Details

Time bar (total: 19.4s)

analyze3.6s (18.8%)

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
0%99.8%0.2%9
0%99.8%0.2%10
0.8%99%0.2%11
1.2%98.6%0.2%12
1.8%98%0.2%13
2%97.7%0.2%14
Compiler

Compiled 25 to 18 computations (28% saved)

sample10.7s (55.5%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results
8.0s5678×body1024valid
1.2s1506×body512valid
796.0ms271×body2048valid
271.0ms490×body256valid
97.0ms311×body128valid
3.0msbody1024invalid
2.0msbody512invalid
Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
47×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01829
12829
24329
35329
46029
57829
610429
712529
814229
915229
1015629
1115829
1214429

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
16.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
16.8b
(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
16.8b
(*.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 136 to 86 computations (36.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b
(*.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)
1.0b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0b
(cos.f64 (-.f64 lambda1 lambda2))

series58.0ms (0.3%)

Counts
4 → 124
Calls

4 calls:

35.0ms
(*.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)
10.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
10.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

rewrite40.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
211×add-sqr-sqrt_binary64
198×log1p-expm1-u_binary64
198×expm1-log1p-u_binary64
194×add-log-exp_binary64
193×add-cube-cbrt_binary64
Counts
4 → 81
Calls

4 calls:

38.0ms
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
38.0ms
(*.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)
38.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
38.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01869
139469
2494469

simplify113.0ms (0.6%)

Algorithm
egg-herbie
Rules
829×fma-neg_binary64
423×distribute-rgt-neg-in_binary64
410×distribute-lft-neg-in_binary64
323×neg-mul-1_binary64
314×neg-sub0_binary64
Counts
205 → 115
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0853348
12553320
27253283
322833264
446803264
550703264

prune145.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New10015115
Fresh101
Picked101
Done000
Total10215117
Error
4.1b
Counts
117 → 15
Alt Table
StatusErrorProgram
16.9b
(*.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
17.0b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2))))) R)
17.0b
(*.f64 (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) R)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
17.4b
(*.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))))) 3) R)
16.9b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))) R)
46.3b
(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)))
17.0b
(*.f64 (/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 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) 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
38.5b
(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)
17.4b
(*.f64 (*.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)) R)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.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))))))))) R)
16.9b
(*.f64 (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)))))) R)
16.8b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) 1)))) R)
17.0b
(*.f64 (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)) R)
16.8b
(*.f64 (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)))))) R)
Compiler

Compiled 3989 to 1407 computations (64.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series65.0ms (0.3%)

Counts
3 → 116
Calls

3 calls:

43.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
13.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
9.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite69.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
243×add-sqr-sqrt_binary64
225×log1p-expm1-u_binary64
225×expm1-log1p-u_binary64
222×add-log-exp_binary64
221×add-cube-cbrt_binary64
Counts
3 → 56
Calls

3 calls:

67.0ms
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
67.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
67.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02283
146063
2486263
3516763

simplify180.0ms (0.9%)

Algorithm
egg-herbie
Rules
487×fma-neg_binary64
444×distribute-rgt-neg-in_binary64
430×sub-neg_binary64
424×unsub-neg_binary64
390×distribute-lft-neg-in_binary64
Counts
172 → 79
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0644272
11594264
24364240
313424216
425054216
537354216
647874216
749664216

prune180.0ms (0.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1049113
Fresh5914
Picked101
Done000
Total11018128
Error
3.8b
Counts
128 → 18
Alt Table
StatusErrorProgram
4.4b
(*.f64 (acos.f64 (+.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 3) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
17.4b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
17.0b
(*.f64 (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)) R)
32.4b
(*.f64 (acos.f64 (+.f64 (pow.f64 (sqrt.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
17.0b
(*.f64 (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) R)
42.1b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (fma.f64 (neg.f64 (sqrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (sqrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3))))))) R)
18.0b
(*.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) R)
46.3b
(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)))
17.0b
(*.f64 (/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 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) 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
38.5b
(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)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.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))))))))) R)
17.0b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2))))) R)
16.9b
(*.f64 (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)))))) R)
16.8b
(*.f64 (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)))))) R)
16.9b
(*.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
17.2b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) R)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda1)) (sin.f64 lambda2))))))) R)
Compiler

Compiled 5553 to 1719 computations (69% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (sin.f64 lambda1) 3)
0.4b
(pow.f64 (sin.f64 lambda2) 3)
1.0b
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3)))))))
25.4b
(cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3)))

series33.0ms (0.2%)

