Details

Time bar (total: 22.7s)

analyze4.3s (19%)

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)

sample12.6s (55.4%)

Results
9.6s5476×body1024valid
1.4s1398×body512valid
811.0ms192×body2048valid
305.0ms803×body128valid
251.0ms387×body256valid
Compiler

Compiled 86 to 53 computations (38.4% saved)

simplify30.0ms (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
16.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
16.7b
(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)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.4b
(sin.f64 (-.f64 lambda1 lambda2))
4.5b
(cos.f64 (-.f64 lambda1 lambda2))

series74.0ms (0.3%)

Counts
4 → 100
Calls

4 calls:

43.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
20.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
6.0ms
(sin.f64 (-.f64 lambda1 lambda2))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms (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:

8.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
6.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

simplify136.0ms (0.6%)

Algorithm
egg-herbie
Rules
980×fma-neg_binary64
457×associate-*r*_binary64
441×distribute-rgt-neg-in_binary64
422×associate-*l*_binary64
395×distribute-lft-neg-in_binary64
Counts
190 → 201
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03994414
18623679
229133547
346813537
450703537

prune400.0ms (1.8%)

Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New18219201
Fresh000
Picked101
Done000
Total18319202
Error
7.7b
Counts
202 → 19
Alt Table
StatusErrorProgram
16.7b
(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)))))))
35.6b
(atan2.f64 (*.f64 (+.f64 (*.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)))))) (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 (*.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))))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
16.7b
(atan2.f64 (*.f64 (log1p.f64 (expm1.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)))))
33.8b
(atan2.f64 (*.f64 (sin.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)))))
26.5b
(atan2.f64 (*.f64 (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (*.f64 1/2 (*.f64 lambda1 (*.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)))))
40.0b
(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 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (sin.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2))))))))
27.8b
(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)))))
28.3b
(atan2.f64 (*.f64 (-.f64 (sin.f64 lambda1) (+.f64 (*.f64 lambda2 (cos.f64 lambda1)) (*.f64 1/2 (*.f64 (sin.f64 lambda1) (pow.f64 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)))))
18.0b
(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))))))
8.1b
(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)))))
22.5b
(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 (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 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))))))))))
25.9b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sqrt.f64 (cos.f64 phi2))) (sqrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.5b
(atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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)))))
16.8b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
39.1b
(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)))))
16.7b
(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)) (cbrt.f64 (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 (-.f64 lambda1 lambda2)))))))
20.8b
(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 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (*.f64 lambda2 1)))) (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (*.f64 lambda2 1))))))))
16.5b
(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 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
24.9b
(atan2.f64 (*.f64 (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (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)))))
Compiler

Compiled 9327 to 2392 computations (74.4% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b
(-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.5b
(cos.f64 (-.f64 lambda1 lambda2))

series33.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

18.0ms
(-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
14.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite9.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 36
Calls

2 calls:

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

simplify88.0ms (0.4%)

Algorithm
egg-herbie
Rules
598×fma-neg_binary64
443×fma-def_binary64
315×distribute-rgt-neg-in_binary64
300×cancel-sign-sub-inv_binary64
278×distribute-lft-neg-in_binary64
Counts
84 → 87
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01281418
13401354
210711317
324101304
447611304
548931304

prune495.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1878195
Fresh15318
Picked101
Done000
Total20311214
Error
0.1b
Counts
214 → 11
Alt Table
StatusErrorProgram
20.8b
(atan2.f64 (*.f64 (log.f64 (exp.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.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)))))
8.1b
(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)) (expm1.f64 (log1p.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
8.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cos.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (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)))))
9.5b
(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 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
8.3b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.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)) (cos.f64 (-.f64 lambda1 lambda2)))))
25.9b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sqrt.f64 (cos.f64 phi2))) (sqrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.5b
(atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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)))))
8.2b
(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 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
16.8b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
12.4b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.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)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 9109 to 2006 computations (78% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series85.0ms (0.4%)

Counts
2 → 84
Calls

2 calls:

58.0ms
(*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
27.0ms
(*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))

rewrite14.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube_binary64
19×add-exp-log_binary64
19×pow1_binary64
11×cbrt-unprod_binary64
11×prod-exp_binary64
Counts
2 → 45
Calls

2 calls:

6.0ms
(*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
5.0ms
(*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))

simplify107.0ms (0.5%)

Algorithm
egg-herbie
Rules
846×fma-neg_binary64
771×cancel-sign-sub-inv_binary64
541×associate-*r*_binary64
435×associate-*l*_binary64
358×distribute-rgt-neg-in_binary64
Counts
129 → 117
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02453163
17342837
225572760
342522752
449752752

prune564.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1977204
Fresh5510
Picked101
Done000
Total20312215
Error
0.0b
Counts
215 → 12
Alt Table
StatusErrorProgram
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 (cos.f64 lambda2) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1))))) (cbrt.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
12.8b
(atan2.f64 (*.f64 (log.f64 (exp.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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
9.5b
(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 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
8.3b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.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)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)) 3))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.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 (cos.f64 lambda2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda1))) (*.f64 (cbrt.f64 (cos.f64 lambda1)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
25.9b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sqrt.f64 (cos.f64 phi2))) (sqrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.5b
(atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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)))))
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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))))
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 (cos.f64 lambda2) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
16.8b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.4b
(atan2.f64 (*.f64 (/.f64 (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 12172 to 2367 computations (80.6% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
0.2b
(*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))
0.2b
(*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))
2.7b
(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))))

series143.0ms (0.6%)

Counts
3 → 132
Calls

3 calls:

58.0ms
(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))))
56.0ms
(*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))
28.0ms
(*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))

rewrite18.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×pow1_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
3 → 61
Calls

3 calls:

8.0ms
(*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))
5.0ms
(*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))
2.0ms
(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))))

simplify135.0ms (0.6%)

Algorithm
egg-herbie
Rules
784×cancel-sign-sub-inv_binary64
482×associate-*r*_binary64
397×fma-neg_binary64
348×distribute-rgt-neg-in_binary64
340×associate-*l*_binary64
Counts
193 → 133
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02414913
16614550
223174139
342734133
449994133

prune509.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1733176
Fresh2911
Picked101
Done000
Total17612188
Error
0.0b
Counts
188 → 12
Alt Table
StatusErrorProgram
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 (cos.f64 lambda2) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1))))) (cbrt.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
12.8b
(atan2.f64 (*.f64 (log.f64 (exp.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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
9.5b
(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 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
8.3b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.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)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)) 3))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.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 (cos.f64 lambda2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda1))) (*.f64 (cbrt.f64 (cos.f64 lambda1)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))))))
25.9b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sqrt.f64 (cos.f64 phi2))) (sqrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0b
(atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (-.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 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))))
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 (cos.f64 lambda2) (log1p.f64 (expm1.f64 (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
16.8b
(atan2.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (cos.f64 phi2))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b
(atan2.f64 (*.f64 (log1p.f64 (expm1.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))))
Compiler

Compiled 10429 to 1980 computations (81% saved)

regimes2.5s (11%)

Accuracy

Total 0.1b remaining (54.6%)

Threshold costs 0.1b (54.6%)

Counts
272 → 1
Compiler

Compiled 74338 to 41682 computations (43.9% saved)

simplify8.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02993
15093
26593
38993
411893
513493
614493
714793
814793

end323.0ms (1.4%)

Compiler

Compiled 733 to 376 computations (48.7% saved)

Profiling

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