Details

Time bar (total: 21.0s)

analyze3.8s (17.9%)

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)

sample490.0ms (2.3%)

Algorithm
intervals
Results
250.0ms172×body1024valid
39.0ms47×body512valid
7.0ms15×body256valid
6.0ms20×body128valid
6.0msbody2048valid
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
12.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
12.2b
(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)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.4b
(sin.f64 (-.f64 lambda1 lambda2))
2.4b
(cos.f64 (-.f64 lambda1 lambda2))

series69.0ms (0.3%)

Counts
4 → 100
Calls

4 calls:

41.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
18.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms (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×sin-sum_binary64
Counts
4 → 90
Calls

4 calls:

8.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
6.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

simplify135.0ms (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

prune451.0ms (2.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New18021201
Fresh000
Picked101
Done000
Total18121202
Error
6.1b
Counts
202 → 21
Alt Table
StatusErrorProgram
39.6b
(atan2.f64 (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.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)))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
17.0b
(atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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)))))
17.0b
(atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 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)))))
12.2b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
12.5b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cbrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (cbrt.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)))))
23.9b
(atan2.f64 (*.f64 (-.f64 (sin.f64 lambda1) (*.f64 lambda2 (cos.f64 lambda1))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
17.0b
(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 lambda1))))
6.4b
(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)))))
31.6b
(atan2.f64 (*.f64 (sin.f64 lambda1) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
18.8b
(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)))))
37.1b
(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 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (sin.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2))))))))
24.7b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sqrt.f64 (cos.f64 phi2))) (sqrt.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)))))
15.8b
(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))))))))
24.0b
(atan2.f64 (*.f64 (-.f64 (fma.f64 1/6 (*.f64 (cos.f64 lambda1) (pow.f64 lambda2 3)) (sin.f64 lambda1)) (fma.f64 lambda2 (cos.f64 lambda1) (*.f64 1/2 (*.f64 lambda2 (*.f64 lambda2 (sin.f64 lambda1)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
40.9b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 1 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 1 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)))))
12.2b
(atan2.f64 (*.f64 (log1p.f64 (expm1.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)))))
12.5b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
12.0b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 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))))))
34.8b
(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)))))
22.8b
(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 9359 to 2416 computations (74.2% saved)

localize28.0ms (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)))
2.4b
(cos.f64 (-.f64 lambda1 lambda2))

series55.0ms (0.3%)

Counts
2 → 60
Calls

2 calls:

41.0ms
(*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
14.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite12.0ms (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:

6.0ms
(*.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))

simplify92.0ms (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

prune658.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2088216
Fresh17320
Picked101
Done000
Total22611237
Error
0.1b
Counts
237 → 11
Alt Table
StatusErrorProgram
6.4b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (expm1.f64 (log1p.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)))))
12.5b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cbrt.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (cbrt.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)))))
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))))))
12.5b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
11.8b
(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)))))
6.6b
(atan2.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 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)))))
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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
10.0b
(atan2.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
12.9b
(atan2.f64 (/.f64 (*.f64 (-.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (cos.f64 phi2)) (+.f64 (*.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (sin.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 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
11.2b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 10335 to 2197 computations (78.7% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series119.0ms (0.6%)

Counts
3 → 104
Calls

3 calls:

55.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
53.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
12.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite22.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
29×add-cbrt-cube_binary64
29×add-exp-log_binary64
29×pow1_binary64
17×cbrt-unprod_binary64
17×prod-exp_binary64
Counts
3 → 75
Calls

3 calls:

8.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
6.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify159.0ms (0.8%)

Algorithm
egg-herbie
Rules
835×associate-*r*_binary64
696×associate-*l*_binary64
609×fma-neg_binary64
551×distribute-rgt-neg-in_binary64
357×*-commutative_binary64
Counts
179 → 171
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03424644
110384148
238534140
354534140

prune742.0ms (3.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2287235
Fresh5510
Picked101
Done000
Total23412246
Error
0.0b
Counts
246 → 12
Alt Table
StatusErrorProgram
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
11.8b
(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)))))
0.5b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
6.6b
(atan2.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 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)))))
0.5b
(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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
11.2b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.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 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1))) (cos.f64 lambda2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
14.7b
(atan2.f64 (*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (sqrt.f64 (cos.f64 phi2))) (sqrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
10.0b
(atan2.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.4b
(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 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (sin.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 14552 to 2744 computations (81.1% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series27.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

27.0ms
(*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*l*_binary64
cbrt-unprod_binary64
Counts
1 → 21
Calls

1 calls:

5.0ms
(*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))

simplify47.0ms (0.2%)

Algorithm
egg-herbie
Rules
840×fma-neg_binary64
397×*-commutative_binary64
393×distribute-lft-out--_binary64
338×distribute-rgt-neg-in_binary64
326×distribute-lft-neg-in_binary64
Counts
33 → 53
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0111824
1321699
2999641
32325618
45136618

prune692.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2202222
Fresh2911
Picked101
Done000
Total22311234
Error
0.0b
Counts
234 → 11
Alt Table
StatusErrorProgram
11.8b
(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)))))
0.5b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
6.6b
(atan2.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 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)))))
0.5b
(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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.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 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1))) (cos.f64 lambda2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
14.7b
(atan2.f64 (*.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (sqrt.f64 (cos.f64 phi2))) (sqrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
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 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1))) (cos.f64 lambda2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
10.0b
(atan2.f64 (/.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.4b
(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 (cbrt.f64 (pow.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (sin.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
11.2b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 12877 to 2280 computations (82.3% saved)

regimes2.8s (13.4%)

Accuracy

Total 0.1b remaining (63.2%)

Threshold costs 0.1b (63.2%)

Counts
271 → 1
Compiler

Compiled 75622 to 41782 computations (44.7% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Rules
21×*-commutative_binary64
15×+-commutative_binary64
14×sub-neg_binary64
12×neg-sub0_binary64
12×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02877
14577
26277
38777
411377
512877
613777
714077
814077

end1.0ms (0%)

Compiler

Compiled 50 to 27 computations (46% saved)

sample10.5s (49.8%)

Algorithm
intervals
Results
7.7s5413×body1024valid
946.0ms1254×body512valid
643.0ms192×body2048valid
192.0ms774×body128valid
183.0ms367×body256valid
Compiler

Compiled 658 to 345 computations (47.6% saved)

Profiling

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