 25 to 18 computations (28% saved)

simplify99.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1230×	`rational.json-simplify-1`
1206×	`rational.json-simplify-64`
906×	`rational.json-simplify-46`
738×	`trig.json-simplify-41`
660×	`trig.json-simplify-49`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	31	39
2	54	39
3	80	39
4	116	39
5	182	39
6	378	39
7	1287	39
8	3255	39

Stop Event

1×	node limit

Counts

1 → 3

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs

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

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

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

eval2.0ms (0%)

Compiler: Compiled 48 to 25 computations (47.9% saved)

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	3	4

Error

0.5b

Counts

4 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize31.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series18.0ms (0.1%)

Counts

3 → 64

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	th	@	-inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
2.0ms	a2	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
2.0ms	th	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
2.0ms	th	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
1.0ms	a1	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

rewrite199.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`exponential.json-3`
946×	`rational.json-1`
946×	`rational.json-2`
946×	`rational.json-4`
946×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	73
1	124	73
2	424	73
3	1715	73
4	7929	73

Stop Event

1×	node limit

Counts

3 → 37

Calls

Call 1

Inputs
(/.f64 (cos.f64 th) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (.f64 a1 a1) (neg.f64 (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (fabs.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (neg.f64 (*.f64 a2 a2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (*.f64 a1 a1) (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (*.f64 a2 a2) (neg.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (-.f64 (neg.f64 (*.f64 a2 a2)) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (-.f64 (neg.f64 (*.f64 a2 a2)) (*.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))))

simplify296.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1172×	`rational.json-simplify-50`
1112×	`rational.json-simplify-54`
974×	`rational.json-simplify-58`
902×	`rational.json-simplify-43`
832×	`rational.json-simplify-41`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	130	3369
1	260	3369
2	568	3369
3	2216	3369
4	5828	3369

Stop Event

1×	node limit

Counts

101 → 74

Calls

Call 1

Inputs
(/.f64 1 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)
(+.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))
(.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(-.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) 1)
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(pow.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(fabs.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(fabs.f64 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1)))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fabs.f64 (-.f64 (.f64 a1 a1) (neg.f64 (.f64 a2 a2))))
(fabs.f64 (-.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))))
(fabs.f64 (-.f64 0 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1))))
(fabs.f64 (/.f64 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))

Outputs
(/.f64 1 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(+.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (/.f64 1 (sqrt.f64 2)) (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)))))
(+.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2)))))
(+.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 1 (sqrt.f64 2)) (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)))) (*.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 1 (sqrt.f64 2)) (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (*.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)))))
(+.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (*.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2)))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2)))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 th 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
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(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
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(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
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(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)
(/.f64 (cos.f64 th) (sqrt.f64 2))
(+.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(-.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 0)
(/.f64 (cos.f64 th) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)
(/.f64 (cos.f64 th) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(*.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (cos.f64 th) (sqrt.f64 2))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)
(/.f64 (cos.f64 th) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
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(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) 1)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(pow.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 (.f64 a1 a1) (neg.f64 (.f64 a2 a2))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 0 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (/.f64 (-.f64 (neg.f64 (.f64 a2 a2)) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series20.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
3.0ms	th	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
1.0ms	a1	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
1.0ms	th	@	-inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
1.0ms	th	@	inf	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
1.0ms	th	@	-inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))

rewrite210.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1056×	`exponential.json-3`
1056×	`rational.json-1`
1056×	`rational.json-2`
1056×	`rational.json-4`
1056×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	113
1	137	93
2	480	93
3	1952	93

Stop Event

1×	node limit

Counts

3 → 26

Calls

Call 1

Inputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Inputs

(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1))

(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))) (/.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))))

simplify406.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

876×	`rational.json-simplify-2`
788×	`rational.json-simplify-50`
706×	`exponential.json-simplify-26`
698×	`rational.json-simplify-79`
678×	`rational.json-simplify-104`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	4790
1	256	4754
2	582	4754
3	1609	4754
4	3751	4754
5	5784	4754
6	7820	4754

Stop Event

1×	node limit

Counts

110 → 81

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (*.f64 -1/2 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 (+.f64 (.f64 1/24 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 4)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(+.f64 (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 2)) (+.f64 (.f64 (+.f64 (.f64 -1/720 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 6)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 (+.f64 (.f64 1/24 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (*.f64 1/24 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 4)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 1)
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) 1)
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2)))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2)))) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a1 th) 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 th a2) 2) (sqrt.f64 2))))
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(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

eval232.0ms (1%)

Compiler: Compiled 6490 to 4225 computations (34.9% saved)

prune86.0ms (0.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	191	10	201
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	191	12	203

Error

0.2b

Counts

203 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.5b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	26.6b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
✓	0.5b	(+.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 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	32.1b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
▶	46.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
▶	32.2b	(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
▶	24.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	1.1b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
	46.9b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
	0.9b	(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 824 to 428 computations (48.1% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.3b	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 63 to 34 computations (46% saved)

series9.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	th	@	inf	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	a2	@	0	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	th	@	-inf	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	a2	@	inf	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	th	@	0	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))

rewrite163.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

792×	`exponential.json-3`
792×	`rational.json-1`
792×	`rational.json-2`
792×	`rational.json-4`
792×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	98	48
2	341	48
3	1407	48
4	6424	48

Stop Event

1×	node limit

Counts

2 → 16

Calls

Call 1

Inputs
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))))))))

simplify166.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1800×	`rational.json-simplify-47`
1126×	`rational.json-simplify-43`
892×	`rational.json-simplify-111`
884×	`rational.json-simplify-76`
826×	`rational.json-simplify-55`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	1882
1	154	1882
2	300	1882
3	725	1882
4	3168	1882
5	6218	1882

Stop Event

1×	node limit

Counts

64 → 49

Calls

Call 1

Inputs
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(+.f64 0 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(-.f64 0 (neg.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(pow.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(neg.f64 (neg.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(-.f64 0 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))

Outputs
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2)))) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2)))) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(+.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 0 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 0 (neg.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(neg.f64 (neg.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 0)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 0 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) 1)
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 38 to 19 computations (50% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	0	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	a2	@	inf	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	a1	@	inf	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	a1	@	0	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	a2	@	-inf	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

rewrite117.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

770×	`rational.json-simplify-49`
728×	`rational.json-simplify-47`
664×	`rational.json-simplify-50`
656×	`rational.json-simplify-55`
624×	`rational.json-simplify-58`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	108	46
2	319	46
3	1179	46
4	4859	46

Stop Event

1×	node limit

Counts

2 → 24

Calls

Call 1

Inputs
(/.f64 1 (sqrt.f64 2))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (/.f64 1 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (/.f64 1 (/.f64 1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) 1) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))) (/.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))))

simplify171.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1438×	`rational.json-simplify-111`
1198×	`rational.json-simplify-2`
1036×	`rational.json-simplify-54`
840×	`rational.json-simplify-1`
614×	`rational.json-simplify-42`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	61	1352
1	120	1352
2	244	1352
3	760	1352
4	2433	1344
5	5420	1332

