Migdal et al, Equation (64)

Time bar (total: 7.3s)

start0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated

analyze0.0ms (0%)

Memory
1.4MiB live, 1.5MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 21 to 14 computations (33.3% saved)

sample1.2s (16%)

Memory
11.3MiB live, 2 162.6MiB allocated
Samples
840.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 600.0ms
ival-cos: 216.0ms (36% of total)
ival-mult: 205.0ms (34.1% of total)
ival-sqrt: 64.0ms (10.7% of total)
ival-div: 54.0ms (9% of total)
ival-add: 44.0ms (7.3% of total)
ival-true: 7.0ms (1.2% of total)
exact: 7.0ms (1.2% of total)
ival-assert: 4.0ms (0.7% of total)
Bogosity

explain194.0ms (2.7%)

Memory
-16.4MiB live, 264.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-a1
00-0-(*.f64 a1 a1)
00-0-(sqrt.f64 #s(literal 2 binary64))
00-0-th
00-0-#s(literal 2 binary64)
00-0-(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
00-0-(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))
00-0-(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
00-0-(*.f64 a2 a2)
00-0-(cos.f64 th)
00-0-(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))
00-0-a2
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
61.0ms512×0valid
Compiler

Compiled 135 to 40 computations (70.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-mult: 20.0ms (48.5% of total)
ival-cos: 11.0ms (26.7% of total)
ival-sqrt: 4.0ms (9.7% of total)
ival-div: 3.0ms (7.3% of total)
ival-add: 2.0ms (4.9% of total)
ival-true: 1.0ms (2.4% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess138.0ms (1.9%)

Memory
-4.6MiB live, 41.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040120
1130120
2373120
31018120
42414120
54784120
65686120
76500120
86573120
96589120
106760120
116878120
126890120
136890120
146890120
01219
02013
13313
25813
38813
410013
010012
Stop Event
1×iter limit
1×saturated
1×iter limit
1×node limit
Calls
Call 1
Inputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Outputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
Symmetry

(abs th)

(abs a2)

(abs a1)

(sort a1 a2)

Compiler

Compiled 19 to 12 computations (36.8% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory
1.1MiB live, 1.1MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify4.0ms (0.1%)

Memory
5.3MiB live, 5.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(cos.f64 th)
cost-diff0
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))
cost-diff8192
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01256
02050
13350
25850
38850
410050
010049
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))
(*.f64 a2 a2)
a2
Outputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 (cos.f64 th)))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (cos.f64 th)))
(*.f64 a2 a2)
a2

localize55.0ms (0.8%)

Memory
10.6MiB live, 49.5MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0
(cos.f64 th)
accuracy0.16796875
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))
accuracy0.174160009768442
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))
accuracy0.764003759768442
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
Samples
47.0ms256×0valid
Compiler

Compiled 58 to 14 computations (75.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 37.0ms
ival-add: 21.0ms (56.7% of total)
ival-mult: 7.0ms (18.9% of total)
ival-cos: 5.0ms (13.5% of total)
ival-div: 2.0ms (5.4% of total)
ival-sqrt: 2.0ms (5.4% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series36.0ms (0.5%)

Memory
-3.3MiB live, 35.5MiB allocated
Counts
5 → 108
Calls
Call 1
Inputs
#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())
#s(alt (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())
Outputs
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2))))) (taylor -inf a1) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a1 2) (cos th)) (sqrt 2)) (taylor -inf a1) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 th) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))) (taylor 0 th) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
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#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) (patch (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (patch (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
17.0ms
a1
@-inf
((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
3.0ms
a2
@0
((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms
a1
@0
((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms
th
@0
((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))
2.0ms
th
@inf
((+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (* (/ (cos th) (sqrt 2)) (* a1 a1)) (/ (cos th) (sqrt 2)) (cos th) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

simplify305.0ms (4.2%)

Memory
-18.8MiB live, 256.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01111498
13431366
212061262
339001233
084281172
Stop Event
1×iter limit
1×node limit
Counts
108 → 108
Calls
Call 1
Inputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* -1/2 (/ (pow a2 2) (sqrt 2))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2)))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* 1/24 (/ (pow a1 2) (sqrt 2))) (+ (* 1/24 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (pow a1 2) (sqrt 2))) (* -1/720 (/ (pow a2 2) (sqrt 2))))))))))) (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))))
(/ (pow a1 2) (sqrt 2))
(+ (* -1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (/ (pow a1 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* 1/24 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))))) (/ (pow a1 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a1 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a1 2) (sqrt 2))))))) (/ (pow a1 2) (sqrt 2)))
(/ 1 (sqrt 2))
(+ (* -1/2 (/ (pow th 2) (sqrt 2))) (/ 1 (sqrt 2)))
(+ (* (pow th 2) (- (* 1/24 (/ (pow th 2) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
(+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/720 (/ (pow th 2) (sqrt 2))) (* 1/24 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))) (/ 1 (sqrt 2)))
1
(+ 1 (* -1/2 (pow th 2)))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(/ (pow a2 2) (sqrt 2))
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* 1/24 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))))) (/ (pow a2 2) (sqrt 2)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(cos th)
(cos th)
(cos th)
(cos th)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(/ (cos th) (sqrt 2))
(cos th)
(cos th)
(cos th)
(cos th)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
Outputs
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
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(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
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(fma.f64 (pow.f64 th #s(literal 4 binary64)) (*.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 th th) #s(literal 1/24 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
(/ (pow a1 2) (sqrt 2))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1)
(+ (* -1/2 (/ (* (pow a1 2) (pow th 2)) (sqrt 2))) (/ (pow a1 2) (sqrt 2)))
(*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 th th)) a1 a1))
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(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (*.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 th th) #s(literal 1/24 binary64)) (*.f64 th th) #s(literal -1/2 binary64))) (*.f64 th th)))
(/ 1 (sqrt 2))
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(*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
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(fma.f64 (*.f64 (/.f64 th (sqrt.f64 #s(literal 2 binary64))) th) (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow th 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* 1/24 (pow th 2)) 1/2)))
(fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))
(+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/24 (* -1/720 (pow th 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 th th) #s(literal 1/24 binary64)) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))
(/ (pow a2 2) (sqrt 2))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(+ (* -1/2 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 th th)) a2 a2))
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(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64)))
(+ (* (pow th 2) (+ (* -1/2 (/ (pow a2 2) (sqrt 2))) (* (pow th 2) (+ (* -1/720 (/ (* (pow a2 2) (pow th 2)) (sqrt 2))) (* 1/24 (/ (pow a2 2) (sqrt 2))))))) (/ (pow a2 2) (sqrt 2)))
(fma.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2 (*.f64 (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (fma.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 th th) #s(literal 1/24 binary64)) (*.f64 th th) #s(literal -1/2 binary64))) (*.f64 th th)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(/ (cos th) (sqrt 2))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(cos th)
(cos.f64 th)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))

rewrite176.0ms (2.4%)

Memory
29.8MiB live, 185.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01244
02038
15838
241138
3733138
0843437
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
5 → 327
Calls
Call 1
Inputs
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))
Outputs
#<batchref>
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#<batchref>
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eval152.0ms (2.1%)