Counts
4 → 80
Calls

4 calls:

14.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3)))))))
9.0ms
(cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3)))
5.0ms
(pow.f64 (sin.f64 lambda2) 3)
5.0ms
(pow.f64 (sin.f64 lambda1) 3)

rewrite38.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
252×add-sqr-sqrt_binary64
234×log1p-expm1-u_binary64
234×expm1-log1p-u_binary64
232×add-cbrt-cube_binary64
230×add-cube-cbrt_binary64
Counts
4 → 71
Calls

4 calls:

37.0ms
(pow.f64 (sin.f64 lambda1) 3)
37.0ms
(pow.f64 (sin.f64 lambda2) 3)
37.0ms
(acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3)))))))
37.0ms
(cbrt.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 3) (pow.f64 (sin.f64 lambda2) 3)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02456
149856
2490856

simplify110.0ms (0.6%)

Algorithm
egg-herbie
Rules
679×fma-neg_binary64
576×distribute-rgt-neg-in_binary64
501×distribute-lft-neg-in_binary64
470×*-commutative_binary64
416×sub-neg_binary64
Counts
151 → 103
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0822192
12252180
26482148
319012124
435132124
547582124
649682124

prune203.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New967103
Fresh9817
Picked101
Done000
Total10615121
Error
3.8b
Counts
121 → 15
Alt Table
StatusErrorProgram
5.1b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.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))))))))) R)
4.5b
(*.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) 3)) R)
17.2b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) R)
4.3b
(*.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
18.0b
(*.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) R)
5.1b
(*.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) 3) R)
46.3b
(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)))
17.0b
(*.f64 (/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 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) 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
38.5b
(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)
17.0b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2))))) R)
4.4b
(*.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
4.4b
(*.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
42.1b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (fma.f64 (neg.f64 (sqrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (sqrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
4.5b
(*.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) 2) R)
Compiler

Compiled 5229 to 1947 computations (62.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.4b
(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.7b
(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
1.0b
(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series47.0ms (0.2%)

Counts
3 → 144
Calls

3 calls:

26.0ms
(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
11.0ms
(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
10.0ms
(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

rewrite40.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
214×add-sqr-sqrt_binary64
197×log1p-expm1-u_binary64
197×expm1-log1p-u_binary64
195×add-log-exp_binary64
194×add-cube-cbrt_binary64
Counts
3 → 68
Calls

3 calls:

38.0ms
(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
38.0ms
(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
38.0ms
(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
021110
140480
2495880

simplify136.0ms (0.7%)

Algorithm
egg-herbie
Rules
122×fma-def_binary64
52×*-commutative_binary64
42×associate-*l*_binary64
26×associate-*r*_binary64
10×distribute-lft-in_binary64
Counts
212 → 49
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0255280
1315280
2575280
31335280
42215280
52675280
62675280

prune135.0ms (0.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New79483
Fresh11314
Picked011
Done000
Total801898
Error
3.7b
Counts
98 → 18
Alt Table
StatusErrorProgram
38.5b
(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)
17.4b
(*.f64 (log.f64 (exp.f64 (*.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) 2)))) R)
17.0b
(*.f64 (log.f64 (exp.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))) (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))))))) R)
17.0b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2))))) R)
16.9b
(*.f64 (log.f64 (pow.f64 (exp.f64 1) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
42.1b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (fma.f64 (neg.f64 (sqrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (sqrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
4.5b
(*.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) 3)) R)
17.2b
(*.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) R)
4.3b
(*.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
18.0b
(*.f64 (+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (*.f64 (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))))) R)
5.1b
(*.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) 3) R)
46.3b
(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)))
17.0b
(*.f64 (/.f64 (-.f64 (*.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 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) 2) (asin.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
4.3b
(*.f64 (acos.f64 (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.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))))))))) R)
4.4b
(*.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
17.0b
(*.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) 3))) R)
4.4b
(*.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
4.5b
(*.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) 2) R)
Compiler

Compiled 3549 to 1163 computations (67.2% saved)

regimes2.7s (13.9%)

Accuracy

Total 0.4b remaining (12.1%)

Threshold costs 0.4b (12.1%)

Counts
185 → 1
Compiler

Compiled 69324 to 45512 computations (34.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02241
12841
22841

end573.0ms (3%)

Remove

(sort lambda1 lambda2)

Compiler

Compiled 1254 to 606 computations (51.7% saved)

Profiling

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