Details

Time bar (total: 17.3s)

analyze2.7s (15.8%)

Algorithm
1×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
9.4%90.4%0.2%9
9.4%90.4%0.2%10
10.9%88.9%0.2%11
10.9%88.9%0.2%12
10.9%88.9%0.2%13
10.9%88.9%0.2%14
Compiler

Compiled 25 to 15 computations (40% saved)

sample7.9s (46%)

Results
5.6s4534×body1024valid
1.3s1825×body512valid
349.0ms755×body256valid
302.0ms113×body2048valid
255.0ms1029×body128valid
Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify36.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
284×fma-def_binary64
141×fma-neg_binary64
44×distribute-rgt-in_binary64
38×cancel-sign-sub-inv_binary64
37×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01532
12130
22830
33530
44230
56830
69830
713230
817630
922030
1028830
1131030
1234630
1339330
1440330
1542130
1644230
1744930
1847030
1947830
2048030
2145330

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
▶1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
Compiler

Compiled 137 to 71 computations (48.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
✓0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓3.2b
(cos.f64 (-.f64 lambda1 lambda2))
✓3.2b
(sin.f64 (-.f64 lambda1 lambda2))

series48.0ms (0.3%)

Counts
4 → 112
Calls

4 calls:

29.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
10.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

rewrite72.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
307×expm1-udef_binary64
307×log1p-udef_binary64
168×add-sqr-sqrt_binary64
159×log1p-expm1-u_binary64
159×expm1-log1p-u_binary64
Counts
4 → 109
Calls

4 calls:

70.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
70.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
70.0ms
(cos.f64 (-.f64 lambda1 lambda2))
70.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01457
131053
2417353
3509053

simplify91.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
594×cancel-sign-sub-inv_binary64
480×fma-def_binary64
479×associate-*r*_binary64
462×associate-*l*_binary64
429×sub-neg_binary64
Counts
221 → 171
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01242746
13932554
212482466
343222462
449682462

prune297.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New15615171
Fresh101
Picked101
Done000
Total15815173
Error
0.7b
Counts
173 → 15
Alt Table
StatusErrorProgram
30.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 1 (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 2) (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))) (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3))))))
33.4b
(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
17.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2)))
▶1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
1.5b
(+.f64 lambda1 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (pow.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2)))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3)))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (pow.f64 (cos.f64 phi1) 2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 1/2 (*.f64 lambda1 (*.f64 lambda1 (sin.f64 lambda2))) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
7.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
1.1b
(+.f64 lambda1 (log1p.f64 (expm1.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (-.f64 (cos.f64 lambda2) (*.f64 lambda1 (-.f64 (*.f64 1/2 (*.f64 (cos.f64 lambda2) lambda1)) (sin.f64 lambda2))))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2))))))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2)) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
Compiler

Compiled 5993 to 1774 computations (70.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.2b
(sin.f64 (-.f64 lambda1 lambda2))

series89.0ms (0.5%)

Counts
3 → 108
Calls

3 calls:

61.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
16.0ms
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
12.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite83.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
925×prod-diff_binary64
210×add-sqr-sqrt_binary64
197×log1p-expm1-u_binary64
197×expm1-log1p-u_binary64
192×add-log-exp_binary64
Counts
3 → 71
Calls

3 calls:

81.0ms
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
81.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
81.0ms
(+.f64 (cos.f64 phi1) (*.f64 (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
01976
139952
2486252
3676252

simplify111.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
850×cancel-sign-sub-inv_binary64
646×sub-neg_binary64
441×associate-+l+_binary64
410×associate--l+_binary64
242×distribute-rgt-neg-in_binary64
Counts
179 → 130
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01643858
15223577
217423483
344983481
452503481

prune384.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1682170
Fresh5914
Picked101
Done000
Total17411185
Error
0.1b
Counts
185 → 11
Alt Table
StatusErrorProgram
7.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (/.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
30.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
33.4b
(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
1.5b
(+.f64 lambda1 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (pow.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2)))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3)))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (pow.f64 (cos.f64 phi1) 2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
1.1b
(+.f64 lambda1 (log1p.f64 (expm1.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
▶0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
17.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2)))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2)) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
Compiler

Compiled 6463 to 1675 computations (74.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓0.3b
(log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.2b
(sin.f64 (-.f64 lambda1 lambda2))

series376.0ms (2.2%)

Counts
2 → 72
Calls

2 calls:

363.0ms
(log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))
12.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite69.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
574×prod-diff_binary64
218×add-sqr-sqrt_binary64
206×expm1-log1p-u_binary64
205×log1p-expm1-u_binary64
199×add-log-exp_binary64
Counts
2 → 32
Calls

2 calls:

69.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
69.0ms
(log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02147
141835
2486135
3609235

simplify153.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
869×times-frac_binary64
567×associate-/l*_binary64
374×associate-/r*_binary64
189×fma-def_binary64
148×associate-/r/_binary64
Counts
104 → 50
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0982423
12932391
210932352
348732346
449832346
550032346

prune694.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1582160
Fresh2810
Picked101
Done000
Total16110171
Error
0.0b
Counts
171 → 10
Alt Table
StatusErrorProgram
17.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))
▶0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
33.4b
(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
1.5b
(+.f64 lambda1 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (pow.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2)))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3)))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (pow.f64 (cos.f64 phi1) 2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
30.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
1.1b
(+.f64 lambda1 (log1p.f64 (expm1.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2)) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
Compiler

Compiled 6600 to 1910 computations (71.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓0.3b
(log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series677.0ms (3.9%)

Counts
3 → 96
Calls

3 calls:

645.0ms
(log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))
16.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
15.0ms
(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))

rewrite82.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
447×prod-diff_binary64
226×add-sqr-sqrt_binary64
211×expm1-log1p-u_binary64
210×log1p-expm1-u_binary64
205×add-cbrt-cube_binary64
Counts
3 → 110
Calls

3 calls:

78.0ms
(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))
78.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
78.0ms
(log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02289
143571
2468571
3559671

simplify109.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
893×times-frac_binary64
623×associate-/l*_binary64
305×fma-def_binary64
256×fma-neg_binary64
191×cancel-sign-sub-inv_binary64
Counts
206 → 145
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01173655
13593585
212983554
348823551
450533551

prune391.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2141215
Fresh099
Picked011
Done000
Total21411225
Error
0.0b
Counts
225 → 11
Alt Table
StatusErrorProgram
17.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))
✓0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
33.4b
(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
1.5b
(+.f64 lambda1 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (pow.f64 (cbrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2)))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3)))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (-.f64 (pow.f64 (cos.f64 phi1) 2) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
30.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
1.1b
(+.f64 lambda1 (log1p.f64 (expm1.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
15.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (+.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi1)))))
4.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2)) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
Compiler

Compiled 10466 to 2201 computations (79% saved)

regimes2.5s (14.5%)

Accuracy

Total 0.1b remaining (51.4%)

Threshold costs 0.1b (51.4%)

Counts
280 → 1
Compiler

Compiled 63231 to 38230 computations (39.5% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Rules
7×*-commutative_binary64
5×+-commutative_binary64
3×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02358
13758
24558
35058
45258
55258

end232.0ms (1.3%)

Compiler

Compiled 481 to 253 computations (47.4% saved)

Profiling

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