Memory
-15.2MiB live, 145.8MiB allocated
Compiler

Compiled 12 965 to 1 060 computations (91.8% saved)

prune41.0ms (0.6%)

Memory
16.7MiB live, 56.0MiB allocated
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New47416490
Fresh000
Picked101
Done000
Total47516491
Accuracy
100.0%
Counts
491 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
99.6%
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
99.6%
(/.f64 (/.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
99.6%
(/.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
▶99.4%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
99.4%
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
69.9%
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #s(approx (* (/ (cos th) (sqrt 2)) (* a2 a2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 th th)) a2 a2))))
99.6%
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
99.6%
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
▶99.7%
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
▶99.6%
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
55.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
65.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
71.0%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
99.0%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
Compiler

Compiled 504 to 394 computations (21.8% saved)

simplify22.0ms (0.3%)

Memory
-19.9MiB live, 19.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(cos.f64 th)
cost-diff0
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
cost-diff8064
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
cost-diff0
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
cost-diff0
(*.f64 a1 a1)
cost-diff0
(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff0
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
cost-diff1344
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
cost-diff0
(fma.f64 a2 a2 (*.f64 a1 a1))
cost-diff0
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
cost-diff0
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
cost-diff0
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
033248
052236
187236
2145236
3255236
4481227
5620227
6620227
0620227
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
(cos.f64 th)
th
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
a2
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
(cos.f64 th)
th
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
a2
Outputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(*.f64 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
(*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
(cos.f64 th)
th
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
a2
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
(/.f64 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
(*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
(cos.f64 th)
th
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(/.f64 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
th
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 a1 a1)
a1
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
a2

localize107.0ms (1.5%)

Memory
7.3MiB live, 127.3MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.08984375
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
accuracy0.13671875
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy0.4765625
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy0.764003759768442
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
accuracy0
(cos.f64 th)
accuracy0.09832001953688403
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
accuracy0.2659626633743209
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
accuracy0.7535445358056176
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
accuracy0
(sqrt.f64 #s(literal 2 binary64))
accuracy0
(cos.f64 th)
accuracy0.09375
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
accuracy0.24513627930532605
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
accuracy0.13671875
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
accuracy0.4375
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
accuracy0.4765625
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy19.470213572182026
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
accuracy0
(*.f64 a1 a1)
accuracy0
(cos.f64 th)
accuracy0.09832001953688403
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
accuracy0.1953125
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
Samples
79.0ms256×0valid
Compiler

Compiled 249 to 31 computations (87.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 58.0ms
ival-add: 17.0ms (29.2% of total)
ival-mult: 15.0ms (25.7% of total)
ival-pow: 11.0ms (18.9% of total)
ival-div: 9.0ms (15.4% of total)
ival-cos: 5.0ms (8.6% of total)
ival-sqrt: 2.0ms (3.4% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series75.0ms (1%)

Memory
1.9MiB live, 82.2MiB allocated
Counts
19 → 420
Calls
Call 1
Inputs
#s(alt (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (patch (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (patch (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (fma.f64 a2 a2 (*.f64 a1 a1)) (patch (fma.f64 a2 a2 (*.f64 a1 a1)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (patch (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) #<representation binary64>) () ())
#s(alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (patch (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 a1 a1) (patch (*.f64 a1 a1) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) (patch (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) #<representation binary64>) () ())
#s(alt (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (cos.f64 th) (patch (cos.f64 th) #<representation binary64>) () ())
#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (patch (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) #<representation binary64>) () ())
Outputs
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (patch (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (patch (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (patch (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (patch (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (pow a2 2) (taylor 0 a1) (#s(alt (fma.f64 a2 a2 (*.f64 a1 a1)) (patch (fma.f64 a2 a2 (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a2 a2 (*.f64 a1 a1)) (patch (fma.f64 a2 a2 (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a2 a2 (*.f64 a1 a1)) (patch (fma.f64 a2 a2 (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a2 a2 (*.f64 a1 a1)) (patch (fma.f64 a2 a2 (*.f64 a1 a1)) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor 0 a1) (#s(alt (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (patch (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (patch (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (patch (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (patch (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))) #<representation binary64>) () ())) ())
#s(alt (/ a1 (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a1 (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a1 (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a1 (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (patch (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (patch (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (patch (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) (patch (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (*.f64 a1 a1) (patch (*.f64 a1 a1) #<representation binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (*.f64 a1 a1) (patch (*.f64 a1 a1) #<representation binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (*.f64 a1 a1) (patch (*.f64 a1 a1) #<representation binary64>) () ())) ())
#s(alt (pow a1 2) (taylor 0 a1) (#s(alt (*.f64 a1 a1) (patch (*.f64 a1 a1) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th)))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th)))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th)))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
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#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) (* (pow a2 2) (cos th))) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2)) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2)) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2)) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) (patch (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) (patch (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) (patch (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) (patch (fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (patch (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (patch (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (patch (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (patch (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) (patch (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
16.0ms
th
@0
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)))
6.0ms
th
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)))
4.0ms
a1
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)))
4.0ms
a2
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)))
4.0ms
a1
@0
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (+ (* a2 a2) (* a1 a1)) (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ a1 (sqrt 2)) (sqrt 2) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a1 a1) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (* (/ a2 (sqrt 2)) a2) (cos th))) (/ (cos th) (sqrt 2)) (cos th) (/ a2 (sqrt 2)) (* (/ a2 (sqrt 2)) a2) (* (* (/ a2 (sqrt 2)) a2) (cos th)))

simplify232.0ms (3.2%)

Memory
16.3MiB live, 211.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02966646
19876098
238276063
080915710
Stop Event
1×iter limit
1×node limit
Counts
420 → 420
Calls
Call 1
Inputs
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ a1 (sqrt 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(pow a1 2)
(pow a1 2)
(pow a1 2)
(pow a1 2)
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
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(/ 1 (sqrt 2))
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1
(+ 1 (* -1/2 (pow th 2)))
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(* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
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(* (pow a2 2) (cos th))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(/ (pow a2 2) (sqrt 2))
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
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(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
Outputs
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(pow a1 2)
(*.f64 a1 a1)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (/.f64 (*.f64 (neg.f64 a1) a1) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) (pow.f64 a2 #s(literal 6 binary64))) (/.f64 a1 (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th)))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 a2 #s(literal 8 binary64))) (/.f64 (*.f64 a1 a1) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th)))) (*.f64 a1 a1) (/.f64 (/.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (pow.f64 a2 #s(literal 4 binary64))) (cos.f64 th))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a1) a1)
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a2) a1) (/.f64 a2 a1) (cos.f64 th)) (*.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a2) a1) (/.f64 a2 a1) (cos.f64 th)) (*.f64 a1 a1))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a2) a1) (/.f64 a2 a1) (cos.f64 th)) (*.f64 a1 a1))
(pow a1 2)
(*.f64 a1 a1)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))
(/ (pow a1 2) (sqrt 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ a1 (sqrt 2))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(/ (pow a1 2) (sqrt 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a2 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1)) (/.f64 a2 a1) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a1 a1))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
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(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 a1) a1) (*.f64 (cos.f64 th) a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (*.f64 a2 a2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) a2) a2)
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (fma.f64 (/.f64 (neg.f64 (pow.f64 a1 #s(literal 6 binary64))) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(pow a2 2)
(*.f64 a2 a2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 a2 a2))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 (*.f64 (neg.f64 a1) a1) (*.f64 (cos.f64 th) a2)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) (*.f64 a2 a2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/.f64 (/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th))) a2) a2)
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (fma.f64 (/.f64 (neg.f64 (pow.f64 a1 #s(literal 6 binary64))) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 6 binary64))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(*.f64 (cos.f64 th) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))

rewrite199.0ms (2.7%)