Stop Event

1×	node limit

Counts

48 → 32

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 1 (sqrt.f64 2)) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 2)))
(-.f64 (/.f64 1 (sqrt.f64 2)) 0)
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 2))))
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 1 (sqrt.f64 2)))) 1)
(*.f64 1 (/.f64 1 (sqrt.f64 2)))
(*.f64 (/.f64 1 (sqrt.f64 2)) 1)
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (/.f64 1 (/.f64 1 (sqrt.f64 2))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) 1))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) 1) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))) (/.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))
(pow.f64 (/.f64 1 (sqrt.f64 2)) 1)
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 2))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 1 (sqrt.f64 2)) 0)
(/.f64 1 (sqrt.f64 2))
(+.f64 0 (/.f64 1 (sqrt.f64 2)))
(/.f64 1 (sqrt.f64 2))
(-.f64 (/.f64 1 (sqrt.f64 2)) 0)
(/.f64 1 (sqrt.f64 2))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 2))))
(/.f64 1 (sqrt.f64 2))
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 1 (sqrt.f64 2)))) 1)
(/.f64 1 (sqrt.f64 2))
(*.f64 1 (/.f64 1 (sqrt.f64 2)))
(/.f64 1 (sqrt.f64 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) 1)
(/.f64 1 (sqrt.f64 2))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (/.f64 1 (/.f64 1 (sqrt.f64 2))))
(/.f64 1 (sqrt.f64 2))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) 1))
(/.f64 1 (sqrt.f64 2))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(/.f64 1 (sqrt.f64 2))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(/.f64 1 (sqrt.f64 2))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) 1) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(/.f64 1 (sqrt.f64 2))
(.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))) (/.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))
(/.f64 1 (sqrt.f64 2))
(pow.f64 (/.f64 1 (sqrt.f64 2)) 1)
(/.f64 1 (sqrt.f64 2))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 2))))
(/.f64 1 (sqrt.f64 2))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 2 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 2 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	44.8b	(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))

Compiler

Compiled 253 to 34 computations (86.6% saved)

series17.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
10.0ms	a2	@	inf	(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
3.0ms	a1	@	-inf	(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
0.0ms	a2	@	0	(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	a1	@	inf	(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	a1	@	0	(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

rewrite81.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1262×	`exponential.json-3`
1262×	`rational.json-1`
1262×	`rational.json-2`
1262×	`rational.json-4`
1262×	`rational.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	401
1	185	401
2	603	101
3	2453	101

Stop Event

1×	node limit

Counts

3 → 33

Calls

Call 1

Inputs

(*.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))

(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))

(*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (neg.f64 (*.f64 a1 a1)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (*.f64 a1 a1) (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 (*.f64 a2 a2) (neg.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (-.f64 (neg.f64 (*.f64 a1 a1)) (*.f64 a2 a2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (neg.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (neg.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (fabs.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))))))

simplify134.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1390×	`rational.json-simplify-2`
1286×	`rational.json-simplify-47`
1162×	`rational.json-simplify-49`
1126×	`rational.json-simplify-111`
814×	`rational.json-simplify-43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	4157
1	225	4157
2	410	4157
3	956	4157
4	2803	4157

Stop Event

1×	node limit

Counts

117 → 71

Calls

Call 1

Inputs
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(+.f64 (.f64 a1 a1) (.f64 a2 a2))
(+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)
(+.f64 0 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(-.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(pow.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(fabs.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(fabs.f64 (-.f64 (neg.f64 (.f64 a1 a1)) (.f64 a2 a2)))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fabs.f64 (-.f64 (.f64 a1 a1) (neg.f64 (.f64 a2 a2))))
(fabs.f64 (-.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))))
(fabs.f64 (-.f64 0 (-.f64 (neg.f64 (.f64 a1 a1)) (.f64 a2 a2))))
(+.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(+.f64 0 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(pow.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(+.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(+.f64 0 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(-.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(pow.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(fabs.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(fabs.f64 (neg.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(fabs.f64 (-.f64 0 (neg.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))))

Outputs
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(+.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2)))))) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 6)) (sqrt.f64 2))))
(+.f64 (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 6)) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (pow.f64 th 6)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(+.f64 (pow.f64 a1 4) (.f64 2 (pow.f64 (.f64 a1 a2) 2)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(+.f64 (pow.f64 a1 4) (.f64 2 (pow.f64 (.f64 a1 a2) 2)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(+.f64 (pow.f64 a1 4) (.f64 2 (pow.f64 (.f64 a1 a2) 2)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(+.f64 (.f64 a1 a1) (.f64 a2 a2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(+.f64 0 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(-.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 0)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(pow.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) 1)
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 (neg.f64 (.f64 a1 a1)) (.f64 a2 a2)))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 (.f64 a1 a1) (neg.f64 (.f64 a2 a2))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 (.f64 a2 a2) (neg.f64 (.f64 a1 a1))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fabs.f64 (-.f64 0 (-.f64 (neg.f64 (.f64 a1 a1)) (.f64 a2 a2))))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(+.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 0 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 0 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(pow.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fabs.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fabs.f64 (neg.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (neg.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fabs.f64 (-.f64 0 (neg.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (fabs.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 a2 2) (cos.f64 th))
✓	0.3b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))

Compiler

Compiled 28 to 18 computations (35.7% saved)

series2.0ms (0%)

Counts

2 → 20

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	inf	(*.f64 (pow.f64 a2 2) (cos.f64 th))
0.0ms	th	@	0	(*.f64 (pow.f64 a2 2) (cos.f64 th))
0.0ms	th	@	0	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
0.0ms	a2	@	inf	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
0.0ms	a2	@	0	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))

rewrite121.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`exponential.json-3`
786×	`rational.json-1`
786×	`rational.json-2`
786×	`rational.json-4`
786×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	97	44
2	341	44
3	1394	44
4	6261	44

Stop Event

1×	node limit

Counts

2 → 21

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (/.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))) (/.f64 (/.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (*.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 a2 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (*.f64 (pow.f64 a2 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th))))))))

simplify173.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

972×	`rational.json-simplify-54`
846×	`rational.json-simplify-111`
772×	`rational.json-simplify-1`
698×	`rational.json-simplify-50`
678×	`rational.json-simplify-55`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1171
1	166	1171
2	319	1171
3	786	1153
4	2997	1153
5	7181	1153

Stop Event

1×	node limit

Counts

41 → 54

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2))) (.f64 -1/720 (.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
(+.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 0)
(+.f64 0 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(-.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 0)
(-.f64 0 (neg.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 1)
(.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (/.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(.f64 (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) 1))
(.f64 (/.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(.f64 (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))) (/.f64 (/.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(pow.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 1)
(neg.f64 (neg.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 0)
(+.f64 0 (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(-.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 0)
(-.f64 0 (neg.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 1)
(/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(pow.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 1)
(neg.f64 (neg.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 th a2) 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th a2) 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(+.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th a2) 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (pow.f64 (.f64 th a2) 2)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (pow.f64 (.f64 a2 th) 2)))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (pow.f64 (.f64 th a2) 2)) (.f64 1/24 (.f64 (pow.f64 a2 2) (pow.f64 th 4)))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (pow.f64 (.f64 a2 th) 2)) (.f64 (pow.f64 a2 2) (.f64 (pow.f64 th 4) 1/24))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (pow.f64 (.f64 a2 th) 2)) (.f64 1/24 (.f64 (pow.f64 a2 2) (pow.f64 th 4)))))
(+.f64 (pow.f64 a2 2) (.f64 (pow.f64 a2 2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/2 (pow.f64 th 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2))) (.f64 -1/720 (.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (pow.f64 (.f64 th a2) 2)) (+.f64 (.f64 1/24 (.f64 (pow.f64 a2 2) (pow.f64 th 4))) (.f64 -1/720 (.f64 (pow.f64 a2 2) (pow.f64 th 6))))))
(+.f64 (+.f64 (.f64 (pow.f64 a2 2) (.f64 (pow.f64 th 4) 1/24)) (.f64 (pow.f64 a2 2) (.f64 (pow.f64 th 6) -1/720))) (+.f64 (pow.f64 a2 2) (.f64 -1/2 (pow.f64 (.f64 a2 th) 2))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (pow.f64 (.f64 a2 th) 2)) (+.f64 (.f64 1/24 (.f64 (pow.f64 a2 2) (pow.f64 th 4))) (.f64 (pow.f64 a2 2) (.f64 -1/720 (pow.f64 th 6))))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (pow.f64 (.f64 a2 th) 2)) (.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/720 (pow.f64 th 6)) (*.f64 1/24 (pow.f64 th 4))))))
(+.f64 (+.f64 (pow.f64 a2 2) (.f64 -1/2 (pow.f64 (.f64 a2 th) 2))) (.f64 (pow.f64 a2 2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(+.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 0)
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 0 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(-.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 0)
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(-.f64 0 (neg.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 1)
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (/.f64 1 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) 1))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))) (/.f64 (/.f64 1 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(pow.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) 1)
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(neg.f64 (neg.f64 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 0)
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(+.f64 0 (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(-.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 0)
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(-.f64 0 (neg.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 1)
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(pow.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) 1)
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(neg.f64 (neg.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th))))
(*.f64 (pow.f64 a2 2) (cos.f64 th))

localize123.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	30.6b	(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))

