Details

Time bar (total: 13.8s)

analyze2.9s (21.3%)

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)

sample217.0ms (1.6%)

Algorithm
1×intervals
Results
159.0ms156×body1024valid
23.0ms45×body512valid
7.0ms23×body256valid
6.0ms3×body2048valid
5.0ms29×body128valid
Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify33.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
49×sub-neg_binary64
44×distribute-rgt-in_binary64
38×cancel-sign-sub-inv_binary64
31×unsub-neg_binary64
27×neg-mul-1_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01532
12132
22632
33232
43832
56232
68932
711332
814732
917432
1022332
1121132
1223232
1326132
1426132
1527132
1628432
1729232
1829932
1929832
2027132

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
0.5b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶0.5b
(+.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 48 to 28 computations (41.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
2.9b
(sin.f64 (-.f64 lambda1 lambda2))
3.2b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite69.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Error
0.3b
Rules
6×add-log-exp_binary64
6×*-un-lft-identity_binary64
6×add-sqr-sqrt_binary64
6×cancel-sign-sub-inv_binary64
6×add-cube-cbrt_binary64
Counts
4 → 44
Calls

4 calls:

5.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
3.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
0.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 1360 to 285 computations (79% saved)

series126.0ms (0.9%)

Error
0.5b
Counts
4 → 50
Calls

4 calls:

54.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
24.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
16.0ms
(cos.f64 (-.f64 lambda1 lambda2))
14.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 2900 to 1546 computations (46.7% saved)

simplify155.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
384×distribute-rgt-neg-in_binary64
361×distribute-lft-neg-in_binary64
333×associate-*r*_binary64
332×associate-*l*_binary64
293×distribute-rgt-in_binary64
Counts
94 → 63
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01621941
13811813
28591774
323241756
447851756
549911756
649931756
749681756

prune51.0ms (0.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New54963
Fresh000
Picked101
Done000
Total55964
Error
0.3b
Counts
64 → 9
Alt Table
StatusErrorProgram
2.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
0.5b
(+.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 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))))
16.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
6.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
▶0.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 1611 to 545 computations (66.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
2.9b
(sin.f64 (-.f64 lambda1 lambda2))

rewrite116.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
9×add-sqr-sqrt_binary64
7×*-un-lft-identity_binary64
7×add-cube-cbrt_binary64
6×add-cbrt-cube_binary64
6×add-exp-log_binary64
Counts
4 → 51
Calls

4 calls:

5.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms
(sin.f64 (-.f64 lambda1 lambda2))
3.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 1892 to 337 computations (82.2% saved)

series209.0ms (1.5%)

Error
0.2b
Counts
4 → 48
Calls

4 calls:

97.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
34.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
21.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
16.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 3612 to 2008 computations (44.4% saved)

simplify121.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
403×distribute-rgt-neg-in_binary64
371×cancel-sign-sub-inv_binary64
366×distribute-lft-neg-in_binary64
354×*-commutative_binary64
289×distribute-rgt-in_binary64
Counts
99 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862729
14622420
212832384
332832371
448442371
549882371

prune90.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New64165
Fresh088
Picked101
Done000
Total65974
Error
0.1b
Counts
74 → 9
Alt Table
StatusErrorProgram
2.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
0.5b
(+.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 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))))
16.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
▶0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
6.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 2119 to 614 computations (71% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite127.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
12×add-sqr-sqrt_binary64
8×*-un-lft-identity_binary64
8×add-cube-cbrt_binary64
8×add-cbrt-cube_binary64
8×add-exp-log_binary64
Counts
4 → 63
Calls

4 calls:

6.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 2781 to 369 computations (86.7% saved)

series274.0ms (2%)

Error
0.1b
Counts
4 → 52
Calls

4 calls:

93.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
61.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
38.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
21.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 4856 to 2329 computations (52% saved)

simplify130.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
516×cancel-sign-sub-inv_binary64
413×distribute-rgt-in_binary64
393×distribute-lft-in_binary64
296×distribute-rgt-neg-in_binary64
277×associate-*r*_binary64
Counts
115 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02203828
15843401
218993357
344473357
450113357

prune101.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New77178
Fresh088
Picked101
Done000
Total78987
Error
0.0b
Counts
87 → 9
Alt Table
StatusErrorProgram
15.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (sqrt.f64 (cos.f64 phi2)) (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (sqrt.f64 (cos.f64 phi2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
2.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
0.5b
(+.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 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))))
16.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
▶0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
6.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 2616 to 645 computations (75.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))
0.6b
(log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))
2.9b
(sin.f64 (-.f64 lambda1 lambda2))
3.2b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite120.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
8×*-un-lft-identity_binary64
8×add-sqr-sqrt_binary64
8×add-cube-cbrt_binary64
6×add-log-exp_binary64
6×cancel-sign-sub-inv_binary64
Counts
4 → 51
Calls

4 calls:

6.0ms
(log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))
5.0ms
(+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
3.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 1592 to 361 computations (77.3% saved)

series246.0ms (1.8%)

Error
0.0b
Counts
4 → 56
Calls

4 calls:

103.0ms
(log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))
57.0ms
(+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))
19.0ms
(cos.f64 (-.f64 lambda1 lambda2))
15.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 3662 to 1996 computations (45.5% saved)

simplify114.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
386×distribute-rgt-neg-in_binary64
360×distribute-lft-neg-in_binary64
324×associate-*r*_binary64
319×associate-*l*_binary64
301×distribute-rgt-in_binary64
Counts
107 → 67
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01872025
13951900
28711825
323341794
447911794
550251794

prune99.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New67067
Fresh088
Picked011
Done000
Total67976
Error
0.0b
Counts
76 → 9
Alt Table
StatusErrorProgram
15.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (sqrt.f64 (cos.f64 phi2)) (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (sqrt.f64 (cos.f64 phi2)))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))) (cbrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
2.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))
0.5b
(+.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 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))))
16.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
6.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 1805 to 522 computations (71.1% saved)

regimes1.5s (10.5%)

Accuracy

Total -0.0b remaining (-21.9%)

Threshold costs -0.0b (-21.9%)

Compiler

Compiled 35672 to 20282 computations (43.1% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02256
13656
24656
35256
45656
55756
65756

end1.0ms (0%)

Compiler

Compiled 38 to 21 computations (44.7% saved)

sample6.9s (50.1%)

Algorithm
1×intervals
Results
4.6s4529×body1024valid
906.0ms1677×body512valid
344.0ms134×body2048valid
231.0ms966×body128valid
225.0ms694×body256valid
Compiler

Compiled 402 to 205 computations (49% saved)

Profiling

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