Memory
-7.8MiB live, 316.3MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
033175
052166
1178153
21275153
08197153
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
19 → 1 889
Calls
Call 1
Inputs
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 a1 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a1 a1)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
(cos.f64 th)
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
(*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th))
Outputs
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eval358.0ms (4.9%)

Memory
44.0MiB live, 813.3MiB allocated
Compiler

Compiled 67 418 to 3 693 computations (94.5% saved)

prune66.0ms (0.9%)

Memory
-14.4MiB live, 223.5MiB allocated
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New2 782232 805
Fresh10111
Picked505
Done000
Total2 797242 821
Accuracy
100.0%
Counts
2 821 → 24
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.6%
(/.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
▶65.3%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
98.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th))))
▶69.4%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
63.2%
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
99.0%
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)))
65.3%
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
71.1%
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
99.0%
(*.f64 (/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
▶99.0%
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
69.4%
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
69.3%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
69.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
69.3%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
33.0%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
68.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
14.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
71.1%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
▶69.4%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
▶99.7%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
Compiler

Compiled 716 to 564 computations (21.2% saved)

simplify26.0ms (0.4%)

Memory
-28.8MiB live, 32.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
cost-diff0
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
cost-diff0
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
cost-diff0
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))
cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
cost-diff0
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff0
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
cost-diff704
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
cost-diff0
(*.f64 a2 a2)
cost-diff0
(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff0
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff0
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
cost-diff0
(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff0
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff0
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
cost-diff0
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042356
065356
196356
2168352
3428352
4735352
5849352
6921352
7927352
8927352
0927352
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(cos.f64 th)
th
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(*.f64 a1 a1)
a1
#s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 th th)
th
#s(literal -1/2 binary64)
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
a2
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(cos.f64 th)
th
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
(/.f64 (*.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
a2
(*.f64 a1 a1)
a1
#s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))
#s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))
(fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))
(fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
#s(literal 1/24 binary64)
(*.f64 th th)
th
#s(literal -1/2 binary64)
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)
a2
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(cos.f64 th)
th

localize96.0ms (1.3%)

Memory
-3.5MiB live, 193.3MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.09375
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
accuracy0.13671875
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
accuracy0.41535625828092837
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
accuracy0.4765625
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
accuracy0.1015625
(fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))
accuracy0.2659626633743209
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
accuracy0.7535445358056176
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))
accuracy26.328784019124413
#s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))
accuracy0.0078125
(fma.f64 a1 a1 (*.f64 a2 a2))
accuracy0.2659626633743209
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
accuracy0.7535445358056176
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
accuracy19.463035929146272
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
accuracy0
(sqrt.f64 #s(literal 1/2 binary64))
accuracy0.0078125
(fma.f64 a1 a1 (*.f64 a2 a2))
accuracy0.1796875
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
accuracy19.470213572182026
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy0
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
accuracy0.0078125
(fma.f64 a1 a1 (*.f64 a2 a2))
accuracy0.09375
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
accuracy0.1796875
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
Samples
67.0ms256×0valid
Compiler

Compiled 272 to 33 computations (87.9% saved)

Precisions
Click to see histograms. Total time spent on operations: 46.0ms
ival-mult: 16.0ms (34.9% of total)
ival-div: 6.0ms (13.1% of total)
ival-cos: 6.0ms (13.1% of total)
ival-add: 5.0ms (10.9% of total)
ival-pow: 5.0ms (10.9% of total)
const: 4.0ms (8.7% of total)
ival-sqrt: 3.0ms (6.5% of total)
exact: 1.0ms (2.2% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series38.0ms (0.5%)

Memory
1.0MiB live, 78.8MiB allocated
Counts
20 → 492
Calls
Call 1
Inputs
#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())
#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 a2 a2) (patch (*.f64 a2 a2) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))) (patch (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th)) (patch (*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th)) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (patch #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (patch (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 1/2 binary64)) (patch (sqrt.f64 #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (patch #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) #<representation binary64>) () ())
Outputs
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow a2 2) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th)))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th)))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th)))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (patch (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (patch (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (patch (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ a2 (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
3.0ms
a2
@-inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (cos th)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* a2 a2) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (sqrt 1/2) (cos th) (+ (* 1/24 (* th th)) -1/2))
2.0ms
a2
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (cos th)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* a2 a2) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (sqrt 1/2) (cos th) (+ (* 1/24 (* th th)) -1/2))
2.0ms
th
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (cos th)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* a2 a2) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (sqrt 1/2) (cos th) (+ (* 1/24 (* th th)) -1/2))
2.0ms
th
@-inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (cos th)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* a2 a2) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (sqrt 1/2) (cos th) (+ (* 1/24 (* th th)) -1/2))
2.0ms
a2
@0
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (cos th)) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* a2 a2) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (cos th)) (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (* a2 (/ a2 (sqrt 2))) (/ a2 (sqrt 2)) (sqrt 1/2) (cos th) (+ (* 1/24 (* th th)) -1/2))

simplify180.0ms (2.5%)

Memory
7.3MiB live, 318.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02558239
18347719
232137371
082116946
Stop Event
1×iter limit
1×node limit
Counts
492 → 492
Calls
Call 1
Inputs
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(* (pow a2 2) (sqrt 1/2))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a1 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a1 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th)))) (pow a1 2))
(/ (- (+ (* -1 (/ (* (pow a2 6) (sqrt 2)) (* (pow a1 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a2 4) (sqrt 2)) (* (pow a1 4) (cos th)))) (/ (* (pow a2 2) (sqrt 2)) (* (pow a1 2) (cos th))))) (pow a1 2))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (* (pow a1 2) (sqrt 2)))))
(/ (pow a1 2) (sqrt 2))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (pow a1 2) (+ (/ 1 (sqrt 2)) (/ (pow a2 2) (* (pow a1 2) (sqrt 2)))))
(* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))
(+ (* -1/2 (* (pow th 2) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
(+ (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))) (* (pow th 2) (+ (* -1/2 (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (* 1/24 (* (pow th 2) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))))))
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1
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-1/2
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(cos th)
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(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
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(pow a2 2)
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(* (pow a2 2) (* (cos th) (sqrt 1/2)))
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(pow a2 2)
(pow a2 2)
(pow a2 2)
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(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
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(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
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(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (sqrt 1/2))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/ (+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (/ (sqrt 2) (cos th))) (pow a2 2))
(/ (- (+ (/ (sqrt 2) (cos th)) (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th)))) (pow a2 2))
(/ (- (+ (* -1 (/ (* (pow a1 6) (sqrt 2)) (* (pow a2 6) (cos th)))) (/ (sqrt 2) (cos th))) (+ (* -1 (/ (* (pow a1 4) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (cos th))))) (pow a2 2))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ (pow a2 2) (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
(/ a2 (sqrt 2))
Outputs
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (sqrt 1/2))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (neg.f64 a1) (/.f64 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (*.f64 (/.f64 (*.f64 a1 a1) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 6 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th)))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (/.f64 a1 (pow.f64 a2 #s(literal 8 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 a2 #s(literal 6 binary64))))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th))))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ (sqrt 2) (* (pow a2 2) (cos th)))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2))
(+ (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 4) (cos th)))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (neg.f64 a1) (/.f64 (*.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 6) (cos th))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (-.f64 (*.f64 (/.f64 (*.f64 a1 a1) (cos.f64 th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 a2 #s(literal 6 binary64)))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th)))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(+ (* (pow a1 2) (- (* (pow a1 2) (- (* -1 (/ (* (pow a1 2) (sqrt 2)) (* (pow a2 8) (cos th)))) (* -1 (/ (sqrt 2) (* (pow a2 6) (cos th)))))) (/ (sqrt 2) (* (pow a2 4) (cos th))))) (/ (sqrt 2) (* (pow a2 2) (cos th))))
(fma.f64 (*.f64 #s(literal -1 binary64) (fma.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)) (fma.f64 a1 (/.f64 a1 (pow.f64 a2 #s(literal 8 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 a2 #s(literal 6 binary64))))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (pow.f64 a2 #s(literal 4 binary64)) (cos.f64 th))))) (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (*.f64 (cos.f64 th) a2) a2)))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)) (*.f64 a1 a1))) (*.f64 a1 a1))
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1
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(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) (/.f64 a1 (*.f64 a2 a2)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(/ a2 (sqrt 2))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))