Compiler

Compiled 164 to 52 computations (68.3% saved)

series9.0ms (0%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
1.0ms	th	@	0	(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
1.0ms	a1	@	0	(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
1.0ms	a1	@	inf	(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
1.0ms	a2	@	inf	(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
1.0ms	th	@	inf	(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))

rewrite80.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1286×	`rational.json-simplify-55`
1200×	`exponential.json-3`
1200×	`rational.json-1`
1200×	`rational.json-2`
1200×	`rational.json-4`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	311
1	178	311
2	578	123
3	2358	123

Stop Event

1×	node limit

Counts

3 → 22

Calls

Call 1

Inputs

(*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))

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

(/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (/.f64 1 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))) (/.f64 (/.f64 1 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (*.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 1)))))

simplify323.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1360×	`rational.json-simplify-2`
1208×	`rational.json-simplify-54`
940×	`rational.json-simplify-1`
618×	`rational.json-simplify-47`
582×	`rational.json-simplify-58`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	161	8246
1	310	8032
2	521	8012
3	1136	7966
4	3042	7960
5	5966	7954

Stop Event

1×	node limit

Counts

130 → 80

Calls

Call 1

Inputs
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/24 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (.f64 -1/4 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (pow.f64 th 4))) (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (.f64 -1/4 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 -1/720 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (.f64 1/48 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/24 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))) (*.f64 -1/4 (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (pow.f64 th 4))) (/.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (pow.f64 a2 4) (cos.f64 th)))) (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (pow.f64 a2 4) (cos.f64 th)))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (pow.f64 a2 4) (cos.f64 th)))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (pow.f64 a2 8) (cos.f64 th)))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 (pow.f64 a2 6) (cos.f64 th))))))
(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (.f64 (pow.f64 a1 6) (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (.f64 (pow.f64 a1 6) (cos.f64 th))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 6)) (*.f64 (pow.f64 a1 8) (cos.f64 th)))))))
(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))))
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(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (.f64 (pow.f64 a1 6) (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 4) (cos.f64 th)))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (.f64 (pow.f64 a1 6) (cos.f64 th))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 6)) (*.f64 (pow.f64 a1 8) (cos.f64 th)))))))
(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (pow.f64 a2 6) (cos.f64 th)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (cos.f64 th) (pow.f64 a2 8)))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 (cos.f64 th) (pow.f64 a2 6))))))
(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (pow.f64 a2 6) (cos.f64 th)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (cos.f64 th) (pow.f64 a2 8)))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 (cos.f64 th) (pow.f64 a2 6))))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(+.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) 0)
(+.f64 0 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(-.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) 0)
(.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1)
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(.f64 (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (.f64 (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (/.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
(pow.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) 1)

Outputs
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
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(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))))))
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(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
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(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
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(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
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(+.f64 (+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (.f64 (cos.f64 th) (pow.f64 a1 6)))) (.f64 -1 (+.f64 (/.f64 (.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 (cos.f64 th) (pow.f64 a1 4))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 6)) (.f64 (cos.f64 th) (pow.f64 a1 8))))))
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(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
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(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (neg.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 (cos.f64 th) (pow.f64 a2 4))))))
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(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 (cos.f64 th) (pow.f64 a2 4))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (*.f64 (cos.f64 th) (pow.f64 a2 8)))))))
(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (.f64 -1 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (neg.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 (cos.f64 th) (pow.f64 a2 4)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (pow.f64 a2 6) (cos.f64 th)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (.f64 -1 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 (cos.f64 th) (pow.f64 a2 4))))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (neg.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 (cos.f64 th) (pow.f64 a2 4))))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 2))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (cos.f64 th) (pow.f64 a2 4)))) (+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (cos.f64 th) (pow.f64 a2 8)))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 (cos.f64 th) (pow.f64 a2 6))))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (cos.f64 th) (pow.f64 a2 8)))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (.f64 -1 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 (cos.f64 th) (pow.f64 a2 4)))))))
(+.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (+.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (cos.f64 th) (pow.f64 a2 8)))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))))) (neg.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 (cos.f64 th) (pow.f64 a2 4)))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (.f64 -1 (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 (cos.f64 th) (pow.f64 a2 4))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (.f64 (cos.f64 th) (pow.f64 a2 8)))))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 (cos.f64 th) (pow.f64 a2 6))) (neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 (cos.f64 th) (pow.f64 a2 4))) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (*.f64 (cos.f64 th) (pow.f64 a2 8)))))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) 0)
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(+.f64 0 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(-.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) 0)
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1)
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (.f64 (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (/.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(pow.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))) 1)
(/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))

eval840.0ms (3.5%)

Compiler: Compiled 20695 to 10643 computations (48.6% saved)

prune453.0ms (1.9%)

Pruning

28 alts after pruning (22 fresh and 6 done)

	Pruned	Kept	Total
New	474	17	491
Fresh	0	5	5
Picked	0	1	1
Done	1	5	6
Total	475	28	503

Error

0.1b

Counts

503 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	40.7b	(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
	38.2b	(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
✓	28.5b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	26.6b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
▶	34.9b	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
✓	0.5b	(+.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 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
	12.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
▶	12.2b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
	47.8b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	32.1b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	54.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
✓	46.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
✓	32.2b	(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	46.0b	(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
▶	32.2b	(.f64 (/.f64 1 (.f64 (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	32.2b	(.f64 (/.f64 1 (.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
	40.7b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
▶	38.2b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
✓	24.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	46.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	54.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
	1.1b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
	46.9b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
	32.6b	(.f64 (.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	0.9b	(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	46.9b	(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))

Compiler

Compiled 2017 to 1062 computations (47.3% saved)

localize131.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))
	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.5b	(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 67 to 32 computations (52.2% saved)

series2.0ms (0%)

Counts

2 → 44

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	th	@	0	(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
0.0ms	th	@	0	(.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))
0.0ms	th	@	inf	(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
0.0ms	a2	@	inf	(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
0.0ms	a2	@	-inf	(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))

rewrite190.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`exponential.json-3`
790×	`rational.json-1`
790×	`rational.json-2`
790×	`rational.json-4`
790×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	98	48
2	340	48
3	1400	48
4	6388	48

Stop Event

1×	node limit

Counts

2 → 21

Calls

Call 1

Inputs
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 a2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))

simplify426.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

778×	`rational.json-simplify-58`
740×	`rational.json-simplify-1`
694×	`rational.json-simplify-47`
636×	`exponential.json-simplify-26`
632×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	1903
1	171	1903
2	321	1903
3	967	1903
4	3325	1903
5	5495	1903
6	7678	1903

Stop Event

1×	node limit

Counts

65 → 49

Calls

Call 1

Inputs
(/.f64 a2 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)
(+.f64 0 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
(-.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)
(-.f64 0 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1))
(.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 (.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(pow.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)
(neg.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(+.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)
(+.f64 0 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(-.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)
(-.f64 0 (neg.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(/.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)
(/.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(pow.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)
(neg.f64 (neg.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))

Outputs
(/.f64 a2 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2)))) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(+.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 a2 th) 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (pow.f64 a2 2)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(+.f64 0 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(-.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(-.f64 0 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(pow.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(neg.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(+.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(+.f64 0 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(-.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(-.f64 0 (neg.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(pow.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (neg.f64 (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))

localize55.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	1.0b	(/.f64 1 (sqrt.f64 2))
✓	2.4b	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)

