Details

Time bar (total: 13.5s)

analyze2.8s (20.8%)

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)

sample237.0ms (1.8%)

Algorithm
1×intervals
Results
176.0ms130×body1024valid
29.0ms60×body512valid
8.0ms24×body256valid
6.0ms39×body128valid
6.0ms3×body2048valid
Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify31.0ms (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
1.1b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶1.1b
(+.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)

localize15.0ms (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)))))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.4b
(sin.f64 (-.f64 lambda1 lambda2))
3.4b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite88.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Error
0.9b
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
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.0ms
(cos.f64 (-.f64 lambda1 lambda2))
3.0ms
(sin.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)

series199.0ms (1.5%)

Error
1.1b
Counts
4 → 54
Calls

4 calls:

71.0ms
(sin.f64 (-.f64 lambda1 lambda2))
54.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
25.0ms
(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))
Compiler

Compiled 3138 to 1662 computations (47% saved)

simplify108.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
534×distribute-rgt-neg-in_binary64
505×distribute-lft-neg-in_binary64
409×associate-*r*_binary64
396×associate-*l*_binary64
388×cancel-sign-sub-inv_binary64
Counts
98 → 67
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01822086
14441954
210701905
330601895
446321895
551411895

prune76.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New531467
Fresh000
Picked101
Done000
Total541468
Error
0.9b
Counts
68 → 14
Alt Table
StatusErrorProgram
1.4b
(+.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))))))
1.1b
(+.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)))))))
31.2b
(+.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))))))
▶1.1b
(+.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))))))
9.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda2) (+.f64 -1 (*.f64 1/2 (*.f64 lambda1 lambda1)))) (*.f64 (cos.f64 lambda2) (-.f64 lambda1 (*.f64 1/6 (pow.f64 lambda1 3)))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
5.4b
(+.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))))))
12.2b
(+.f64 lambda1 (log.f64 (exp.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))))))
1.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) lambda1) (sin.f64 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
1.2b
(+.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))))))
5.6b
(+.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))))))
1.2b
(+.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))))))
1.1b
(+.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))))))))
27.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (+.f64 1 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (*.f64 1/24 (pow.f64 phi1 4))) (+.f64 (*.f64 1/2 (*.f64 phi1 phi1)) (*.f64 1/720 (pow.f64 phi1 6))))))
5.7b
(+.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 2123 to 833 computations (60.8% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
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)))))
0.5b
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.4b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite113.0ms (0.8%)

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 lambda2) (sin.f64 lambda1))
3.0ms
(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) (-.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)

series193.0ms (1.4%)

Error
0.7b
Counts
4 → 54
Calls

4 calls:

60.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
30.0ms
(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)))))
22.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
18.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 4003 to 2172 computations (45.7% saved)

simplify115.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
632×unsub-neg_binary64
410×cancel-sign-sub-inv_binary64
377×distribute-rgt-neg-in_binary64
353×*-commutative_binary64
333×distribute-lft-neg-in_binary64
Counts
104 → 72
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02082489
15132314
213572242
327162208
444832208
550972208

prune102.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New69372
Fresh5813
Picked101
Done000
Total751186
Error
0.1b
Counts
86 → 11
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)))))))
1.4b
(+.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))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
5.4b
(+.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))))))
1.1b
(+.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) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))))
12.2b
(+.f64 lambda1 (log.f64 (exp.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))))))
5.6b
(+.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))))))
31.2b
(+.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))))))
1.1b
(+.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))))))))
27.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (+.f64 1 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (*.f64 1/24 (pow.f64 phi1 4))) (+.f64 (*.f64 1/2 (*.f64 phi1 phi1)) (*.f64 1/720 (pow.f64 phi1 6))))))
5.7b
(+.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 2215 to 742 computations (66.5% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite125.0ms (0.9%)

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 → 57
Calls

4 calls:

4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
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 2398 to 354 computations (85.2% saved)

series242.0ms (1.8%)

Error
0.1b
Counts
4 → 53
Calls

4 calls:

100.0ms
(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
36.0ms
(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))))))
23.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
23.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 4877 to 2339 computations (52% saved)

simplify112.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
585×cancel-sign-sub-inv_binary64
425×sub-neg_binary64
294×distribute-rgt-in_binary64
282×distribute-rgt-neg-in_binary64
273×distribute-lft-in_binary64
Counts
110 → 75
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02123346
15692979
217822907
345012907
450682907

prune115.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New73275
Fresh3710
Picked011
Done000
Total761086
Error
0.1b
Counts
86 → 10
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)))))))
1.4b
(+.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))))))
▶1.1b
(+.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))))))))
4.5b
(+.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 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (*.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (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))))))))
5.6b
(+.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))))))
31.2b
(+.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))))))
12.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (+.f64 (cos.f64 phi1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
27.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (+.f64 1 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (*.f64 1/24 (pow.f64 phi1 4))) (+.f64 (*.f64 1/2 (*.f64 phi1 phi1)) (*.f64 1/720 (pow.f64 phi1 6))))))
5.7b
(+.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)))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
Compiler

Compiled 2864 to 802 computations (72% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b
(sin.f64 (-.f64 lambda1 lambda2))
3.4b
(cos.f64 (-.f64 lambda1 lambda2))
3.4b
(cos.f64 (-.f64 lambda1 lambda2))
3.4b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite132.0ms (1%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
12×cancel-sign-sub-inv_binary64
12×cos-sum_binary64
8×*-un-lft-identity_binary64
8×add-sqr-sqrt_binary64
8×add-cube-cbrt_binary64
Counts
4 → 48
Calls

4 calls:

4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
3.0ms
(cos.f64 (-.f64 lambda1 lambda2))
3.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 2788 to 625 computations (77.6% saved)

series160.0ms (1.2%)

Error
0.1b
Counts
4 → 42
Calls

4 calls:

26.0ms
(cos.f64 (-.f64 lambda1 lambda2))
24.0ms
(sin.f64 (-.f64 lambda1 lambda2))
21.0ms
(cos.f64 (-.f64 lambda1 lambda2))
20.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 5205 to 2182 computations (58.1% saved)

simplify150.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
591×distribute-rgt-neg-in_binary64
575×sub-neg_binary64
503×distribute-lft-neg-in_binary64
422×*-commutative_binary64
406×unswap-sqr_binary64
Counts
90 → 44
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01021182
12201112
24531085
313561070
428291070
541881070
648821070
749611070
848451070

prune94.0ms (0.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New43144
Fresh178
Picked011
Done011
Total441054
Error
0.1b
Counts
54 → 10
Alt Table
StatusErrorProgram
5.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (/.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))))))))
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)))))))
1.4b
(+.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))))))
1.1b
(+.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))))))))
4.5b
(+.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 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (*.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (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))))))))
31.2b
(+.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))))))
12.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (+.f64 (cos.f64 phi1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
27.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (+.f64 1 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (*.f64 1/24 (pow.f64 phi1 4))) (+.f64 (*.f64 1/2 (*.f64 phi1 phi1)) (*.f64 1/720 (pow.f64 phi1 6))))))
5.7b
(+.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)))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (+.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))))))
Compiler

Compiled 2205 to 664 computations (69.9% saved)

regimes1.4s (10.2%)

Accuracy

Total 0.1b remaining (48.1%)

Threshold costs 0.1b (48.1%)

Compiler

Compiled 38346 to 21290 computations (44.5% saved)

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
10×*-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
02361
13861
24861
35461
45861
55961
65961

end1.0ms (0%)

Compiler

Compiled 41 to 22 computations (46.3% saved)

sample6.8s (50.4%)

Algorithm
1×intervals
Results
4.5s4526×body1024valid
942.0ms1716×body512valid
255.0ms110×body2048valid
210.0ms665×body256valid
171.0ms983×body128valid
Compiler

Compiled 502 to 260 computations (48.2% saved)

Profiling

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