Details

Time bar (total: 17.6s)

analyze2.8s (15.6%)

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)

sample221.0ms (1.3%)

Algorithm
1×intervals
Results
151.0ms164×body1024valid
29.0ms53×body512valid
10.0ms5×body2048valid
10.0ms20×body128valid
5.0ms14×body256valid
Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify24.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
83×cancel-sign-sub-inv_binary64
59×distribute-rgt-neg-in_binary64
56×sub-neg_binary64
47×distribute-rgt-in_binary64
42×unsub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13139
25939
310539
412939
519639
624839
730939
842039
943039
1043639
1138539

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
11.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶11.7b
(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 84 to 51 computations (39.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite145.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Error
5.2b
Rules
11×add-sqr-sqrt_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
9×add-cube-cbrt_binary64 *-un-lft-identity_binary64
6×cancel-sign-sub-inv_binary64 associate-*r*_binary64
4×sin-sum_binary64 add-log-exp_binary64 cos-sum_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
3×cos-diff_binary64
Counts
4 → 64
Calls

4 calls:

7.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
7.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
5.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 1966 to 330 computations (83.2% saved)

series258.0ms (1.5%)

Error
7.6b
Counts
4 → 58
Calls

4 calls:

89.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
52.0ms
(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
27.0ms
(sin.f64 (-.f64 lambda1 lambda2))
26.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 4167 to 2025 computations (51.4% saved)

simplify132.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
698×distribute-rgt-neg-in_binary64
564×cancel-sign-sub-inv_binary64
404×neg-mul-1_binary64
401×sub-neg_binary64
373×neg-sub0_binary64
Counts
122 → 72
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02452367
16442118
219612010
335852010
447232010
549752010

prune129.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New581472
Fresh000
Picked101
Done000
Total591473
Error
5.2b
Counts
73 → 14
Alt Table
StatusErrorProgram
11.9b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (*.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.7b
(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 (cos.f64 lambda2) (*.f64 lambda1 (sin.f64 lambda2))))))
30.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
24.6b
(atan2.f64 (*.f64 (-.f64 (-.f64 (*.f64 lambda1 (cos.f64 lambda2)) (sin.f64 lambda2)) (*.f64 (*.f64 lambda1 lambda1) (*.f64 (sin.f64 lambda2) -1/2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
38.4b
(atan2.f64 (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶5.4b
(atan2.f64 (*.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)))))
21.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (/.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (+.f64 (sin.f64 (-.f64 phi1 phi2)) (sin.f64 (+.f64 phi2 phi1)))) 2)))
11.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
14.8b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
27.1b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda1) (-.f64 (*.f64 1/6 (pow.f64 lambda2 3)) lambda2)) (-.f64 (*.f64 1/2 (*.f64 (sin.f64 lambda1) (*.f64 lambda2 lambda2))) (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)))))
19.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))))
11.6b
(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 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
25.5b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 lambda1 (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/2))))))
23.4b
(atan2.f64 (log.f64 (pow.f64 (exp.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 2652 to 951 computations (64.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.1b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite184.0ms (1%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
14×add-sqr-sqrt_binary64
13×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64
9×associate-*r*_binary64
7×associate-*l*_binary64
Counts
4 → 71
Calls

4 calls:

10.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
7.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 2666 to 378 computations (85.8% saved)

series332.0ms (1.9%)

Error
4.8b
Counts
4 → 57
Calls

4 calls:

91.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
90.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
33.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
30.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 5092 to 2555 computations (49.8% saved)

simplify120.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
672×cancel-sign-sub-inv_binary64
428×associate-*r*_binary64
411×associate-*l*_binary64
360×distribute-rgt-neg-in_binary64
321×neg-mul-1_binary64
Counts
128 → 86
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02882898
17742625
225042493
342652491
449882491

prune161.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New80686
Fresh9413
Picked101
Done000
Total9010100
Error
0.1b
Counts
100 → 10
Alt Table
StatusErrorProgram
11.9b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (*.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
30.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (sqrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
38.4b
(atan2.f64 (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
14.8b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
7.4b
(atan2.f64 (/.f64 (*.f64 (cos.f64 phi2) (-.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)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
5.7b
(atan2.f64 (*.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)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
32.9b
(atan2.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.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 (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 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
8.4b
(atan2.f64 (*.f64 (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (*.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)))))
5.8b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 3300 to 893 computations (72.9% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite242.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
17×add-sqr-sqrt_binary64
15×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
12×associate-*r*_binary64
11×add-cube-cbrt_binary64 *-un-lft-identity_binary64
10×associate-*l*_binary64
Counts
4 → 84
Calls

4 calls:

10.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
7.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
5.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 3785 to 478 computations (87.4% saved)

series403.0ms (2.3%)

Error
0.1b
Counts
4 → 57
Calls

4 calls:

145.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
89.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
33.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
32.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 6225 to 2832 computations (54.5% saved)

simplify122.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
751×associate-*r*_binary64
676×associate-*l*_binary64
513×distribute-rgt-neg-in_binary64
354×*-commutative_binary64
210×sub-neg_binary64
Counts
141 → 102
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03774127
110843646
241763646
352493646

prune261.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New957102
Fresh369
Picked101
Done000
Total9913112
Error
0.1b
Counts
112 → 13
Alt Table
StatusErrorProgram
1.2b
(atan2.f64 (*.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)) (log.f64 (pow.f64 (exp.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
▶0.2b
(atan2.f64 (*.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 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
11.9b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (*.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.4b
(atan2.f64 (*.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 (cbrt.f64 (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
12.0b
(atan2.f64 (log.f64 (exp.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.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))))))
38.4b
(atan2.f64 (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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 (*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2))) (*.f64 (sin.f64 lambda1) (cbrt.f64 (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))))))
14.8b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
7.4b
(atan2.f64 (/.f64 (*.f64 (cos.f64 phi2) (-.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)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.2b
(atan2.f64 (*.f64 (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (*.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))))))
5.7b
(atan2.f64 (*.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)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
32.9b
(atan2.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
23.7b
(atan2.f64 (*.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 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (sqrt.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))) (sqrt.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
Compiler

Compiled 5071 to 1250 computations (75.4% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite316.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
20×add-sqr-sqrt_binary64
12×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64 associate-*l*_binary64 associate-*r*_binary64
4×pow-prod-down_binary64 prod-exp_binary64 add-log-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
3×associate-*r/_binary64
2×sin-mult_binary64 associate-*l/_binary64
Counts
4 → 80
Calls

4 calls:

9.0ms
(*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
7.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms
(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
4.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
Compiler

Compiled 3494 to 469 computations (86.6% saved)

series340.0ms (1.9%)

Error
0.1b
Counts
4 → 51
Calls

4 calls:

88.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
82.0ms
(*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
34.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
33.0ms
(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
Compiler

Compiled 5205 to 2449 computations (52.9% saved)

simplify130.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
730×cancel-sign-sub-inv_binary64
474×associate-*r*_binary64
441×associate-*l*_binary64
370×distribute-rgt-neg-in_binary64
327×distribute-lft-neg-in_binary64
Counts
131 → 78
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02923130
18142881
228672779
342292779
449782779

prune224.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New75378
Fresh3912
Picked101
Done000
Total791291
Error
0.1b
Counts
91 → 12
Alt Table
StatusErrorProgram
1.2b
(atan2.f64 (*.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)) (log.f64 (pow.f64 (exp.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
11.9b
(atan2.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (*.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
12.0b
(atan2.f64 (log.f64 (exp.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.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))))))
38.4b
(atan2.f64 (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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 (*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2))) (*.f64 (sin.f64 lambda1) (cbrt.f64 (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))))))
0.3b
(atan2.f64 (*.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 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (sin.f64 phi1))) (cbrt.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (sin.f64 phi1)))) (cbrt.f64 (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (sin.f64 phi1)))))))
7.4b
(atan2.f64 (/.f64 (*.f64 (cos.f64 phi2) (-.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)))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.2b
(atan2.f64 (*.f64 (-.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (*.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))))))
3.4b
(atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 3)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 phi1) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
5.7b
(atan2.f64 (*.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)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
32.9b
(atan2.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (sqrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.4b
(atan2.f64 (*.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 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (*.f64 (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (sin.f64 phi1)))))))
Compiler

Compiled 3319 to 774 computations (76.7% saved)

regimes3.6s (20.7%)

Accuracy

Total 0.1b remaining (63.2%)

Threshold costs 0.1b (63.2%)

Compiler

Compiled 72615 to 41494 computations (42.9% saved)

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
21×*-commutative_binary64
15×+-commutative_binary64
14×sub-neg_binary64
12×neg-mul-1_binary64 neg-sub0_binary64
10×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02763
14963
26663
38463
410063
512263
613263
713863
814063
913963

end1.0ms (0%)

Compiler

Compiled 42 to 24 computations (42.9% saved)

sample7.4s (41.8%)

Algorithm
1×intervals
Results
4.8s5336×body1024valid
954.0ms1295×body512valid
348.0ms179×body2048valid
147.0ms397×body256valid
135.0ms793×body128valid
Compiler

Compiled 655 to 350 computations (46.6% saved)

Profiling

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