Details

Time bar (total: 19.8s)

analyze3.8s (18.9%)

Algorithm
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)

sample493.0ms (2.5%)

Algorithm
intervals
Results
258.0ms179×body1024valid
31.0ms40×body512valid
17.0msbody2048valid
5.0ms12×body256valid
4.0ms19×body128valid
Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify27.0ms (0.1%)

Algorithm
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
12.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
12.6b
(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 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 108 to 55 computations (49.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.6b
(sin.f64 (-.f64 lambda1 lambda2))
2.6b
(cos.f64 (-.f64 lambda1 lambda2))

series57.0ms (0.3%)

Counts
4 → 72
Calls

4 calls:

37.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
12.0ms
(*.f64 (sin.f64 phi1) (cos.f64 phi2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64
21×add-cube-cbrt_binary64
18×prod-diff_binary64
13×sin-sum_binary64
Counts
4 → 90
Calls

4 calls:

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

simplify111.0ms (0.6%)

Algorithm
egg-herbie
Rules
453×fma-neg_binary64
422×associate-*r*_binary64
380×associate-*l*_binary64
380×distribute-rgt-neg-in_binary64
340×distribute-lft-neg-in_binary64
Counts
162 → 194
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03683902
17823174
226332887
346522788
450112788

prune389.0ms (2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New17618194
Fresh000
Picked101
Done000
Total17718195
Error
6.4b
Counts
195 → 18
Alt Table
StatusErrorProgram
12.4b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))))
39.4b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.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)))))
12.7b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
50.5b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.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)))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
6.7b
(atan2.f64 (*.f64 (-.f64 (*.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)) (cos.f64 (-.f64 lambda1 lambda2)))))
24.3b
(atan2.f64 (*.f64 (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (*.f64 (*.f64 lambda1 lambda1) (-.f64 (*.f64 1/2 (sin.f64 lambda2)) (*.f64 (*.f64 (cos.f64 lambda2) 1/6) 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)))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
16.6b
(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)))))
26.1b
(atan2.f64 (*.f64 (fma.f64 (cos.f64 lambda2) lambda1 (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)))))
23.6b
(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)) (-.f64 (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))))))
23.3b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (*.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.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)))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
12.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
12.6b
(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)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
16.9b
(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)) (-.f64 (*.f64 (cos.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (*.f64 (sin.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))))))
41.3b
(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 (*.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (*.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))))))))
Compiler

Compiled 8961 to 2416 computations (73% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b
(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.6b
(cos.f64 (-.f64 lambda1 lambda2))

series9.0ms (0%)

Counts
1 → 24
Calls

1 calls:

9.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))

rewrite4.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
associate-*r*_binary64
associate-*l*_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
1 → 20
Calls

1 calls:

3.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify91.0ms (0.5%)

Algorithm
egg-herbie
Rules
595×fma-neg_binary64
480×distribute-rgt-neg-in_binary64
423×distribute-lft-neg-in_binary64
325×*-commutative_binary64
265×associate-*l*_binary64
Counts
44 → 45
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
078572
1191512
2572487
31551483
43033483
54866483
64975483
74902483

prune506.0ms (2.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1927199
Fresh11617
Picked101
Done000
Total20413217
Error
0.1b
Counts
217 → 13
Alt Table
StatusErrorProgram
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
6.7b
(atan2.f64 (*.f64 (-.f64 (*.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)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
35.9b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
16.6b
(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)))))
6.7b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 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)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
12.7b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
12.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
6.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
6.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 9304 to 2120 computations (77.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.2b
(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (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))

series110.0ms (0.6%)

Counts
3 → 72
Calls

3 calls:

79.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
22.0ms
(+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
9.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite23.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
10×pow1_binary64
add-sqr-sqrt_binary64
associate-*r*_binary64
Counts
3 → 65
Calls

3 calls:

11.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
4.0ms
(+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify132.0ms (0.7%)

Algorithm
egg-herbie
Rules
658×fma-neg_binary64
628×associate-*r*_binary64
567×associate-*l*_binary64
307×*-commutative_binary64
304×fma-def_binary64
Counts
137 → 166
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03164176
110193884
239303878
348563878
449833878

prune594.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2066212
Fresh7512
Picked101
Done000
Total21411225
Error
0.0b
Counts
225 → 11
Alt Table
StatusErrorProgram
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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 (log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) (cbrt.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))))
35.9b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
6.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.6b
(atan2.f64 (*.f64 (-.f64 (*.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)) (log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
16.6b
(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)))))
0.3b
(atan2.f64 (*.f64 (-.f64 (*.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 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
6.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 11684 to 2353 computations (79.9% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
0.2b
(*.f64 (cos.f64 phi2) (sin.f64 phi1))
0.2b
(*.f64 (log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series125.0ms (0.6%)

Counts
3 → 96
Calls

3 calls:

103.0ms
(*.f64 (log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
12.0ms
(log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
9.0ms
(*.f64 (cos.f64 phi2) (sin.f64 phi1))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
3 → 56
Calls

3 calls:

7.0ms
(*.f64 (log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
3.0ms
(*.f64 (cos.f64 phi2) (sin.f64 phi1))
0.0ms
(log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1))))

simplify164.0ms (0.8%)

Algorithm
egg-herbie
Rules
822×fma-neg_binary64
579×associate-*r*_binary64
498×associate-*l*_binary64
337×distribute-rgt-neg-in_binary64
308×distribute-lft-neg-in_binary64
Counts
152 → 133
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02843846
18303571
233563559
349073555
451833555

prune477.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1800180
Fresh01010
Picked011
Done000
Total18011191
Error
0.0b
Counts
191 → 11
Alt Table
StatusErrorProgram
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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 (log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) (cbrt.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))) 3))))
35.9b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))) (sqrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.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)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
6.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (cbrt.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.6b
(atan2.f64 (*.f64 (-.f64 (*.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)) (log.f64 (pow.f64 (exp.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
12.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
16.6b
(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)))))
0.3b
(atan2.f64 (*.f64 (-.f64 (*.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 (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
6.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 9796 to 1925 computations (80.3% saved)

regimes1.9s (9.6%)

Accuracy

Total 0.1b remaining (58.3%)

Threshold costs 0.1b (58.3%)

Counts
201 → 1
Compiler

Compiled 52895 to 29460 computations (44.3% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Rules
19×*-commutative_binary64
14×+-commutative_binary64
13×sub-neg_binary64
11×neg-sub0_binary64
11×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02767
14667
27067
39067
411367
512367
612767
712867
812867

end1.0ms (0%)

Compiler

Compiled 44 to 26 computations (40.9% saved)

sample10.7s (54%)

Algorithm
intervals
Results
8.1s5305×body1024valid
959.0ms1334×body512valid
595.0ms174×body2048valid
179.0ms804×body128valid
179.0ms383×body256valid
Compiler

Compiled 633 to 322 computations (49.1% saved)

Profiling

Loading profile data...