Compiler

Compiled 88 to 48 computations (45.5% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a2	@	0	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
1.0ms	a1	@	0	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
1.0ms	a2	@	inf	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
0.0ms	a1	@	inf	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
0.0ms	a2	@	-inf	(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)

rewrite172.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

920×	`rational.json-simplify-47`
890×	`rational.json-simplify-49`
700×	`rational.json-simplify-55`
686×	`exponential.json-3`
686×	`rational.json-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	47
1	163	35
2	466	35
3	1535	35
4	6167	35

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (*.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (*.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 -1 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))) (/.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))))

simplify279.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

784×	`rational.json-simplify-111`
688×	`rational.json-simplify-1`
678×	`rational.json-simplify-104`
652×	`rational.json-simplify-2`
616×	`rational.json-simplify-50`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	1679
1	115	1679
2	256	1679
3	657	1679
4	1306	1679
5	3038	1679
6	4847	1679
7	7567	1679

Stop Event

1×	node limit

Counts

49 → 29

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(+.f64 -1 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(+.f64 1 (+.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(+.f64 (+.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) 1)
(.f64 -1 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1)
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) -1)
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) 1))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 -1 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(/.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 -1 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 1 (+.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (+.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 -1 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) -1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 1 (sqrt.f64 2))) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) 1))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))) (/.f64 -1 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

localize22.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 a1 2)
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 23 to 20 computations (13% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a1	@	-inf	(pow.f64 a1 2)
1.0ms	a1	@	inf	(pow.f64 a1 2)
0.0ms	a1	@	0	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
0.0ms	a1	@	inf	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
0.0ms	a1	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))

rewrite116.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1540×	`exponential.json-3`
1540×	`rational.json-1`
1540×	`rational.json-2`
1540×	`rational.json-4`
1540×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	81	30
2	236	30
3	858	30
4	3206	30

Stop Event

1×	node limit

Counts

2 → 27

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
(pow.f64 a1 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 a1 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 a1 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 a1 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (pow.f64 a1 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 a1 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 a1 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)) (pow.f64 a1 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 a1 a1) 2) (/.f64 1 (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 a1 a1) 2) (pow.f64 (/.f64 1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (*.f64 a1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 a1 a1) (*.f64 a1 a1)) 2) (/.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (*.f64 a1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (*.f64 a1 a1) 2)) (pow.f64 (*.f64 (*.f64 a1 a1) (*.f64 a1 a1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 a1 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 a1 2)))))))

simplify223.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1316×	`rational.json-simplify-111`
1058×	`rational.json-simplify-54`
886×	`rational.json-simplify-1`
846×	`rational.json-simplify-50`
620×	`rational.json-simplify-55`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	537
1	108	537
2	237	537
3	778	537
4	2894	537
5	7544	537

Stop Event

1×	node limit

Counts

39 → 30

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(-.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))) 1)
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(+.f64 (pow.f64 a1 2) 0)
(+.f64 0 (pow.f64 a1 2))
(-.f64 (pow.f64 a1 2) 0)
(-.f64 0 (neg.f64 (pow.f64 a1 2)))
(-.f64 (-.f64 0 (-.f64 -1 (pow.f64 a1 2))) 1)
(*.f64 1 (pow.f64 a1 2))
(*.f64 (pow.f64 a1 2) 1)
(*.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(*.f64 (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)) (pow.f64 a1 2))
(.f64 (pow.f64 (.f64 a1 a1) 2) (/.f64 1 (pow.f64 a1 2)))
(.f64 (pow.f64 (.f64 a1 a1) 2) (pow.f64 (/.f64 1 a1) 2))
(.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (.f64 a1 a1) 2))
(.f64 (pow.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) 2) (/.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (*.f64 a1 a1) 2)))
(.f64 (/.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (.f64 a1 a1) 2)) (pow.f64 (.f64 (.f64 a1 a1) (*.f64 a1 a1)) 2))
(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))
(/.f64 (pow.f64 a1 2) 1)
(/.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(neg.f64 (neg.f64 (pow.f64 a1 2)))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))) 1)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(+.f64 (pow.f64 a1 2) 0)
(pow.f64 a1 2)
(+.f64 0 (pow.f64 a1 2))
(pow.f64 a1 2)
(-.f64 (pow.f64 a1 2) 0)
(pow.f64 a1 2)
(-.f64 0 (neg.f64 (pow.f64 a1 2)))
(pow.f64 a1 2)
(-.f64 (-.f64 0 (-.f64 -1 (pow.f64 a1 2))) 1)
(pow.f64 a1 2)
(*.f64 1 (pow.f64 a1 2))
(pow.f64 a1 2)
(*.f64 (pow.f64 a1 2) 1)
(pow.f64 a1 2)
(*.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(pow.f64 a1 2)
(*.f64 (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)) (pow.f64 a1 2))
(pow.f64 a1 2)
(.f64 (pow.f64 (.f64 a1 a1) 2) (/.f64 1 (pow.f64 a1 2)))
(pow.f64 a1 2)
(.f64 (pow.f64 (.f64 a1 a1) 2) (pow.f64 (/.f64 1 a1) 2))
(pow.f64 a1 2)
(.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (.f64 a1 a1) 2))
(pow.f64 a1 2)
(.f64 (pow.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) 2) (/.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (*.f64 a1 a1) 2)))
(pow.f64 a1 2)
(.f64 (/.f64 (/.f64 1 (pow.f64 a1 2)) (pow.f64 (.f64 a1 a1) 2)) (pow.f64 (.f64 (.f64 a1 a1) (*.f64 a1 a1)) 2))
(pow.f64 a1 2)
(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))
(pow.f64 a1 2)
(/.f64 (pow.f64 a1 2) 1)
(pow.f64 a1 2)
(/.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(pow.f64 a1 2)
(neg.f64 (neg.f64 (pow.f64 a1 2)))
(pow.f64 a1 2)

localize50.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	0.3b	(*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 66 to 41 computations (37.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	a1	@	0	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
0.0ms	a1	@	inf	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
0.0ms	a1	@	-inf	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))

rewrite112.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1794×	`exponential.json-3`
1794×	`rational.json-1`
1794×	`rational.json-2`
1794×	`rational.json-4`
1794×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	84	23
2	252	23
3	923	23
4	3700	23

Stop Event

1×	node limit

Counts

1 → 6

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 a1 a1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 a1 a1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 a1 a1)) 1)))))

simplify254.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1894×	`rational.json-simplify-79`
1470×	`rational.json-simplify-47`
1402×	`rational.json-simplify-104`
844×	`rational.json-simplify-73`
808×	`rational.json-simplify-41`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	386
1	37	386
2	81	386
3	226	386
4	852	386
5	2511	386
6	4147	386
7	5730	386
8	7175	386

Stop Event

1×	node limit

Counts

18 → 11

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 0)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (sqrt.f64 2) (.f64 a1 a1))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 1)

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 0)
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 0)
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (sqrt.f64 2) (.f64 a1 a1))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (.f64 a1 (.f64 a1 (sqrt.f64 2))) (.f64 a1 (.f64 a1 (sqrt.f64 2)))))
(/.f64 (.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2)))) (/.f64 (.f64 a1 (.f64 a1 (sqrt.f64 2))) (.f64 a1 (.f64 a1 (sqrt.f64 2)))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))

localize260.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	0.8b	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
✓	30.6b	(.f64 (/.f64 1 (.f64 (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))

Compiler

Compiled 243 to 107 computations (56% saved)

series12.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	th	@	inf	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	th	@	-inf	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	th	@	0	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	th	@	0	(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
1.0ms	th	@	inf	(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))

rewrite106.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1446×	`exponential.json-3`
1446×	`rational.json-1`
1446×	`rational.json-2`
1446×	`rational.json-4`
1446×	`rational.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	235
1	207	189
2	690	95
3	2821	95

Stop Event

1×	node limit

Counts

3 → 27

Calls

Call 1

Inputs

(*.f64 (/.f64 1 (*.f64 (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))

