Details

Time bar (total: 11.9s)

analyze2.1s (17.5%)

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)

sample142.0ms (1.2%)

Algorithm
1×intervals
Results
99.0ms158×body1024valid
17.0ms45×body512valid
5.0ms22×body256valid
3.0ms29×body128valid
3.0ms2×body2048valid
Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify29.0ms (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)

localize16.0ms (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))))
3.8b
(sin.f64 (-.f64 lambda1 lambda2))
4.1b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite103.0ms (0.9%)

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
(cos.f64 (-.f64 lambda1 lambda2))
5.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
1.0ms
(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)

series160.0ms (1.3%)

Error
0.5b
Counts
4 → 48
Calls

4 calls:

65.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
31.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
18.0ms
(sin.f64 (-.f64 lambda1 lambda2))
16.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 2761 to 1475 computations (46.6% saved)

simplify111.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
471×sub-neg_binary64
313×associate-*l*_binary64
303×associate-*r*_binary64
291×distribute-rgt-neg-in_binary64
279×distribute-lft-neg-in_binary64
Counts
92 → 60
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01651933
13731785
28231765
322011743
443401743
550491743

prune79.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New471360
Fresh000
Picked101
Done000
Total481361
Error
0.3b
Counts
61 → 13
Alt Table
StatusErrorProgram
15.8b
(+.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))))))
0.5b
(+.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)))))))
0.7b
(+.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))) (cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)) 3))))
▶0.4b
(+.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) (cos.f64 (-.f64 lambda1 lambda2))))))
15.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.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))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
38.2b
(+.f64 lambda1 (exp.f64 (log.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))))))
0.9b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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))))))
3.9b
(+.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))))))
6.5b
(+.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)))
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))))))))
Compiler

Compiled 1922 to 697 computations (63.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

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) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.6b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.1b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite184.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.1b
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 → 50
Calls

4 calls:

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

Compiled 1803 to 322 computations (82.1% saved)

series245.0ms (2.1%)

Error
0.3b
Counts
4 → 49
Calls

4 calls:

74.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 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) (cos.f64 (-.f64 lambda1 lambda2)))))
25.0ms
(cos.f64 (-.f64 lambda1 lambda2))
24.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 3716 to 2028 computations (45.4% saved)

simplify144.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
513×sub-neg_binary64
308×distribute-rgt-neg-in_binary64
304×cancel-sign-sub-inv_binary64
295×associate-+l+_binary64
293×*-commutative_binary64
Counts
99 → 66
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01882313
14482099
211442084
321392060
442432060
549702060
649552060

prune148.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New65166
Fresh11112
Picked101
Done000
Total671279
Error
0.1b
Counts
79 → 12
Alt Table
StatusErrorProgram
▶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)))))))
15.8b
(+.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))))))
0.7b
(+.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))) (cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)) 3))))
15.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.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))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
38.2b
(+.f64 lambda1 (exp.f64 (log.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))))))
0.9b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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))))))
3.9b
(+.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))))))
6.5b
(+.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)))
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))))))))
Compiler

Compiled 2181 to 674 computations (69.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.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 (cos.f64 lambda1) (sin.f64 lambda2))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite203.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Error
0.1b
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 → 62
Calls

4 calls:

8.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
5.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
4.0ms
(+.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 2741 to 340 computations (87.6% saved)

series385.0ms (3.2%)

Error
0.1b
Counts
4 → 55
Calls

4 calls:

120.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
75.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
46.0ms
(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))))))
22.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 5482 to 2528 computations (53.9% saved)

simplify145.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
824×cancel-sign-sub-inv_binary64
625×distribute-rgt-in_binary64
330×associate-*r*_binary64
303×distribute-rgt-neg-in_binary64
286×associate-*l*_binary64
Counts
117 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02544111
16863762
224293677
348003677
450653677

prune223.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New90696
Fresh5611
Picked101
Done000
Total9612108
Error
0.1b
Counts
108 → 12
Alt Table
StatusErrorProgram
15.8b
(+.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))))))
▶0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2))) (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cbrt.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)))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (cbrt.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
6.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.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))) (cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)) 3))))
31.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sqrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (sqrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
31.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (exp.f64 (log.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.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))) (+.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 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
38.2b
(+.f64 lambda1 (exp.f64 (log.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))))))
3.9b
(+.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))))))
6.5b
(+.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 3906 to 963 computations (75.3% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(cbrt.f64 (cos.f64 phi2))
0.3b
(cbrt.f64 (cos.f64 phi2))
0.3b
(cbrt.f64 (cos.f64 phi2))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite183.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
9×cbrt-prod_binary64
7×*-un-lft-identity_binary64
7×add-sqr-sqrt_binary64
7×add-cube-cbrt_binary64
6×add-log-exp_binary64
Counts
4 → 46
Calls

4 calls:

4.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
1.0ms
(cbrt.f64 (cos.f64 phi2))
1.0ms
(cbrt.f64 (cos.f64 phi2))
1.0ms
(cbrt.f64 (cos.f64 phi2))
Compiler

Compiled 2351 to 266 computations (88.7% saved)

series293.0ms (2.5%)

Error
0.1b
Counts
4 → 38
Calls

4 calls:

124.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
22.0ms
(cbrt.f64 (cos.f64 phi2))
21.0ms
(cbrt.f64 (cos.f64 phi2))
19.0ms
(cbrt.f64 (cos.f64 phi2))
Compiler

Compiled 4467 to 1931 computations (56.8% saved)

simplify137.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
536×cancel-sign-sub-inv_binary64
499×distribute-rgt-in_binary64
477×distribute-lft-in_binary64
251×associate--l+_binary64
203×neg-mul-1_binary64
Counts
84 → 57
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01411805
13901678
214291638
346521638
449521638
549901638
649661638

prune154.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New57057
Fresh01111
Picked011
Done000
Total571269
Error
0.1b
Counts
69 → 12
Alt Table
StatusErrorProgram
15.8b
(+.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))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2))) (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cbrt.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)))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (cbrt.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
6.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.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))) (cbrt.f64 (pow.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)) 3))))
31.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sqrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (sqrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
31.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (exp.f64 (log.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.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))) (+.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 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
38.2b
(+.f64 lambda1 (exp.f64 (log.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))))))
3.9b
(+.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))))))
6.5b
(+.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 2645 to 623 computations (76.4% saved)

regimes2.0s (16.5%)

Accuracy

Total 0.1b remaining (51.4%)

Threshold costs 0.1b (51.4%)

Compiler

Compiled 39620 to 20366 computations (48.6% 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)

sample4.7s (39.4%)

Algorithm
1×intervals
Results
2.8s4434×body1024valid
714.0ms1777×body512valid
174.0ms702×body256valid
153.0ms111×body2048valid
114.0ms976×body128valid
Compiler

Compiled 578 to 282 computations (51.2% saved)

Profiling

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