rewrite177.0ms (2.4%)

Memory
-3.4MiB live, 359.5MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
042275
065275
1191269
21132269
08583269
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 700
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(fma.f64 a1 a1 (*.f64 a2 a2))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 a2 a2)
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(sqrt.f64 #s(literal 2 binary64))
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
#s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 1/2 binary64))
#s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64))
Outputs
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eval208.0ms (2.9%)

Memory
27.3MiB live, 456.6MiB allocated
Compiler

Compiled 36 675 to 3 365 computations (90.8% saved)

prune58.0ms (0.8%)

Memory
12.8MiB live, 174.7MiB allocated
Pruning

30 alts after pruning (29 fresh and 1 done)

PrunedKeptTotal
New1 536171 553
Fresh71219
Picked415
Done000
Total1 547301 577
Accuracy
100.0%
Counts
1 577 → 30
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶69.4%
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
▶69.4%
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
98.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th))))
68.9%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
14.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
69.4%
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
65.1%
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
65.2%
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
71.1%
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
69.4%
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
✓99.0%
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
99.0%
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
69.3%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
69.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
▶69.3%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
33.0%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
68.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
14.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
71.1%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
69.4%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
▶99.6%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
68.9%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
14.8%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
68.9%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
▶14.8%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
Compiler

Compiled 778 to 668 computations (14.1% saved)

simplify104.0ms (1.4%)

Memory
-19.9MiB live, 135.4MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
cost-diff0
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
cost-diff960
(fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
cost-diff1408
(/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
cost-diff1600
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
cost-diff0
(/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
cost-diff0
(sqrt.f64 #s(literal 2 binary64))
cost-diff384
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
cost-diff1024
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
cost-diff0
(*.f64 a2 a2)
cost-diff0
(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff0
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
cost-diff0
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
cost-diff0
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
cost-diff0
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
cost-diff0
#s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
cost-diff0
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
cost-diff0
(fma.f64 a1 a1 (*.f64 a2 a2))
cost-diff0
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
cost-diff0
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
cost-diff0
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046351
066333
1109321
2188321
3326315
4449315
5613315
6883311
71292311
83110305
97749305
08693304
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(cos.f64 th)
th
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
a1
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(*.f64 a1 a1)
a1
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
a2
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(cos.f64 th)
th
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
(sqrt.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
a1
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal -1/2 binary64))
#s(literal -1 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(fma.f64 a1 a1 (*.f64 a2 a2))
a1
(*.f64 a2 a2)
a2
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(*.f64 (fma.f64 (/.f64 a1 a2) a1 a2) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 a1 a1)
a1
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
a2
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 #s(literal 2 binary64) a2)

localize109.0ms (1.5%)

Memory
17.4MiB live, 229.8MiB allocated
Localize:

Found 20 expressions of interest:

NewMetricScoreProgram
accuracy0.39585878907376815
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
accuracy0.44921875
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
accuracy4.31661398638806
(fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
accuracy19.470213572182026
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
accuracy0.3636189133743209
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
accuracy0.607059338101916
(/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
accuracy1.0
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
accuracy19.463035929146272
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
accuracy0
(sqrt.f64 #s(literal 2 binary64))
accuracy0.0078125
(fma.f64 a1 a1 (*.f64 a2 a2))
accuracy0.20769501953688405
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
accuracy19.463035929146272
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
accuracy0.1328125
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
accuracy0.43359375
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
accuracy19.470213572182026
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
accuracy53.07385992843421
#s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
accuracy0
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
accuracy0.0078125
(fma.f64 a1 a1 (*.f64 a2 a2))
accuracy0.09832001953688403
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
accuracy0.1953125
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
Samples
80.0ms256×0valid
Compiler

Compiled 268 to 38 computations (85.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 58.0ms
ival-mult: 29.0ms (49.7% of total)
ival-div: 10.0ms (17.1% of total)
ival-add: 5.0ms (8.6% of total)
ival-cos: 5.0ms (8.6% of total)
ival-pow: 4.0ms (6.8% of total)
ival-sqrt: 3.0ms (5.1% of total)
exact: 1.0ms (1.7% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)

series51.0ms (0.7%)