(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))

(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))))

simplify288.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1318×	`rational.json-simplify-49`
1276×	`rational.json-simplify-111`
1014×	`rational.json-simplify-2`
682×	`rational.json-simplify-54`
590×	`rational.json-simplify-104`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	3533
1	279	3455
2	517	3443
3	1229	3415
4	2932	3415
5	7627	3415

Stop Event

1×	node limit

Counts

87 → 81

Calls

Call 1

Inputs
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 1 (pow.f64 (sqrt.f64 2) 2))
(+.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) (*.f64 -1 (/.f64 (pow.f64 th 2) (pow.f64 (sqrt.f64 2) 2))))
(+.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 th 2) (pow.f64 (sqrt.f64 2) 2))) (.f64 1/3 (/.f64 (pow.f64 th 4) (pow.f64 (sqrt.f64 2) 2)))))
(+.f64 (.f64 -2/45 (/.f64 (pow.f64 th 6) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 th 2) (pow.f64 (sqrt.f64 2) 2))) (*.f64 1/3 (/.f64 (pow.f64 th 4) (pow.f64 (sqrt.f64 2) 2))))))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/720 (sqrt.f64 2)) (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2)))) (.f64 1/48 (sqrt.f64 2)))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (*.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4))))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(+.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(fabs.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(fabs.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(fabs.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(fabs.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(fabs.f64 (-.f64 0 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(fabs.f64 (-.f64 0 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
(+.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(+.f64 0 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(*.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(pow.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)

Outputs
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))))) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 1 (pow.f64 (sqrt.f64 2) 2))
1/2
(+.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) (*.f64 -1 (/.f64 (pow.f64 th 2) (pow.f64 (sqrt.f64 2) 2))))
(+.f64 1/2 (*.f64 -1 (/.f64 (pow.f64 th 2) 2)))
(+.f64 1/2 (neg.f64 (/.f64 (pow.f64 th 2) 2)))
(+.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 th 2) (pow.f64 (sqrt.f64 2) 2))) (.f64 1/3 (/.f64 (pow.f64 th 4) (pow.f64 (sqrt.f64 2) 2)))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 th 2) 2)) (+.f64 (.f64 1/3 (/.f64 (pow.f64 th 4) 2)) 1/2))
(+.f64 (neg.f64 (/.f64 (pow.f64 th 2) 2)) (+.f64 1/2 (*.f64 1/3 (/.f64 (pow.f64 th 4) 2))))
(+.f64 1/2 (+.f64 (neg.f64 (/.f64 (pow.f64 th 2) 2)) (*.f64 1/3 (/.f64 (pow.f64 th 4) 2))))
(+.f64 (.f64 -2/45 (/.f64 (pow.f64 th 6) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (/.f64 1 (pow.f64 (sqrt.f64 2) 2)) (+.f64 (.f64 -1 (/.f64 (pow.f64 th 2) (pow.f64 (sqrt.f64 2) 2))) (*.f64 1/3 (/.f64 (pow.f64 th 4) (pow.f64 (sqrt.f64 2) 2))))))
(+.f64 (+.f64 (.f64 -1 (/.f64 (pow.f64 th 2) 2)) (+.f64 (.f64 1/3 (/.f64 (pow.f64 th 4) 2)) 1/2)) (*.f64 -2/45 (/.f64 (pow.f64 th 6) 2)))
(+.f64 (neg.f64 (/.f64 (pow.f64 th 2) 2)) (+.f64 (+.f64 1/2 (.f64 1/3 (/.f64 (pow.f64 th 4) 2))) (.f64 -2/45 (/.f64 (pow.f64 th 6) 2))))
(+.f64 (neg.f64 (/.f64 (pow.f64 th 2) 2)) (+.f64 (.f64 -2/45 (/.f64 (pow.f64 th 6) 2)) (+.f64 1/2 (.f64 1/3 (/.f64 (pow.f64 th 4) 2)))))
(+.f64 (neg.f64 (/.f64 (pow.f64 th 2) 2)) (+.f64 (.f64 1/3 (/.f64 (pow.f64 th 4) 2)) (+.f64 1/2 (.f64 -2/45 (/.f64 (pow.f64 th 6) 2)))))
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(/.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 (cos.f64 th) 2) 2)
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2)))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2)) (.f64 (+.f64 (.f64 (sqrt.f64 2) 1/24) (.f64 (sqrt.f64 2) -1/4)) (.f64 (pow.f64 th 4) -1))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2)) (.f64 (.f64 (sqrt.f64 2) -5/24) (neg.f64 (pow.f64 th 4)))))
(+.f64 (+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2))) (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) 5/24)))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 th 2) 1/2) (*.f64 (neg.f64 (pow.f64 th 4)) -5/24))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/720 (sqrt.f64 2)) (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2)))) (.f64 1/48 (sqrt.f64 2)))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (*.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2)) (+.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) 1/24) (.f64 (sqrt.f64 2) -1/4)) (.f64 (pow.f64 th 4) -1)) (.f64 (+.f64 (.f64 1/2 (+.f64 (.f64 (sqrt.f64 2) 1/24) (.f64 (sqrt.f64 2) -1/4))) (+.f64 (.f64 (sqrt.f64 2) 1/48) (.f64 (sqrt.f64 2) -1/720))) (*.f64 (pow.f64 th 6) -1)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2)) (.f64 -1 (+.f64 (.f64 (pow.f64 th 6) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) -5/24)) (.f64 (sqrt.f64 2) 7/360))) (.f64 (pow.f64 th 4) (*.f64 (sqrt.f64 2) -5/24))))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 th 2) 1/2)) (+.f64 (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) 5/24)) (.f64 (+.f64 (.f64 (sqrt.f64 2) -5/48) (*.f64 (sqrt.f64 2) 7/360)) (neg.f64 (pow.f64 th 6))))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 th 2) 1/2) (.f64 (neg.f64 (pow.f64 th 4)) -5/24))) (.f64 (pow.f64 th 6) (neg.f64 (*.f64 (sqrt.f64 2) -61/720)))))
(+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 (pow.f64 th 2) 1/2) (.f64 (neg.f64 (pow.f64 th 4)) -5/24))) (+.f64 (sqrt.f64 2) (.f64 (pow.f64 th 6) (neg.f64 (*.f64 (sqrt.f64 2) -61/720)))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 0)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(fabs.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(fabs.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(fabs.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(fabs.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(fabs.f64 (-.f64 0 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(fabs.f64 (-.f64 0 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 0 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 0)
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 1 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))

eval844.0ms (3.5%)

Compiler: Compiled 20639 to 12234 computations (40.7% saved)

prune441.0ms (1.8%)

Pruning

33 alts after pruning (26 fresh and 7 done)

	Pruned	Kept	Total
New	483	12	495
Fresh	3	14	17
Picked	1	0	1
Done	3	7	10
Total	490	33	523

Error

0.1b

Counts

523 → 33

Alt Table

Click to see full alt table

Status	Error	Program
	40.7b	(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
	38.2b	(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
✓	28.5b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	26.6b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	46.3b	(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))) 1)
	43.3b	(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) 1)
▶	34.9b	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
✓	0.5b	(+.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 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
	39.6b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
	12.2b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
	24.2b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
	12.2b	(+.f64 (.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2)))) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
▶	47.8b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	32.1b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	54.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
✓	46.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
✓	32.2b	(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	46.1b	(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))
	32.2b	(.f64 (/.f64 1 (.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	32.2b	(.f64 (/.f64 1 (.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
▶	40.7b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
✓	38.2b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
✓	24.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	54.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))
	46.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	54.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
	1.1b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
	46.9b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
	32.6b	(.f64 (.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	46.0b	(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
	0.9b	(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2170 to 1210 computations (44.2% saved)

localize230.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
	0.5b	(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	20.5b	(.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))

