Details

Time bar (total: 8.7s)

analyze918.0ms (10.6%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.8%0.2%0%0%0%0
0%0%99.8%0.2%0%0%0%1
0%0%99.8%0.2%0%0%0%2
0%0%99.8%0.2%0%0%0%3
0%0%99.8%0.2%0%0%0%4
0%0%99.8%0.2%0%0%0%5
0%0%99.8%0.2%0%0%0%6
0%0%99.8%0.2%0%0%0%7
0%0%99.8%0.2%0%0%0%8
0%0%99.8%0.2%0%0%0%9
0%0%99.8%0.2%0%0%0%10
0.8%0.8%99%0.2%0%0%0%11
1.2%1.2%98.6%0.2%0%0%0%12
Compiler

Compiled 25 to 18 computations (28% saved)

sample7.4s (85.5%)

Results
5.6s5609×body1024valid
916.0ms1504×body512valid
615.0ms288×body2048valid
278.0ms855×body256valid
3.0msbody1024infinite
1.0msbody512infinite
Bogosity

preprocess164.0ms (1.9%)

Algorithm
egg-herbie
Rules
1574×fma-def
1388×associate--r+
1128×distribute-lft-in
1098×distribute-lft-neg-in
1026×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
094627
1187627
2300627
3383627
4443627
5655627
61049627
71373627
82186627
93016627
103933627
115074627
126099627
137074627
055
155
Stop Event
unsound
node limit
Calls
Call 1
Inputs
0
1
2
3
4
Outputs
0
1
2
1
3
4
3
Call 2
Inputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 R lambda2))))) lambda1)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R))))) lambda2)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 R) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 R) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) phi1)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 R)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 R)) (cos.f64 (-.f64 lambda1 lambda2))))) phi2)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 (-.f64 phi1 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda1)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda1)) (cos.f64 (-.f64 phi2 lambda2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda2) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 phi1))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi2))))) R)
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi2) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
Outputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 R lambda2))))) lambda1)
(*.f64 lambda1 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 R lambda2)))))))
(*.f64 lambda1 (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 R lambda2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 lambda1 (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 R lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R))))) lambda2)
(*.f64 lambda2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 R))))))
(*.f64 lambda2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 R)))))))
(*.f64 lambda2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 R)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 R) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 R) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) phi1)
(*.f64 phi1 (acos.f64 (fma.f64 (sin.f64 R) (sin.f64 phi2) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 R))))))
(*.f64 phi1 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 R)) (*.f64 (sin.f64 phi2) (sin.f64 R)))))
(*.f64 phi1 (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 R)) (*.f64 (sin.f64 phi2) (sin.f64 R)))))
(*.f64 phi1 (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 R) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 R))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 R)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 R)) (cos.f64 (-.f64 lambda1 lambda2))))) phi2)
(*.f64 phi2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 R) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 R))))))
(*.f64 phi2 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 R) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 R))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 (-.f64 phi1 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 phi2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2))) (*.f64 (sin.f64 phi2) (sin.f64 lambda1)))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda1) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 lambda1)) (cos.f64 (-.f64 phi1 lambda2))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 (-.f64 phi1 lambda2))) (*.f64 (sin.f64 phi2) (sin.f64 lambda1)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda1)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda1)) (cos.f64 (-.f64 phi2 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 lambda1) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 lambda1) (cos.f64 (-.f64 phi2 lambda2)))))))
(*.f64 R (acos.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda1)) (cos.f64 (-.f64 phi2 lambda2)) (*.f64 (sin.f64 phi1) (sin.f64 lambda1)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 lambda2) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 phi1))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 phi2) (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 phi1)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda2) (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 phi1)) (cos.f64 lambda2)) (cos.f64 phi2)))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda2) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda2) (cos.f64 (-.f64 lambda1 phi1)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi2) (sin.f64 lambda2) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda2) (cos.f64 (-.f64 phi1 lambda1)))))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 lambda2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 lambda2)) (cos.f64 (-.f64 lambda1 phi2))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 phi2)))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 lambda2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 lambda2) (cos.f64 (-.f64 phi2 lambda1)))))))
(*.f64 R (acos.f64 (fma.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 phi2))) (*.f64 (sin.f64 phi1) (sin.f64 lambda2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi2) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))
(*.f64 R (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify20.0ms (0.2%)

Algorithm
egg-herbie
Rules
96×fma-def
48×associate--r+
40×*-commutative
38×associate-+l-
32×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02057
13157
24657
35757
46657
58457
613657
718157
822557
927357
1029757
1129957
Stop Event
saturated
Counts
1 → 3
Calls
Call 1
Inputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
Outputs
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))) R)

eval2.0ms (0%)

Compiler

Compiled 60 to 27 computations (55% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New123
Fresh011
Picked000
Done000
Total134
Error
72.8%
Counts
4 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
72.8%
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
72.8%
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
Compiler

Compiled 47 to 33 computations (29.8% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
99.7%
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
99.5%
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
97.5%
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
95.2%
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 97 to 17 computations (82.5% saved)

series14.0ms (0.2%)

Counts
4 → 132
Calls

39 calls:

TimeVariablePointExpression
3.0ms
phi2
@0
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms
phi2
@inf
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms
phi1
@inf
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms
phi1
@0
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms
phi2
@inf
(*.f64 (sin.f64 phi1) (sin.f64 phi2))

rewrite109.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
1678×associate-*r/
492×associate-+l+
474×add-sqr-sqrt
470×pow1
470×*-un-lft-identity
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020134
1434134
25947134
Stop Event
node limit
Calls
Call 1
Inputs
(cos.f64 (-.f64 lambda1 lambda2))
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
Outputs
((((x +.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (((x +.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))))) (((x +.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 1) (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 1)))) (((x +.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 1) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 1)))) (((x -.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) 1))) (((x -.f64 (*.f64 (cos.f64 lambda1) (cos.f64 (neg.f64 lambda2))) (*.f64 (sin.f64 lambda1) (sin.f64 (neg.f64 lambda2)))))) (((x *.f64 (cos.f64 (-.f64 lambda1 lambda2)) 1))) (((x *.f64 1 (cos.f64 (-.f64 lambda1 lambda2))))) (((x *.f64 (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (((x *.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2)))) (((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (((x /.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (((x /.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (((x /.f64 (*.f64 1 (-.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (((x /.f64 (*.f64 1 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (((x pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 1))) (((x pow.f64 (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2))) (((x pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3))) (((x pow.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3) 1/3))) (((x sqrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 2)))) (((x log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (((x log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))))) (((x cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))) (((x expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (((x exp.f64 (log.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (((x exp.f64 (*.f64 (log.f64 (cos.f64 (-.f64 lambda1 lambda2))) 1)))) (((x log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) (((x fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
((((x +.f64 (*.f64 (PI.f64) 1/2) (neg.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x +.f64 (neg.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (*.f64 (PI.f64) 1/2)))) (((x +.f64 (-.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (((x -.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (((x -.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) 1))) (((x *.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 1))) (((x *.f64 1 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (((x *.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x *.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2)))) (((x *.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x /.f64 (-.f64 (*.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (*.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x /.f64 (-.f64 (pow.f64 (*.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)) (+.f64 (*.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (+.f64 (*.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (*.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) (((x /.f64 (*.f64 1 (-.f64 (*.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (*.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (+.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x /.f64 (*.f64 1 (-.f64 (pow.f64 (*.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3))) (+.f64 (*.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (+.f64 (*.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (*.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) (((x pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 1))) (((x pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 2))) (((x pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 3))) (((x pow.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) 1/3))) (((x sqrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2)))) (((x log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) (((x cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3)))) (((x expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x exp.f64 (log.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x exp.f64 (*.f64 (log.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) 1)))) (((x log1p.f64 (expm1.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))
((((x -.f64 (exp.f64 (log1p.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))) 1))) (((x /.f64 (*.f64 R (-.f64 (*.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (*.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (+.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x /.f64 (*.f64 R (-.f64 (pow.f64 (*.f64 (PI.f64) 1/2) 3) (pow.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3))) (+.f64 (*.f64 (*.f64 (PI.f64) 1/2) (*.f64 (PI.f64) 1/2)) (+.f64 (*.f64 (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) (*.f64 (*.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) (((x pow.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 1))) (((x pow.f64 (sqrt.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) 2))) (((x pow.f64 (cbrt.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) 3))) (((x pow.f64 (pow.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 3) 1/3))) (((x sqrt.f64 (pow.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 2)))) (((x log.f64 (pow.f64 (exp.f64 R) (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))))) (((x cbrt.f64 (pow.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R) 3)))) (((x cbrt.f64 (*.f64 (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3) (pow.f64 R 3))))) (((x cbrt.f64 (*.f64 (pow.f64 R 3) (pow.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 3))))) (((x expm1.f64 (log1p.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))))) (((x exp.f64 (log.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))))) (((x exp.f64 (*.f64 (log.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) 1)))) (((x log1p.f64 (expm1.f64 (*.f64 (acos.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))))))
((((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 1))) (((x -.f64 (/.f64 (cos.f64 (-.f64 phi1 phi2)) 2) (/.f64 (cos.f64 (+.f64 phi1 phi2)) 2)))) (((x /.f64 1 (/.f64 2 (-.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi1 phi2))))))) (((x /.f64 (-.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi1 phi2))) 2))) (((x /.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi1 phi2)))) -2))) (((x /.f64 (-.f64 (cos.f64 (-.f64 phi2 phi1)) (cos.f64 (+.f64 phi1 phi2))) 2))) (((x /.f64 (*.f64 1 (neg.f64 (-.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi1 phi2))))) -2))) (((x /.f64 (*.f64 1 (-.f64 (cos.f64 (-.f64 phi2 phi1)) (cos.f64 (+.f64 phi1 phi2)))) 2))) (((x /.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) (sqrt.f64 (-.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi1 phi2))))) (sqrt.f64 2)))) (((x /.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 2) (cbrt.f64 (-.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi1 phi2))))) (cbrt.f64 2)))) (((x pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 1))) (((x pow.f64 (sqrt.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 2))) (((x pow.f64 (cbrt.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 3))) (((x pow.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3) 1/3))) (((x sqrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 2)))) (((x log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (sin.f64 phi2))))) (((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (((x cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)))) (((x expm1.f64 (log1p.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (((x exp.f64 (log.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (((x exp.f64 (*.f64 (log.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 1)))) (((x log1p.f64 (expm1.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))

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