Memory
2.0MiB live, 119.1MiB allocated
Counts
20 → 480
Calls
Call 1
Inputs
#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())
#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())
#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) (patch #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) #<representation binary64>) () ())
#s(alt (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) (patch (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) (patch (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())
#s(alt (*.f64 a2 a2) (patch (*.f64 a2 a2) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) (patch (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (patch (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))) #<representation binary64>) () ())
#s(alt (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (patch (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (patch (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) #<representation binary64>) () ())
#s(alt (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (patch (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #<representation binary64>) () ())
Outputs
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) (patch (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (pow a2 2) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (+ (pow a1 2) (pow a2 2)) (taylor 0 a1) (#s(alt (fma.f64 a1 a1 (*.f64 a2 a2)) (patch (fma.f64 a1 a1 (*.f64 a2 a2)) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (* (cos th) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2)))) (taylor 0 a1) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (sqrt 1/2)) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) (patch #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) (patch #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) (patch #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) (patch #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) (patch (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) (patch (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) (patch (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) #<representation binary64>) () ())) ())
#s(alt (* (pow a1 2) (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) (patch (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1) #<representation binary64>) () ())) ())
#s(alt (* a1 (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) (patch (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) #<representation binary64>) () ())) ())
#s(alt (* a1 (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) (patch (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) #<representation binary64>) () ())) ())
#s(alt (* a1 (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) (patch (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) #<representation binary64>) () ())) ())
#s(alt (* a1 (sqrt 1/2)) (taylor 0 a1) (#s(alt (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) (patch (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor 0 a1) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2))) (taylor 0 a1) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (cos th)) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th))) (taylor 0 a1) (#s(alt #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (patch #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) #<representation binary64>) () ())) ())
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#s(alt (* (cos th) (+ (pow a1 2) (pow a2 2))) (taylor inf th) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (cos th) (+ (pow a1 2) (pow a2 2))) (taylor inf th) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
#s(alt (* (cos th) (+ (pow a1 2) (pow a2 2))) (taylor inf th) (#s(alt (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (patch (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (taylor inf th) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (taylor inf th) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (taylor inf th) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2)))) (taylor inf th) (#s(alt #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) (patch #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2)) (taylor inf th) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2)) (taylor inf th) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2)) (taylor inf th) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2)) (taylor inf th) (#s(alt (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) (patch (/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (/ (pow a2 2) (sqrt 2)) (taylor -inf a2) (#s(alt (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (patch (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (patch (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (patch (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) (patch (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))) #<representation binary64>) () ())) ())
#s(alt (* a2 (sqrt 2)) (taylor -inf a2) (#s(alt (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (patch (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))) (taylor -inf a2) (#s(alt (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (patch (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))) (taylor -inf a2) (#s(alt (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (patch (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2)))))) (taylor -inf a2) (#s(alt (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (patch (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) #<representation binary64>) () ())) ())
#s(alt (/ (* (pow a2 2) (cos th)) (sqrt 2)) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) #<representation binary64>) () ())) ())
#s(alt (* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2))))) (taylor -inf a2) (#s(alt #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) (patch #s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) a2) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) a2) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) a2) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 2) a2) (taylor -inf a2) (#s(alt (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (patch (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) #<representation binary64>) () ())) ())
Calls

9 calls:

TimeVariablePointExpression
4.0ms
a2
@0
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* a2 a2) (/ (/ -1 (sqrt 2)) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ -1 (sqrt 2)) (sqrt 2) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 2) (/ (sqrt 2) a2)) (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (sqrt 2) a2))
4.0ms
a2
@-inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* a2 a2) (/ (/ -1 (sqrt 2)) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ -1 (sqrt 2)) (sqrt 2) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 2) (/ (sqrt 2) a2)) (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (sqrt 2) a2))
3.0ms
a1
@0
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* a2 a2) (/ (/ -1 (sqrt 2)) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ -1 (sqrt 2)) (sqrt 2) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 2) (/ (sqrt 2) a2)) (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (sqrt 2) a2))
3.0ms
a1
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* a2 a2) (/ (/ -1 (sqrt 2)) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ -1 (sqrt 2)) (sqrt 2) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 2) (/ (sqrt 2) a2)) (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (sqrt 2) a2))
3.0ms
a2
@inf
((* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 1/2)) (* (+ (* a1 a1) (* a2 a2)) (cos th)) (+ (* a1 a1) (* a2 a2)) (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (* (* (sqrt 1/2) a1) a1) (* (sqrt 1/2) a1) (/ (* (+ (* a2 a2) (* a1 a1)) (cos th)) (sqrt 2)) (* (+ (* a2 a2) (* a1 a1)) (cos th)) (* a2 a2) (/ (/ -1 (sqrt 2)) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/ -1 (sqrt 2)) (sqrt 2) (/ -1 (* (+ (* a2 a2) (* a1 a1)) (cos th))) (* (sqrt 2) (/ (sqrt 2) a2)) (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/ (sqrt 2) a2))

simplify182.0ms (2.5%)