Compiler

Compiled 153 to 78 computations (49% saved)

series13.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	a2	@	inf	(.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
2.0ms	a2	@	0	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
1.0ms	a2	@	inf	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
1.0ms	th	@	inf	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
1.0ms	th	@	-inf	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))

rewrite215.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

896×	`exponential.json-3`
896×	`rational.json-1`
896×	`rational.json-2`
896×	`rational.json-4`
896×	`rational.json-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	126
1	124	68
2	406	68
3	1624	68
4	7803	68

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

Inputs

(*.f64 (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))

(*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (neg.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 2 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (*.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (neg.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (-.f64 0 (fabs.f64 (/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))))))

simplify278.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1290×	`rational.json-simplify-55`
1188×	`rational.json-simplify-80`
1182×	`rational.json-simplify-79`
1078×	`rational.json-simplify-104`
1066×	`rational.json-simplify-112`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	166	3618
1	332	3612
2	505	3612
3	2357	3612
4	4897	3612

Stop Event

1×	node limit

Counts

98 → 83

Calls

Call 1

Inputs
(/.f64 a2 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (pow.f64 (sqrt.f64 2) 2))) (/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (pow.f64 (sqrt.f64 2) 2))) (/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (.f64 -2/45 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (pow.f64 (sqrt.f64 2) 2))) (/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2)))))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (*.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2)) (pow.f64 (sqrt.f64 2) 2))
(+.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)
(+.f64 0 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))
(-.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 0)
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)
(/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(pow.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)) 1)
(+.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)
(+.f64 0 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(-.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 0)
(/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)
(/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(pow.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 1)
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(fabs.f64 (neg.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(fabs.f64 (-.f64 0 (neg.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (.f64 (neg.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(fabs.f64 (.f64 (neg.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (neg.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))
(fabs.f64 (.f64 (neg.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(fabs.f64 (.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (/.f64 (*.f64 (cos.f64 th) a2) (fabs.f64 (sqrt.f64 2)))))
(fabs.f64 (.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (fabs.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 2))))
(fabs.f64 (/.f64 (neg.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (/.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (-.f64 0 (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))

Outputs
(/.f64 a2 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2)))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a2 (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))))))
(+.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 (.f64 1/24 (/.f64 (.f64 a2 (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (.f64 -1/2 (/.f64 (.f64 a2 (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 a2 (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2))
(/.f64 (pow.f64 a2 2) 2)
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (pow.f64 (sqrt.f64 2) 2))) (/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2)))
(+.f64 (/.f64 (pow.f64 a2 2) 2) (.f64 -1 (/.f64 (pow.f64 (.f64 a2 th) 2) 2)))
(+.f64 (/.f64 (pow.f64 a2 2) 2) (neg.f64 (/.f64 (pow.f64 (*.f64 a2 th) 2) 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (pow.f64 (sqrt.f64 2) 2))) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (pow.f64 (sqrt.f64 2) 2))) (/.f64 (pow.f64 a2 2) (pow.f64 (sqrt.f64 2) 2))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 (.f64 a2 th) 2) 2)) (+.f64 (/.f64 (pow.f64 a2 2) 2) (.f64 1/3 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) 2))))
(+.f64 (/.f64 (pow.f64 a2 2) 2) (+.f64 (.f64 1/3 (/.f64 (.f64 (pow.f64 th 4) (pow.f64 a2 2)) 2)) (neg.f64 (/.f64 (pow.f64 (*.f64 a2 th) 2) 2))))
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(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (fabs.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (neg.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (fabs.f64 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) 2))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) (/.f64 (.f64 2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) (.f64 2 (fabs.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) (/.f64 (.f64 2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) (fabs.f64 (.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) -2)))))
(fabs.f64 (/.f64 (neg.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(fabs.f64 (/.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))) (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(fabs.f64 (/.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (-.f64 0 (fabs.f64 (/.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	1.0b	(/.f64 1 (sqrt.f64 2))
✓	2.4b	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)

Compiler

Compiled 69 to 36 computations (47.8% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a2	@	inf	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
0.0ms	a2	@	0	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
0.0ms	a1	@	inf	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
0.0ms	a2	@	-inf	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
0.0ms	a1	@	-inf	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)

rewrite126.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`rational.json-simplify-49`
800×	`rational.json-simplify-47`
716×	`rational.json-simplify-50`
688×	`rational.json-simplify-54`
682×	`rational.json-simplify-55`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	135	35
2	386	35
3	1374	35
4	5537	35

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 2 (-.f64 2 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -1 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) -1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 2 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 -2 (-.f64 -2 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) -3) 3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 3) -3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 -1 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -2 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (*.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (/.f64 1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (/.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (/.f64 (*.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) 1) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (/.f64 (/.f64 (/.f64 1 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (*.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (/.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))))))

simplify231.0ms (1%)

Algorithm

1×	egg-herbie

Rules

978×	`rational.json-simplify-50`
940×	`rational.json-simplify-2`
816×	`rational.json-simplify-104`
730×	`rational.json-simplify-55`
698×	`rational.json-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	2029
1	182	2029
2	708	2029
3	1629	2029
4	2665	2029
5	4902	2029
6	7340	2029

Stop Event

1×	node limit

Counts

59 → 39

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(-.f64 1 (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(-.f64 2 (-.f64 2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(-.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) 1)
(-.f64 -1 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(-.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) -1) -1)
(-.f64 (+.f64 2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) 2)
(-.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 2) -2)
(-.f64 -2 (-.f64 -2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(-.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) -3) 3)
(-.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 3) -3)
(-.f64 (-.f64 -1 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) -1)
(-.f64 (-.f64 0 (-.f64 -2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 2)
(-.f64 (-.f64 0 (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) -1)
(.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1)
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) 1))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (/.f64 1 (sqrt.f64 2)))))
(.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (/.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (/.f64 (.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) 1) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))))
(.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (/.f64 (/.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
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(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
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(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))
(-.f64 1 (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 2 (-.f64 2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 0)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 -1 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
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(-.f64 (+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) -1) -1)
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(-.f64 (+.f64 2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) 2)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 2) -2)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 -2 (-.f64 -2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) -3) 3)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 3) -3)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 -1 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) -1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 0 (-.f64 -2 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 2)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(-.f64 (-.f64 0 (-.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) -1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) 1)
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(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
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(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
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(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))) (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (/.f64 1 (sqrt.f64 2)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
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(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (/.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (/.f64 (.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) 1) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))) (/.f64 (/.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) 1)
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 23 to 20 computations (13% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	0	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
0.0ms	a2	@	inf	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
0.0ms	a2	@	-inf	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))

rewrite94.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1540×	`exponential.json-3`
1540×	`rational.json-1`
1540×	`rational.json-2`
1540×	`rational.json-4`
1540×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	81	23
2	236	23
3	858	23
4	3206	23

Stop Event

1×	node limit

Counts

1 → 9

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 2) (pow.f64 a2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))))))))

simplify209.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1978×	`rational.json-simplify-79`
1250×	`rational.json-simplify-43`
936×	`rational.json-simplify-104`
902×	`rational.json-simplify-73`
830×	`rational.json-simplify-47`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	455
1	51	455
2	104	455
3	259	455
4	777	455
5	2957	455
6	4351	455
7	5382	455
8	6801	455

Stop Event

1×	node limit

Counts

21 → 12

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 0)
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 0)
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))))
(-.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)))) 1)
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 1)
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 0)
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)))
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 0)
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))))
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)))) 1)
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 1)
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(/.f64 (.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2))) (/.f64 (.f64 (pow.f64 a2 2) (sqrt.f64 2)) (*.f64 (pow.f64 a2 2) (sqrt.f64 2))))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2)) 1)
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))))
(*.f64 (pow.f64 a2 2) (/.f64 1 (sqrt.f64 2)))

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))
✓	0.4b	(pow.f64 (/.f64 1 a1) 2)
	1.0b	(/.f64 1 (sqrt.f64 2))
✓	40.1b	(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))

