Details

Time bar (total: 24.2s)

analyze3.7s (15.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
7.8%92%0.2%9
7.8%92%0.2%10
10.1%89.7%0.2%11
10.1%89.7%0.2%12
13.9%85.9%0.2%13
13.9%85.9%0.2%14
Compiler

Compiled 29 to 18 computations (37.9% saved)

sample517.0ms (2.1%)

Algorithm
intervals
Results
268.0ms179×body1024valid
31.0ms40×body512valid
23.0msbody2048valid
5.0ms22×body128valid
4.0msbody256valid
Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify30.0ms (0.1%)

Algorithm
egg-herbie
Rules
543×fma-def_binary64
194×fma-neg_binary64
83×cancel-sign-sub-inv_binary64
59×distribute-rgt-neg-in_binary64
47×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13239
26139
311539
415539
524639
634839
743739
857239
962239
1069439
1172039
1266939

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
14.4b
Counts
3 → 1
Alt Table
StatusErrorProgram
14.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 108 to 55 computations (49.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.3b
(cos.f64 (-.f64 lambda1 lambda2))
3.6b
(sin.f64 (-.f64 lambda1 lambda2))

series69.0ms (0.3%)

Counts
4 → 100
Calls

4 calls:

40.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
18.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
18×prod-diff_binary64
13×cos-sum_binary64
Counts
4 → 90
Calls

4 calls:

7.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
6.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

simplify134.0ms (0.6%)

Algorithm
egg-herbie
Rules
980×fma-neg_binary64
457×associate-*r*_binary64
441×distribute-rgt-neg-in_binary64
422×associate-*l*_binary64
395×distribute-lft-neg-in_binary64
Counts
190 → 201
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03994414
18623679
229133547
346813537
450703537

prune599.0ms (2.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New18021201
Fresh000
Picked101
Done000
Total18121202
Error
8.2b
Counts
202 → 21
Alt Table
StatusErrorProgram
17.3b
(atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
49.7b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (*.f64 (cos.f64 (fma.f64 (sqrt.f64 lambda1) (sqrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
23.3b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
25.5b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (*.f64 lambda2 1)))) (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (*.f64 lambda2 1))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (*.f64 (sin.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))))))
14.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))))
36.8b
(atan2.f64 (sin.f64 (-.f64 lambda1 lambda2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
36.6b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
27.3b
(atan2.f64 (*.f64 (-.f64 (+.f64 (*.f64 (cos.f64 (neg.f64 lambda2)) lambda1) (sin.f64 (neg.f64 lambda2))) (*.f64 1/2 (*.f64 (sin.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
22.7b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (fma.f64 (sin.f64 lambda1) (*.f64 lambda2 (*.f64 (cos.f64 phi2) (sin.f64 phi1))) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
14.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
28.5b
(atan2.f64 (*.f64 (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
14.6b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
14.5b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
14.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
8.5b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
50.2b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
33.6b
(atan2.f64 (*.f64 (sin.f64 (neg.f64 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
14.4b
(atan2.f64 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
37.8b
(atan2.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (sqrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
25.7b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))))))
Compiler

Compiled 9707 to 2489 computations (74.4% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.3b
(cos.f64 (-.f64 lambda1 lambda2))

series55.0ms (0.2%)

Counts
2 → 60
Calls

2 calls:

45.0ms
(*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
10.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64
associate-*r*_binary64
associate-*l*_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 42
Calls

2 calls:

7.0ms
(*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
3.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

simplify97.0ms (0.4%)

Algorithm
egg-herbie
Rules
947×fma-neg_binary64
803×fma-def_binary64
529×cancel-sign-sub-inv_binary64
242×distribute-rgt-neg-in_binary64
240×associate-*r*_binary64
Counts
102 → 108
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01892294
15322178
218242115
344252109
450692109

prune1.4s (5.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2097216
Fresh18220
Picked101
Done000
Total2289237
Error
0.1b
Counts
237 → 9
Alt Table
StatusErrorProgram
8.6b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
8.5b
(atan2.f64 (expm1.f64 (log1p.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
11.4b
(atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
15.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
50.2b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
37.8b
(atan2.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (sqrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
8.5b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
Compiler

Compiled 10215 to 2111 computations (79.3% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series89.0ms (0.4%)

Counts
2 → 56
Calls

2 calls:

77.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
11.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-sqr-sqrt_binary64
associate-*r*_binary64
Counts
2 → 50
Calls

2 calls:

8.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify95.0ms (0.4%)

Algorithm
egg-herbie
Rules
618×associate-*r*_binary64
563×associate-*l*_binary64
546×fma-neg_binary64
385×distribute-rgt-neg-in_binary64
300×*-commutative_binary64
Counts
106 → 119
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03013509
19653263
237643255
350523255

prune455.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2207227
Fresh718
Picked101
Done000
Total2288236
Error
0.0b
Counts
236 → 8
Alt Table
StatusErrorProgram
0.2b
(atan2.f64 (expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (*.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
0.4b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.4b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (cos.f64 phi2) (cbrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
8.5b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
29.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cos.f64 lambda1) (sqrt.f64 (sin.f64 lambda2))) (sqrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
3.1b
(atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
30.3b
(atan2.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 12504 to 2367 computations (81.1% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b
(expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))))
0.2b
(log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))

series1.9s (8.1%)

Counts
3 → 108
Calls

3 calls:

1.9s
(log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))
42.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
41.0ms
(expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))))

rewrite11.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 50
Calls

3 calls:

7.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
0.0ms
(log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))
0.0ms
(expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))))

simplify147.0ms (0.6%)

Algorithm
egg-herbie
Rules
503×associate-*r*_binary64
376×associate-*l*_binary64
263×fma-neg_binary64
240×times-frac_binary64
234×fma-def_binary64
Counts
158 → 124
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03646782
111036255
248236255
350186255

prune449.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2012203
Fresh257
Picked011
Done000
Total2038211
Error
0.0b
Counts
211 → 8
Alt Table
StatusErrorProgram
0.2b
(atan2.f64 (expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (*.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
30.2b
(atan2.f64 (*.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 (expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.4b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (cos.f64 phi2) (cbrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
8.5b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
29.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cos.f64 lambda1) (sqrt.f64 (sin.f64 lambda2))) (sqrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
3.1b
(atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
9.7b
(atan2.f64 (expm1.f64 (log.f64 (fma.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) 1))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 13679 to 2986 computations (78.2% saved)

regimes3.8s (15.6%)

Accuracy

Total 0.1b remaining (53.8%)

Threshold costs 0.1b (53.8%)

Counts
366 → 1
Compiler

Compiled 101175 to 56169 computations (44.5% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
20×*-commutative_binary64
15×+-commutative_binary64
14×sub-neg_binary64
12×distribute-rgt-neg-in_binary64
12×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02763
14963
27663
39563
412363
513563
614163
714363
814163

end1.0ms (0%)

Compiler

Compiled 42 to 24 computations (42.9% saved)

sample10.4s (43%)

Algorithm
intervals
Results
7.7s5454×body1024valid
998.0ms1259×body512valid
657.0ms192×body2048valid
183.0ms382×body256valid
164.0ms713×body128valid
Compiler

Compiled 532 to 267 computations (49.8% saved)

Profiling

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