Memory
2.8MiB live, 310.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02667379
18596877
231296699
085446288
Stop Event
1×iter limit
1×node limit
Counts
480 → 480
Calls
Call 1
Inputs
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(pow a2 2)
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(+ (pow a1 2) (pow a2 2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(* (pow a2 2) (sqrt 1/2))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (sqrt 1/2))
(* a1 (sqrt 1/2))
(* a1 (sqrt 1/2))
(* a1 (sqrt 1/2))
(* a1 (sqrt 1/2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(* (pow a2 2) (cos th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ -1 (* (pow a2 2) (cos th)))
(- (/ (pow a1 2) (* (pow a2 4) (cos th))) (/ 1 (* (pow a2 2) (cos th))))
(- (* (pow a1 2) (+ (* -1 (/ (pow a1 2) (* (pow a2 6) (cos th)))) (/ 1 (* (pow a2 4) (cos th))))) (/ 1 (* (pow a2 2) (cos th))))
(- (* (pow a1 2) (+ (* (pow a1 2) (- (/ (pow a1 2) (* (pow a2 8) (cos th))) (/ 1 (* (pow a2 6) (cos th))))) (/ 1 (* (pow a2 4) (cos th))))) (/ 1 (* (pow a2 2) (cos th))))
(/ (pow a2 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(* a2 (sqrt 2))
(+ (* a2 (sqrt 2)) (/ (* (pow a1 2) (sqrt 2)) a2))
(+ (* a2 (sqrt 2)) (/ (* (pow a1 2) (sqrt 2)) a2))
(+ (* a2 (sqrt 2)) (/ (* (pow a1 2) (sqrt 2)) a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (cos th))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(* (pow a1 2) (+ (cos th) (/ (* (pow a2 2) (cos th)) (pow a1 2))))
(pow a1 2)
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (+ 1 (/ (pow a2 2) (pow a1 2))))
(* (pow a1 2) (* (cos th) (sqrt 1/2)))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a2 2) (* (cos th) (sqrt 1/2))) (pow a1 2))))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (+ (sqrt 1/2) (/ (* (pow a2 2) (sqrt 1/2)) (pow a1 2))))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (sqrt 1/2))
(* (pow a1 2) (sqrt 1/2))
(* a1 (sqrt 1/2))
(* a1 (sqrt 1/2))
(* a1 (sqrt 1/2))
(* a1 (sqrt 1/2))
(/ (* (pow a1 2) (cos th)) (sqrt 2))
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(* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
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(* (cos th) (+ (pow a1 2) (pow a2 2)))
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(* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
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(* (cos th) (* (sqrt 1/2) (+ (pow a1 2) (pow a2 2))))
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(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
(/ (* (cos th) (+ (pow a1 2) (pow a2 2))) (sqrt 2))
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(pow a1 2)
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(pow a2 2)
(pow a2 2)
(pow a2 2)
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(- (/ (pow a2 2) (* (pow a1 4) (cos th))) (/ 1 (* (pow a1 2) (cos th))))
(- (* (pow a2 2) (+ (* -1 (/ (pow a2 2) (* (pow a1 6) (cos th)))) (/ 1 (* (pow a1 4) (cos th))))) (/ 1 (* (pow a1 2) (cos th))))
(- (* (pow a2 2) (+ (* (pow a2 2) (- (/ (pow a2 2) (* (pow a1 8) (cos th))) (/ 1 (* (pow a1 6) (cos th))))) (/ 1 (* (pow a1 4) (cos th))))) (/ 1 (* (pow a1 2) (cos th))))
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow a1 2) (sqrt 2))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(/ (* (pow a1 2) (sqrt 2)) a2)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a2)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a2)
(/ (+ (* (pow a1 2) (sqrt 2)) (* (pow a2 2) (sqrt 2))) a2)
(/ (* (pow a1 2) (cos th)) (sqrt 2))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (sqrt 1/2))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ -1 (* (pow a2 2) (cos th)))
(/ (- (/ (pow a1 2) (* (pow a2 2) (cos th))) (/ 1 (cos th))) (pow a2 2))
(/ (- (* -1 (/ (pow a1 4) (* (pow a2 4) (cos th)))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (cos th)))) (/ 1 (cos th)))) (pow a2 2))
(/ (- (/ (pow a1 6) (* (pow a2 6) (cos th))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (cos th)))) (+ (/ 1 (cos th)) (/ (pow a1 4) (* (pow a2 4) (cos th)))))) (pow a2 2))
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* a2 (sqrt 2))
(* a2 (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* a2 (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(* a2 (+ (sqrt 2) (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(* (pow a2 2) (sqrt 1/2))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (cos th))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(pow a2 2)
(pow a2 2)
(pow a2 2)
(pow a2 2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ -1 (* (pow a2 2) (cos th)))
(/ (- (/ (pow a1 2) (* (pow a2 2) (cos th))) (/ 1 (cos th))) (pow a2 2))
(/ (- (* -1 (/ (pow a1 4) (* (pow a2 4) (cos th)))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (cos th)))) (/ 1 (cos th)))) (pow a2 2))
(/ (- (/ (pow a1 6) (* (pow a2 6) (cos th))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (cos th)))) (+ (/ 1 (cos th)) (/ (pow a1 4) (* (pow a2 4) (cos th)))))) (pow a2 2))
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow (sqrt 2) 2) a2)
(/ (pow a2 2) (sqrt 2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(* a2 (sqrt 2))
(* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))))
(* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))))
(* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
(/ (sqrt 2) a2)
Outputs
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(pow a2 2)
(*.f64 a2 a2)
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(+ (pow a1 2) (pow a2 2))
(fma.f64 a1 a1 (*.f64 a2 a2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(+ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (* (pow a2 2) (* (cos th) (sqrt 1/2))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th))
(* (pow a2 2) (sqrt 1/2))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* (pow a1 2) (sqrt 1/2)) (* (pow a2 2) (sqrt 1/2)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))
(* (pow a1 2) (sqrt 1/2))
(*.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a1)
(* (pow a1 2) (sqrt 1/2))
(*.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a1)
(* (pow a1 2) (sqrt 1/2))
(*.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a1)
(* (pow a1 2) (sqrt 1/2))
(*.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a1)
(* a1 (sqrt 1/2))
(*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64)))
(* a1 (sqrt 1/2))
(*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64)))
(* a1 (sqrt 1/2))
(*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64)))
(* a1 (sqrt 1/2))
(*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64)))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(+ (* (pow a1 2) (cos th)) (* (pow a2 2) (cos th)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (* (pow a1 2) (cos th)) (sqrt 2)) (/ (* (pow a2 2) (cos th)) (sqrt 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(/ -1 (* (pow a2 2) (cos th)))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 a2 a2)) (cos.f64 th))
(- (/ (pow a1 2) (* (pow a2 4) (cos th))) (/ 1 (* (pow a2 2) (cos th))))
(fma.f64 (/.f64 a1 (pow.f64 a2 #s(literal 4 binary64))) (/.f64 a1 (cos.f64 th)) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 a2 a2)) (cos.f64 th)))
(- (* (pow a1 2) (+ (* -1 (/ (pow a1 2) (* (pow a2 6) (cos th)))) (/ 1 (* (pow a2 4) (cos th))))) (/ 1 (* (pow a2 2) (cos th))))
(fma.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (*.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))) #s(literal -1 binary64) (fma.f64 (/.f64 a1 (pow.f64 a2 #s(literal 4 binary64))) (/.f64 a1 (cos.f64 th)) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 a2 a2)) (cos.f64 th))))
(- (* (pow a1 2) (+ (* (pow a1 2) (- (/ (pow a1 2) (* (pow a2 8) (cos th))) (/ 1 (* (pow a2 6) (cos th))))) (/ 1 (* (pow a2 4) (cos th))))) (/ 1 (* (pow a2 2) (cos th))))
(fma.f64 (pow.f64 a1 #s(literal 4 binary64)) (fma.f64 (/.f64 a1 (pow.f64 a2 #s(literal 8 binary64))) (/.f64 a1 (cos.f64 th)) (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 a2 #s(literal 6 binary64))) (cos.f64 th))) (fma.f64 (/.f64 a1 (pow.f64 a2 #s(literal 4 binary64))) (/.f64 a1 (cos.f64 th)) (/.f64 (/.f64 #s(literal -1 binary64) (*.f64 a2 a2)) (cos.f64 th))))
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(+ (/ (pow a1 2) (sqrt 2)) (/ (pow a2 2) (sqrt 2)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2)))
(* a2 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(+ (* a2 (sqrt 2)) (/ (* (pow a1 2) (sqrt 2)) a2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 (*.f64 a1 a1) a2) a2))
(+ (* a2 (sqrt 2)) (/ (* (pow a1 2) (sqrt 2)) a2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 (*.f64 a1 a1) a2) a2))
(+ (* a2 (sqrt 2)) (/ (* (pow a1 2) (sqrt 2)) a2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (+.f64 (/.f64 (*.f64 a1 a1) a2) a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
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(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(pow a2 2)
(*.f64 a2 a2)
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (+ 1 (/ (pow a1 2) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (*.f64 a2 a2))
(* (pow a2 2) (* (cos th) (sqrt 1/2)))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (+ (* (cos th) (sqrt 1/2)) (/ (* (pow a1 2) (* (cos th) (sqrt 1/2))) (pow a2 2))))
(*.f64 (fma.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th) (/.f64 (*.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th))) (*.f64 a2 a2))) (*.f64 a2 a2))
(* (pow a2 2) (sqrt 1/2))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 a2 a2))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 a2 a2))
(* (pow a2 2) (+ (sqrt 1/2) (/ (* (pow a1 2) (sqrt 1/2)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 a1 (sqrt.f64 #s(literal 1/2 binary64))) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 a2 a2))
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (cos th))
(*.f64 (*.f64 (cos.f64 th) a2) a2)
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(* (pow a2 2) (+ (cos th) (/ (* (pow a1 2) (cos th)) (pow a2 2))))
(*.f64 (fma.f64 (/.f64 (*.f64 (cos.f64 th) a1) a2) (/.f64 a1 a2) (cos.f64 th)) (*.f64 a2 a2))
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(pow a2 2)
(*.f64 a2 a2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ -1 (* (pow a2 2) (cos th)))
(/.f64 (/.f64 #s(literal -1 binary64) (*.f64 a2 a2)) (cos.f64 th))
(/ (- (/ (pow a1 2) (* (pow a2 2) (cos th))) (/ 1 (cos th))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 a1 (*.f64 (cos.f64 th) a2)) (/.f64 a1 a2) (/.f64 #s(literal -1 binary64) (cos.f64 th))) (*.f64 a2 a2))
(/ (- (* -1 (/ (pow a1 4) (* (pow a2 4) (cos th)))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (cos th)))) (/ 1 (cos th)))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (/.f64 #s(literal -1 binary64) (cos.f64 th))) (*.f64 a2 a2))
(/ (- (/ (pow a1 6) (* (pow a2 6) (cos th))) (+ (* -1 (/ (pow a1 2) (* (pow a2 2) (cos th)))) (+ (/ 1 (cos th)) (/ (pow a1 4) (* (pow a2 4) (cos th)))))) (pow a2 2))
(/.f64 (fma.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)) (-.f64 (/.f64 (pow.f64 a1 #s(literal 4 binary64)) (pow.f64 a2 #s(literal 4 binary64))) (*.f64 (/.f64 a1 a2) (/.f64 a1 a2))) (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 th)) (/.f64 (pow.f64 a1 #s(literal 6 binary64)) (*.f64 (pow.f64 a2 #s(literal 6 binary64)) (cos.f64 th))))) (*.f64 a2 a2))
(/ (pow (sqrt 2) 2) a2)
(/.f64 #s(literal 2 binary64) a2)
(/ (pow (sqrt 2) 2) a2)
(/.f64 #s(literal 2 binary64) a2)
(/ (pow (sqrt 2) 2) a2)
(/.f64 #s(literal 2 binary64) a2)
(/ (pow (sqrt 2) 2) a2)
(/.f64 #s(literal 2 binary64) a2)
(/ (pow a2 2) (sqrt 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ 1 (sqrt 2)) (/ (pow a1 2) (* (pow a2 2) (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 a1 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a1 a2) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* a2 (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 2 binary64))) a2)
(* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 2 binary64))) a2)
(* -1 (* a2 (+ (* -1 (sqrt 2)) (* -1 (/ (* (pow a1 2) (sqrt 2)) (pow a2 2))))))
(*.f64 (fma.f64 (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) a1) a2) (/.f64 a1 a2) (sqrt.f64 #s(literal 2 binary64))) a2)
(/ (* (pow a2 2) (cos th)) (sqrt 2))
(/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64)))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(* (pow a2 2) (+ (/ (cos th) (sqrt 2)) (/ (* (pow a1 2) (cos th)) (* (pow a2 2) (sqrt 2)))))
(*.f64 (*.f64 (fma.f64 (/.f64 a1 a2) (/.f64 a1 a2) #s(literal 1 binary64)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (*.f64 a2 a2))
(/ (sqrt 2) a2)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(/ (sqrt 2) a2)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(/ (sqrt 2) a2)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
(/ (sqrt 2) a2)
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)

