Details

Time bar (total: 21.6s)

analyze3.8s (17.8%)

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
7.8%92%0.2%9
7.8%92%0.2%10
10.1%89.7%0.2%11
10.1%89.7%0.2%12
13.9%85.9%0.2%13
13.9%85.9%0.2%14
Compiler

Compiled 29 to 18 computations (37.9% saved)

sample12.3s (56.8%)

Results
9.6s5500×body1024valid
1.2s1286×body512valid
813.0ms212×body2048valid
261.0ms861×body128valid
232.0ms397×body256valid
Compiler

Compiled 86 to 53 computations (38.4% saved)

simplify27.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
543×fma-def_binary64
194×fma-neg_binary64
83×cancel-sign-sub-inv_binary64
59×distribute-rgt-neg-in_binary64
47×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13239
26139
311539
415539
524639
634839
743739
857239
962239
1069439
1172039
1266939

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
13.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 108 to 55 computations (49.1% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
✓0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓3.1b
(sin.f64 (-.f64 lambda1 lambda2))
✓3.2b
(cos.f64 (-.f64 lambda1 lambda2))

series59.0ms (0.3%)

Counts
4 → 88
Calls

4 calls:

42.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
10.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

rewrite68.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
315×expm1-udef_binary64
315×log1p-udef_binary64
173×add-sqr-sqrt_binary64
161×log1p-expm1-u_binary64
161×expm1-log1p-u_binary64
Counts
4 → 90
Calls

4 calls:

66.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
66.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
66.0ms
(sin.f64 (-.f64 lambda1 lambda2))
66.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01536
132136
2416136
3509836

simplify78.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
866×cancel-sign-sub-inv_binary64
560×sub-neg_binary64
358×distribute-rgt-neg-in_binary64
356×fma-neg_binary64
336×distribute-lft-neg-in_binary64
Counts
178 → 166
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01881845
15741774
218931605
341371597
451321597

prune423.0ms (2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New14917166
Fresh000
Picked101
Done000
Total15017167
Error
7.4b
Counts
167 → 17
Alt Table
StatusErrorProgram
19.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda2))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))))
▶11.0b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
25.8b
(atan2.f64 (*.f64 (-.f64 (sin.f64 lambda1) (*.f64 lambda2 (cos.f64 lambda1))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
33.5b
(atan2.f64 (*.f64 (sin.f64 (neg.f64 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
14.5b
(atan2.f64 (*.f64 (/.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)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
26.7b
(atan2.f64 (*.f64 (-.f64 (fma.f64 1/6 (*.f64 (cos.f64 lambda1) (pow.f64 lambda2 3)) (sin.f64 lambda1)) (*.f64 lambda2 (+.f64 (cos.f64 lambda1) (*.f64 (*.f64 1/2 (sin.f64 lambda1)) lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 2)))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
39.7b
(atan2.f64 (*.f64 (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.2b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
27.0b
(atan2.f64 (*.f64 (fma.f64 (cos.f64 lambda2) lambda1 (*.f64 (+.f64 (*.f64 -1/2 (*.f64 lambda1 lambda1)) 1) (sin.f64 (neg.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
21.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))
21.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
17.5b
(atan2.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
19.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (sqrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 2)))))
Compiler

Compiled 6644 to 1948 computations (70.7% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
✓0.4b
(*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
3.2b
(cos.f64 (-.f64 lambda1 lambda2))
✓5.0b
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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))))

series192.0ms (0.9%)

Counts
3 → 72
Calls

3 calls:

120.0ms
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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))))
47.0ms
(*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
26.0ms
(*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))

rewrite84.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
289×log1p-udef_binary64
163×add-sqr-sqrt_binary64
160×associate-*r*_binary64
156×log1p-expm1-u_binary64
156×expm1-log1p-u_binary64
Counts
3 → 83
Calls

3 calls:

82.0ms
(*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
82.0ms
(*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
82.0ms
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01464
132140
2450540
3495940

simplify100.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
771×associate-*r*_binary64
705×associate-*l*_binary64
448×fma-def_binary64
414×cancel-sign-sub-inv_binary64
310×distribute-rgt-out--_binary64
Counts
155 → 131
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01041884
13211840
210631751
344911741
454151741

prune651.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1657172
Fresh14216
Picked101
Done000
Total1809189
Error
0.1b
Counts
189 → 9
Alt Table
StatusErrorProgram
11.8b
(atan2.f64 (*.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) 3)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
10.4b
(atan2.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 2))) 2) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 2)) (cbrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))))
7.9b
(atan2.f64 (*.f64 (*.f64 (/.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 2)) (/.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶3.5b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.5b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
3.5b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
13.8b
(atan2.f64 (*.f64 (/.f64 (-.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2))) 1) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 10373 to 2159 computations (79.2% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.3b
(*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.4b
(*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)))
5.0b
(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.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))))

series74.0ms (0.3%)

Counts
1 → 48
Calls

1 calls:

74.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite62.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
698×prod-diff_binary64
162×add-sqr-sqrt_binary64
149×log1p-expm1-u_binary64
149×expm1-log1p-u_binary64
148×add-log-exp_binary64
Counts
1 → 20
Calls

1 calls:

62.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
130616
2381716
3518016

simplify97.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
902×cancel-sign-sub-inv_binary64
612×sub-neg_binary64
357×fma-neg_binary64
339×associate-*r*_binary64
297×associate--l+_binary64
Counts
68 → 53
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01681923
15511846
219611692
342501692
449781692
551841692

prune476.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1786184
Fresh448
Picked101
Done000
Total18310193
Error
0.0b
Counts
193 → 10
Alt Table
StatusErrorProgram
7.9b
(atan2.f64 (*.f64 (*.f64 (/.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 2)) (/.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
8.9b
(atan2.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 2)) 3) (pow.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) 3))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.3b
(atan2.f64 (*.f64 (+.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (fma.f64 (neg.f64 (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) 2) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))))
▶0.1b
(atan2.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
2.9b
(atan2.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 2))) 2) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 2)) (cbrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
3.4b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 2) (pow.f64 (cos.f64 lambda2) 2)) (*.f64 (pow.f64 (sin.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2))) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
3.8b
(atan2.f64 (*.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) 2) 3) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.8b
(atan2.f64 (*.f64 (/.f64 (-.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2))) 1) (*.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)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 12544 to 2561 computations (79.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
✓0.2b
(fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
✓0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series37.0ms (0.2%)

Counts
3 → 56
Calls

3 calls:

17.0ms
(fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
11.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite115.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
630×prod-diff_binary64
452×fma-udef_binary64
361×fma-def_binary64
267×fma-neg_binary64
202×expm1-udef_binary64
Counts
3 → 102
Calls

3 calls:

112.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
112.0ms
(fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
112.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01134
122932
2266722
3473422
4473322
5499222

simplify74.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
541×distribute-rgt-neg-in_binary64
512×distribute-lft-neg-in_binary64
390×cancel-sign-sub-inv_binary64
388×fma-def_binary64
349×associate-*r*_binary64
Counts
158 → 145
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
096962
1300934
2912877
32978854
44850854
55045854

prune431.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1953198
Fresh459
Picked101
Done000
Total2008208
Error
0.0b
Counts
208 → 8
Alt Table
StatusErrorProgram
7.9b
(atan2.f64 (*.f64 (*.f64 (/.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 2)) (/.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
8.9b
(atan2.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 2)) 3) (pow.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) 3))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.1b
(atan2.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (expm1.f64 (log1p.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
2.9b
(atan2.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 2) (pow.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 2))) 2) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 2)) (cbrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.4b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (pow.f64 (sin.f64 lambda1) 2) (pow.f64 (cos.f64 lambda2) 2)) (*.f64 (pow.f64 (sin.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2))) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.3b
(atan2.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (pow.f64 (cbrt.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) 3))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
8.3b
(atan2.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) 3)))))
Compiler

Compiled 9714 to 2165 computations (77.7% saved)

regimes2.1s (9.5%)

Accuracy

Total 0.1b remaining (56.3%)

Threshold costs 0.1b (56.3%)

Counts
223 → 1
Compiler

Compiled 59493 to 34769 computations (41.6% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
14×*-commutative_binary64
9×+-commutative_binary64
9×sub-neg_binary64
8×neg-sub0_binary64
8×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02665
14565
26765
38265
49265
59565
69565

end260.0ms (1.2%)

Compiler

Compiled 512 to 285 computations (44.3% saved)

Profiling

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