Compiler

Compiled 55 to 39 computations (29.1% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	a1	@	-inf	(pow.f64 (/.f64 1 a1) 2)
0.0ms	a1	@	inf	(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))
0.0ms	a1	@	0	(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))
0.0ms	a1	@	-inf	(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))
0.0ms	a1	@	0	(pow.f64 (/.f64 1 a1) 2)

rewrite131.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1448×	`rational.json-simplify-49`
1172×	`rational.json-simplify-47`
660×	`rational.json-simplify-55`
614×	`exponential.json-3`
614×	`rational.json-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	79
1	121	79
2	384	43
3	1446	43
4	5717	43

Stop Event

1×	node limit

Counts

3 → 35

Calls

Call 1

Inputs
(.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (.f64 a1 a1) 2))
(pow.f64 (/.f64 1 a1) 2)
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 a1 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 a1 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 a1 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (pow.f64 a1 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 a1 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 a1 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 a1 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 a1 2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (/.f64 1 a1) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (/.f64 1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (/.f64 1 a1) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (/.f64 1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (pow.f64 (/.f64 1 a1) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (/.f64 1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1 a1) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1 a1) 2) (/.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (/.f64 1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (/.f64 1 (pow.f64 (/.f64 1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (*.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (pow.f64 (/.f64 1 (/.f64 1 a1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 a1) (*.f64 (/.f64 1 a1) (*.f64 (/.f64 1 a1) (/.f64 1 a1)))) 2) (/.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (/.f64 1 a1) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (/.f64 1 a1) 2) (/.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (/.f64 1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (/.f64 1 a1) 2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))))))

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1724×	`rational.json-simplify-47`
1452×	`rational.json-simplify-49`
1140×	`rational.json-simplify-2`
834×	`rational.json-simplify-55`
658×	`rational.json-simplify-41`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	973
1	148	973
2	304	973
3	928	953
4	3087	947

Stop Event

1×	node limit

Counts

71 → 42

Calls

Call 1

Inputs
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 0 (pow.f64 a1 2))
(+.f64 (pow.f64 a1 2) 0)
(-.f64 0 (neg.f64 (pow.f64 a1 2)))
(-.f64 (pow.f64 a1 2) 0)
(-.f64 (-.f64 0 (-.f64 -1 (pow.f64 a1 2))) 1)
(/.f64 (pow.f64 a1 2) 1)
(/.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(pow.f64 a1 2)
(pow.f64 (pow.f64 a1 2) 1)
(neg.f64 (neg.f64 (pow.f64 a1 2)))
(+.f64 (pow.f64 (/.f64 1 a1) 2) 0)
(+.f64 0 (pow.f64 (/.f64 1 a1) 2))
(-.f64 (pow.f64 (/.f64 1 a1) 2) 0)
(-.f64 0 (neg.f64 (pow.f64 (/.f64 1 a1) 2)))
(-.f64 (-.f64 0 (-.f64 -1 (pow.f64 (/.f64 1 a1) 2))) 1)
(*.f64 1 (pow.f64 (/.f64 1 a1) 2))
(*.f64 (pow.f64 (/.f64 1 a1) 2) 1)
(*.f64 (pow.f64 (/.f64 1 a1) 2) (/.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (/.f64 1 a1) 2)))
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (/.f64 1 (pow.f64 (/.f64 1 a1) 2)))
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (*.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) 1))
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (pow.f64 (/.f64 1 (/.f64 1 a1)) 2))
(.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2))
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (.f64 (/.f64 1 a1) (.f64 (/.f64 1 a1) (/.f64 1 a1)))) 2) (/.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2)))
(/.f64 (pow.f64 (/.f64 1 a1) 2) 1)
(/.f64 (pow.f64 (/.f64 1 a1) 2) (/.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (/.f64 1 a1) 2)))
(neg.f64 (neg.f64 (pow.f64 (/.f64 1 a1) 2)))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(-.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))) 1)
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))

Outputs
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 a1 2)
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (pow.f64 a1 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 0 (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a1 2) 0)
(pow.f64 a1 2)
(-.f64 0 (neg.f64 (pow.f64 a1 2)))
(pow.f64 a1 2)
(-.f64 (pow.f64 a1 2) 0)
(pow.f64 a1 2)
(-.f64 (-.f64 0 (-.f64 -1 (pow.f64 a1 2))) 1)
(pow.f64 a1 2)
(/.f64 (pow.f64 a1 2) 1)
(pow.f64 a1 2)
(/.f64 (pow.f64 a1 2) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(pow.f64 a1 2)
(pow.f64 a1 2)
(pow.f64 (pow.f64 a1 2) 1)
(pow.f64 a1 2)
(neg.f64 (neg.f64 (pow.f64 a1 2)))
(pow.f64 a1 2)
(+.f64 (pow.f64 (/.f64 1 a1) 2) 0)
(pow.f64 (/.f64 1 a1) 2)
(+.f64 0 (pow.f64 (/.f64 1 a1) 2))
(pow.f64 (/.f64 1 a1) 2)
(-.f64 (pow.f64 (/.f64 1 a1) 2) 0)
(pow.f64 (/.f64 1 a1) 2)
(-.f64 0 (neg.f64 (pow.f64 (/.f64 1 a1) 2)))
(pow.f64 (/.f64 1 a1) 2)
(-.f64 (-.f64 0 (-.f64 -1 (pow.f64 (/.f64 1 a1) 2))) 1)
(pow.f64 (/.f64 1 a1) 2)
(*.f64 1 (pow.f64 (/.f64 1 a1) 2))
(pow.f64 (/.f64 1 a1) 2)
(*.f64 (pow.f64 (/.f64 1 a1) 2) 1)
(pow.f64 (/.f64 1 a1) 2)
(*.f64 (pow.f64 (/.f64 1 a1) 2) (/.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (/.f64 1 a1) 2)))
(pow.f64 (/.f64 1 a1) 2)
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (/.f64 1 (pow.f64 (/.f64 1 a1) 2)))
(pow.f64 (/.f64 1 a1) 2)
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (*.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) 1))
(pow.f64 (/.f64 1 a1) 2)
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2) (pow.f64 (/.f64 1 (/.f64 1 a1)) 2))
(pow.f64 (/.f64 1 a1) 2)
(.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) (pow.f64 (.f64 (/.f64 1 a1) (/.f64 1 a1)) 2))
(pow.f64 (/.f64 1 a1) 2)
(.f64 (pow.f64 (.f64 (/.f64 1 a1) (.f64 (/.f64 1 a1) (.f64 (/.f64 1 a1) (/.f64 1 a1)))) 2) (/.f64 (/.f64 1 (pow.f64 (/.f64 1 a1) 2)) (pow.f64 (*.f64 (/.f64 1 a1) (/.f64 1 a1)) 2)))
(pow.f64 (/.f64 1 a1) 2)
(/.f64 (pow.f64 (/.f64 1 a1) 2) 1)
(pow.f64 (/.f64 1 a1) 2)
(/.f64 (pow.f64 (/.f64 1 a1) 2) (/.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (/.f64 1 a1) 2)))
(pow.f64 (/.f64 1 a1) 2)
(neg.f64 (neg.f64 (pow.f64 (/.f64 1 a1) 2)))
(pow.f64 (/.f64 1 a1) 2)
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 0)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(-.f64 (-.f64 0 (-.f64 -1 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))) 1)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(/.f64 (.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2))) (/.f64 (.f64 (pow.f64 a1 2) (sqrt.f64 2)) (*.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (pow.f64 a1 2)))
(.f64 (pow.f64 (.f64 a1 a1) 2) (/.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)))
(pow.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2)) 1)
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))
(neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))))
(*.f64 (pow.f64 a1 2) (/.f64 1 (sqrt.f64 2)))

localize69.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
✓	0.3b	(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	25.6b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))

Compiler

Compiled 147 to 52 computations (64.6% saved)

series21.0ms (0.1%)

Counts

3 → 76

Calls

24 calls:

Time	Variable		Point	Expression
7.0ms	th	@	-inf	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
1.0ms	th	@	inf	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
1.0ms	th	@	0	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
1.0ms	a1	@	-inf	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
1.0ms	a1	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))

rewrite179.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1310×	`exponential.json-3`
1310×	`rational.json-1`
1310×	`rational.json-2`
1310×	`rational.json-4`
1310×	`rational.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	205
1	180	205
2	616	205
3	2486	205

Stop Event

1×	node limit

Counts

3 → 21

Calls

Call 1

Inputs

(*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))

(/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (/.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (*.f64 (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))) (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))) (*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))) 1)))))

simplify637.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

816×	`rational.json-simplify-50`
738×	`rational.json-simplify-2`
710×	`exponential.json-simplify-26`
704×	`rational.json-simplify-1`
692×	`rational.json-simplify-79`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	7523
1	302	7297
2	569	7283
3	1419	7255
4	3219	7255
5	5179	7255
6	7774	7255

Stop Event

1×	node limit

Counts

97 → 106

Calls

Call 1

Inputs
(/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 2 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
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(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 0)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1)
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1)

Outputs
(/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 2 (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
(+.f64 (.f64 2 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))) (+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))))
(/.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (*.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (*.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (pow.f64 th 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (/.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 -1/2 (/.f64 (pow.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) th) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (pow.f64 th 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (/.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (*.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) th) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (*.f64 (sqrt.f64 2) (pow.f64 a1 2))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (pow.f64 th 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (/.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) th) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))))
(+.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 (.f64 th (+.f64 (pow.f64 a1 2) (pow.f64 a2 2))) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 4)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2) (pow.f64 th 6)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) 2)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2))
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(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))))
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(+.f64 (/.f64 (.f64 (pow.f64 a2 4) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a1 2)) (sqrt.f64 2)) (.f64 2 (/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)))))
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(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(-.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 0)
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(/.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(/.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (/.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(pow.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(+.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 0)
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(+.f64 0 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(-.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 0)
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) 1)
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))))
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(.f64 (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))) (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))))
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))) (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th)))))
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 a1 2) (cos.f64 th))) 1)
(/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 a1 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 0)
(.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 0)
(.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1)
(.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) 1)
(.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))

eval1.1s (4.8%)

Compiler: Compiled 20645 to 12848 computations (37.8% saved)

prune360.0ms (1.5%)

Pruning

34 alts after pruning (22 fresh and 12 done)

	Pruned	Kept	Total
New	509	8	517
Fresh	7	14	21
Picked	0	1	1
Done	0	11	11
Total	516	34	550

Error

0.1b

Counts

550 → 34

Alt Table

Click to see full alt table

Status	Error	Program
	53.7b	(/.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (*.f64 (sqrt.f64 2) (pow.f64 a1 2)))
	40.7b	(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
	38.2b	(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
	47.1b	(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
✓	28.5b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	26.6b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	46.3b	(+.f64 (+.f64 1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) -1)
	43.3b	(+.f64 (+.f64 1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) -1)
✓	34.9b	(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
✓	0.5b	(+.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 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (pow.f64 (.f64 a2 (cos.f64 th)) 2) 2))))
	11.8b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) 2))))
✓	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
	12.2b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
	24.2b	(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
	12.2b	(+.f64 (.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2)))) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
✓	47.8b	(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	32.1b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	54.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
✓	46.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
✓	32.2b	(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	46.0b	(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
	32.2b	(.f64 (/.f64 1 (.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
✓	40.7b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
✓	38.2b	(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
✓	24.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	54.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))
	46.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
	54.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
	1.1b	(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
	48.2b	(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))) (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
	46.0b	(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
	0.9b	(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 1003 to 598 computations (40.4% saved)

regimes652.0ms (2.7%)

Counts

49 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
(+.f64 (+.f64 1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) -1)
(+.f64 (+.f64 1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) 1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2)))) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(/.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (*.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (pow.f64 a2 2) 2))))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) 2) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (/.f64 (pow.f64 (.f64 a2 (cos.f64 th)) 2) 2))))
(.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))))
(.f64 (/.f64 1 (.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (/.f64 1 (.f64 (.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (.f64 (/.f64 1 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))) (.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th)))) (.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (cos.f64 th))))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (/.f64 (/.f64 1 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))))
(.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 (.f64 (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))) (.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (sqrt.f64 2)))))))
(.f64 (/.f64 1 (.f64 (.f64 (.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (/.f64 (/.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))

Calls

8 calls:

167.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
153.0ms	(cos.f64 th)
118.0ms	a1
44.0ms	a2
41.0ms	th

Results

Error	Segments	Branch
0.5b	1	`a1`
0.5b	1	`a2`
0.5b	1	`th`
0.5b	1	`(+.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	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.5b	1	`(cos.f64 th)`
0.5b	1	`(*.f64 a1 a1)`
0.5b	1	`(*.f64 a2 a2)`

Compiler

Compiled 1643 to 764 computations (53.5% saved)

regimes630.0ms (2.6%)

Counts

29 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
(+.f64 (+.f64 1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) -1)
(+.f64 (+.f64 1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) 1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2)))) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))

Calls

7 calls:

191.0ms	a1
134.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
31.0ms	th
26.0ms	a2
23.0ms	(cos.f64 th)

Results

Error	Segments	Branch
0.5b	1	`a1`
0.5b	1	`a2`
0.5b	1	`th`
0.5b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.5b	1	`(cos.f64 th)`
0.5b	1	`(*.f64 a1 a1)`
0.5b	1	`(*.f64 a2 a2)`

Compiler

Compiled 656 to 307 computations (53.2% saved)

regimes313.0ms (1.3%)

Counts

28 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
(+.f64 (+.f64 1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) -1)
(+.f64 (+.f64 1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) 1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))) 1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (/.f64 1 a1) 2) (pow.f64 (*.f64 a1 a1) 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2)))) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))))
(.f64 (/.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))))

Outputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Calls

7 calls:

123.0ms	a1
70.0ms	th
25.0ms	a2
21.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
21.0ms	(cos.f64 th)

Results

Error	Segments	Branch
0.5b	1	`a1`
0.5b	1	`a2`
0.5b	1	`th`
0.5b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.5b	1	`(cos.f64 th)`
0.5b	1	`(*.f64 a1 a1)`
0.5b	1	`(*.f64 a2 a2)`

Compiler

Compiled 637 to 297 computations (53.4% saved)

regimes246.0ms (1%)

Accuracy

Total -39.2b remaining (-162.1%)

Threshold costs -39.2b (-162.1%)

Counts

14 → 1

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))) 1)
(.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (/.f64 1 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (/.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a1 2))
(*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 2))
(+.f64 (+.f64 1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2))) -1)
(+.f64 (+.f64 1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) -1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) 1)
(-.f64 (-.f64 0 (-.f64 -1 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)))) 1)

Outputs
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Calls

5 calls:

190.0ms	th
14.0ms	a2
13.0ms	a1
11.0ms	(*.f64 a2 a2)
9.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
24.2b	1	`a1`
24.2b	1	`a2`
24.2b	1	`th`
24.2b	1	`(*.f64 a1 a1)`
24.2b	1	`(*.f64 a2 a2)`

Compiler

Compiled 267 to 140 computations (47.6% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	192

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Compiler

Compiled 75 to 52 computations (30.7% saved)

soundness356.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

876×	`rational.json-simplify-2`
788×	`rational.json-simplify-50`
706×	`exponential.json-simplify-26`
698×	`rational.json-simplify-79`
678×	`rational.json-simplify-104`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	4790
1	256	4754
2	582	4754
3	1609	4754
4	3751	4754
5	5784	4754
6	7820	4754

Stop Event

1×	node limit

Compiler

Compiled 62 to 36 computations (41.9% saved)

end276.0ms (1.2%)

Remove: (sort a1 a2)
Compiler: Compiled 110 to 66 computations (40% saved)