rewrite194.0ms (2.7%)

Memory
-1.6MiB live, 317.6MiB allocated
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
046283
066266
1208252
21407252
08259252
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
20 → 440
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
(*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64)))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th))
(fma.f64 a1 a1 (*.f64 a2 a2))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1))
(*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1)
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(*.f64 a2 a2)
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
(/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)))
(fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)
Outputs
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eval159.0ms (2.2%)

Memory
-6.7MiB live, 387.3MiB allocated
Compiler

Compiled 27 012 to 2 446 computations (90.9% saved)

prune81.0ms (1.1%)

Memory
-10.6MiB live, 244.7MiB allocated
Pruning

40 alts after pruning (37 fresh and 3 done)

PrunedKeptTotal
New1 252191 271
Fresh61824
Picked325
Done011
Total1 261401 301
Accuracy
100.0%
Counts
1 301 → 40
Alt Table
Click to see full alt table
StatusAccuracyProgram
41.0%
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
68.8%
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
14.8%
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
71.1%
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
99.0%
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 2 binary64)))
68.9%
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
14.8%
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
98.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th))))
14.8%
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
69.4%
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
65.1%
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
65.2%
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
71.1%
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓99.0%
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
69.3%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
69.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
69.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
69.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
69.2%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
33.0%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
69.3%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
68.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
69.4%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
68.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
14.8%
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
71.1%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
69.4%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
✓99.6%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
68.9%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
14.8%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
71.1%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
99.0%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
68.9%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
✓14.8%
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
Compiler

Compiled 1 670 to 729 computations (56.3% saved)

regimes204.0ms (2.8%)

Memory
7.0MiB live, 316.2MiB allocated
Counts
76 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (*.f64 (cos.f64 th) a2) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (*.f64 (*.f64 (cos.f64 th) a2) a2) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 #s(approx (/ (+ (* a2 a2) (* a1 a1)) (sqrt 2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))) (cos.f64 th))
(*.f64 (/.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) (cos.f64 th))
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (cos.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 (*.f64 a1 (cos.f64 th)) (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) #s(approx (* (/ (cos th) (sqrt 2)) (* a2 a2)) (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal -1/2 binary64) (*.f64 th th)) a2 a2))))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 #s(approx (+ (* a2 a2) (* a1 a1)) (*.f64 a2 a2)) (cos.f64 th)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1) (*.f64 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2) (cos.f64 th)))
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
(*.f64 (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 (cos.f64 th) #s(literal -1 binary64))))
(/.f64 (/.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
Calls

8 calls:

50.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
23.0ms
a2
22.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
22.0ms
a1
22.0ms
th
Results
AccuracySegmentsBranch
99.7%1a1
99.7%1a2
99.7%1th
99.7%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
99.7%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
99.7%1(cos.f64 th)
99.7%1(*.f64 a1 a1)
99.7%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes181.0ms (2.5%)

Memory
-21.5MiB live, 232.2MiB allocated
Counts
55 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

38.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
31.0ms
th
28.0ms
a2
20.0ms
(*.f64 a2 a2)
17.0ms
(cos.f64 th)
Results
AccuracySegmentsBranch
99.6%1a1
99.6%1a2
99.6%1th
99.6%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
99.6%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
99.6%1(cos.f64 th)
99.6%1(*.f64 a1 a1)
99.6%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes164.0ms (2.3%)

Memory
20.6MiB live, 253.9MiB allocated
Counts
54 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (cos.f64 th)) (*.f64 a2 a2)))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
Calls

8 calls:

46.0ms
(cos.f64 th)
21.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
18.0ms
a1
17.0ms
th
17.0ms
(*.f64 a2 a2)
Results
AccuracySegmentsBranch
99.0%1a1
99.0%1a2
99.0%1th
99.0%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
99.0%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
99.0%1(cos.f64 th)
99.0%1(*.f64 a1 a1)
99.0%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes123.0ms (1.7%)

Memory
15.6MiB live, 260.9MiB allocated
Counts
52 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

17.0ms
th
16.0ms
(*.f64 a2 a2)
16.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
16.0ms
a2
15.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Results
AccuracySegmentsBranch
99.0%1a1
99.0%1a2
99.0%1th
99.0%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
99.0%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
99.0%1(cos.f64 th)
99.0%1(*.f64 a1 a1)
99.0%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes119.0ms (1.6%)

Memory
-26.3MiB live, 255.8MiB allocated
Counts
51 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
Calls

8 calls:

17.0ms
(cos.f64 th)
15.0ms
a1
14.0ms
a2
14.0ms
th
14.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
99.0%1a1
99.0%1a2
99.0%1th
99.0%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
99.0%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
99.0%1(cos.f64 th)
99.0%1(*.f64 a1 a1)
99.0%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes112.0ms (1.5%)

Memory
21.3MiB live, 218.4MiB allocated
Counts
50 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

16.0ms
th
15.0ms
a1
13.0ms
(*.f64 a2 a2)
13.0ms
a2
13.0ms
(*.f64 a1 a1)
Results
AccuracySegmentsBranch
99.0%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
99.0%1(cos.f64 th)
99.0%1a1
99.0%1a2
99.0%1th
99.0%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
99.0%1(*.f64 a1 a1)
99.0%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes148.0ms (2%)

Memory
-9.4MiB live, 181.3MiB allocated
Counts
49 → 2
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
(/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 2 binary64))) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (/.f64 #s(approx (cos th) (fma.f64 (fma.f64 (*.f64 th th) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (*.f64 (neg.f64 a2) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))) a2)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 th th) #s(literal 1 binary64)) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) #s(approx (cos th) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) (*.f64 th th) #s(literal 1 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (fma.f64 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))) a1 (*.f64 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))) a2)) (fma.f64 (*.f64 (fma.f64 #s(literal 1/24 binary64) (*.f64 th th) #s(literal -1/2 binary64)) th) th #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 (fma.f64 (/.f64 a2 a1) (/.f64 a2 a1) #s(literal 1 binary64)) (*.f64 a1 a1))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 (neg.f64 a2) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1))) (*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 #s(approx (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) a2))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 th th)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (*.f64 (fma.f64 (/.f64 (*.f64 a1 a1) a2) (sqrt.f64 #s(literal 2 binary64)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 a2 (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (neg.f64 a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) a2))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 a2) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (/.f64 (fma.f64 a2 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2)) (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) a2) (/.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 a1 a1)))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

43.0ms
(*.f64 a2 a2)
21.0ms
(cos.f64 th)
16.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
15.0ms
a2
14.0ms
a1
Results
AccuracySegmentsBranch
73.7%2a1
74.5%2a2
71.1%1th
81.1%2(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
80.5%2(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
80.5%2(cos.f64 th)
72.7%2(*.f64 a1 a1)
74.5%2(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes61.0ms (0.8%)

Memory
-14.6MiB live, 72.2MiB allocated
Counts
19 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (+ (* (/ a1 (sqrt 2)) a1) (* (/ a2 (sqrt 2)) a2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a1 (/.f64 a1 (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) #s(approx (/ (+ (* (* a1 a1) (/ (sqrt 2) a2)) (* (sqrt 2) a2)) (* (sqrt 2) (/ (sqrt 2) a2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1))) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (/ 1 (/ (sqrt 2) (* (+ (* a2 a2) (* a1 a1)) (cos th)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 2 binary64))))
(/.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 2 binary64)))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 a1 a1 (*.f64 a2 a2))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 2 binary64)) #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)))))
#s(approx (+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2))) (*.f64 (neg.f64 (fma.f64 a2 a2 (*.f64 a1 a1))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 2 binary64))) (neg.f64 #s(approx (* (+ (* a2 a2) (* a1 a1)) (cos th)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

16.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
10.0ms
th
6.0ms
a1
6.0ms
a2
5.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Results
AccuracySegmentsBranch
69.4%1th
69.4%1(*.f64 a1 a1)
69.4%1a1
69.4%1a2
69.4%1(*.f64 a2 a2)
69.4%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
69.4%1(cos.f64 th)
69.4%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes21.0ms (0.3%)

Memory
-2.7MiB live, 35.8MiB allocated
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

4.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
2.0ms
a2
2.0ms
a1
2.0ms
th
2.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
69.4%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
69.4%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
69.4%1(cos.f64 th)
69.4%1th
69.4%1a1
69.4%1(*.f64 a1 a1)
69.4%1a2
69.4%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes17.0ms (0.2%)

Memory
37.5MiB live, 37.5MiB allocated
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
Calls

8 calls:

2.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
2.0ms
a1
2.0ms
a2
2.0ms
th
2.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
Results
AccuracySegmentsBranch
68.9%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
68.9%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
68.9%1(cos.f64 th)
68.9%1th
68.9%1a1
68.9%1(*.f64 a1 a1)
68.9%1a2
68.9%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes17.0ms (0.2%)

Memory
-3.2MiB live, 35.4MiB allocated
Counts
3 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
Calls

8 calls:

3.0ms
(*.f64 a2 a2)
2.0ms
a1
2.0ms
a2
2.0ms
th
2.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
Results
AccuracySegmentsBranch
68.9%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
68.9%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
68.9%1(cos.f64 th)
68.9%1th
68.9%1a1
68.9%1(*.f64 a1 a1)
68.9%1a2
68.9%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

regimes13.0ms (0.2%)

Memory
-5.7MiB live, 31.7MiB allocated
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts
1 → 1
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
Calls

8 calls:

3.0ms
a2
1.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
1.0ms
a1
1.0ms
(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
1.0ms
th
Results
AccuracySegmentsBranch
14.8%1(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)))
14.8%1(/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64)))
14.8%1(cos.f64 th)
14.8%1th
14.8%1a1
14.8%1(*.f64 a1 a1)
14.8%1a2
14.8%1(*.f64 a2 a2)
Compiler

Compiled 35 to 40 computations (-14.3% saved)

bsearch1.0ms (0%)

Memory
1.4MiB live, 1.4MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-4.6659944579954894e-133
-8.936077099482395e-173
Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify27.0ms (0.4%)

Memory
-25.4MiB live, 58.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
070417
195417
Stop Event
1×saturated
Calls
Call 1
Inputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #s(literal -2557336412418861/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448 binary64)) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))
Outputs
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 (cos.f64 th) (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)) (cos.f64 th)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (*.f64 (cos.f64 th) a2) a2)) (sqrt.f64 #s(literal 1/2 binary64))))
(if (<=.f64 (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2))) #s(literal -2557336412418861/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448 binary64)) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64)))))
(if (<=.f64 (+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))) (*.f64 a2 a2)) (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 #s(literal 2 binary64))))) #s(literal -2557336412418861/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448 binary64)) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (* (+ (* a1 a1) (* a2 a2)) (cos th)) (*.f64 (fma.f64 (*.f64 th th) #s(literal -1/2 binary64) #s(literal 1 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64)))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (fma.f64 a1 a1 (*.f64 a2 a2))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) (*.f64 #s(approx (+ (* a1 a1) (* a2 a2)) (*.f64 a2 a2)) (sqrt.f64 #s(literal 1/2 binary64))))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a2) a2)))
#s(approx (* (pow 2 -1/2) (* (+ (* a2 a2) (* a1 a1)) (cos th))) #s(approx (* (+ (* a1 a1) (* a2 a2)) (sqrt 1/2)) (*.f64 (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) a1) a1)))

soundness907.0ms (12.5%)

Memory
50.9MiB live, 713.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
042275
065275
1191269
21132269
08583269
02966646
19876098
238276063
080915710
01244
02038
15838
241138
3733138
0843437
02558239
18347719
232137371
082116946
02667379
18596877
231296699
085446288
Stop Event
1×fuel
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 790 to 484 computations (38.7% saved)

preprocess160.0ms (2.2%)

Memory
-24.8MiB live, 209.8MiB allocated
Remove

(abs a2)

(abs th)

Compiler

Compiled 990 to 670 computations (32.3% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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