Details

Time bar (total: 32.8s)

analyze7.4s (22.6%)

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
0%99.8%0.2%9
0%99.8%0.2%10
0%99.8%0.2%11
0%99.8%0.2%12
0.6%99.2%0.2%13
1.8%98%0.2%14
Compiler

Compiled 71 to 47 computations (33.8% saved)

sample469.0ms (1.4%)

Algorithm
intervals
Results
341.0ms182×body1024valid
44.0ms15×body2048valid
31.0ms27×body512valid
9.0ms12×body256valid
7.0ms20×body128valid
2.0msbody1024invalid
Compiler

Compiled 146 to 98 computations (32.9% saved)

simplify188.0ms (0.6%)

Algorithm
egg-herbie
Rules
714×distribute-rgt-neg-in_binary64
578×sub-neg_binary64
479×fabs-mul_binary64
468×cube-prod_binary64
458×sqr-pow_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027103
159103
2119103
3235103
4459103
5811103
61302103
72017103
82988103
93479103
104058103
114322103
124127103
133850103
144705103
154800103

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
24.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
24.9b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
Compiler

Compiled 210 to 138 computations (34.3% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite133.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
24.6b
Rules
div-sub_binary64 sin-diff_binary64 pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
Counts
4 → 32
Calls

4 calls:

5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
Compiler

Compiled 2333 to 1346 computations (42.3% saved)

series285.0ms (0.9%)

Error
24.0b
Counts
4 → 46
Calls

4 calls:

40.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
39.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
39.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
36.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
Compiler

Compiled 7729 to 5049 computations (34.7% saved)

simplify132.0ms (0.4%)

Algorithm
egg-herbie
Rules
637×distribute-rgt-neg-in_binary64
610×cancel-sign-sub-inv_binary64
566×sub-neg_binary64
486×distribute-lft-neg-in_binary64
337×neg-mul-1_binary64
Counts
78 → 26
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0631524
11461448
23571358
39531330
422391330
542801330
644641330
748711330

prune127.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New18826
Fresh000
Picked101
Done000
Total19827
Error
24.5b
Counts
27 → 8
Alt Table
StatusErrorProgram
37.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 (sin.f64 (*.f64 -1/2 lambda2)) (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8))) (*.f64 lambda1 (*.f64 (cos.f64 (*.f64 -1/2 lambda2)) (+.f64 1/2 (*.f64 lambda1 (*.f64 lambda1 -1/48))))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
36.5b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (sin.f64 (*.f64 1/2 lambda1)) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1)))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))) (*.f64 (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8)) (sin.f64 (*.f64 lambda2 1/2)))))))))))
24.9b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.7b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2))))))))))))
36.4b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.2b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (sin.f64 (*.f64 1/2 lambda1)) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1))))))))))
Compiler

Compiled 3273 to 2068 computations (36.8% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
9.1b
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

rewrite232.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
24.2b
Rules
12×cbrt-prod_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
unpow-prod-down_binary64 cube-prod_binary64 div-sub_binary64 sin-diff_binary64
pow1/3_binary64 unpow3_binary64 cube-mult_binary64 sqr-pow_binary64 rem-cbrt-cube_binary64
Counts
4 → 45
Calls

4 calls:

6.0ms
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
Compiler

Compiled 3223 to 1914 computations (40.6% saved)

series324.0ms (1%)

Error
24.0b
Counts
4 → 45
Calls

4 calls:

43.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
43.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
43.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
40.0ms
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
Compiler

Compiled 7863 to 5216 computations (33.7% saved)

simplify227.0ms (0.7%)

Algorithm
egg-herbie
Rules
637×distribute-rgt-neg-in_binary64
626×fabs-mul_binary64
610×cancel-sign-sub-inv_binary64
528×unswap-sqr_binary64
379×*-commutative_binary64
Counts
90 → 44
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0891641
11821587
24651510
312301482
427521464
544371464
647451464
748601464
847401464
949711464
1049421464

prune196.0ms (0.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New38644
Fresh167
Picked101
Done000
Total401252
Error
24.4b
Counts
52 → 12
Alt Table
StatusErrorProgram
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
37.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 (sin.f64 (*.f64 -1/2 lambda2)) (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8))) (*.f64 lambda1 (*.f64 (cos.f64 (*.f64 -1/2 lambda2)) (+.f64 1/2 (*.f64 lambda1 (*.f64 lambda1 -1/48))))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
36.5b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (sin.f64 (*.f64 1/2 lambda1)) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1)))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.2b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
50.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))) (*.f64 (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8)) (sin.f64 (*.f64 lambda2 1/2)))))))))))
38.7b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2))))))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
24.9b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
36.4b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
38.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (sin.f64 (*.f64 1/2 lambda1)) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1))))))))))
Compiler

Compiled 4552 to 2897 computations (36.4% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b
(log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))

rewrite187.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
24.2b
Rules
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
pow1_binary64
log-pow_binary64 div-sub_binary64 sin-diff_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
exp-prod_binary64 log-prod_binary64
exp-diff_binary64 log-div_binary64 rem-log-exp_binary64
Counts
4 → 40
Calls

4 calls:

6.0ms
(log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
Compiler

Compiled 2869 to 1690 computations (41.1% saved)

series343.0ms (1%)

Error
24.0b
Counts
4 → 45
Calls

4 calls:

60.0ms
(log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))
42.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
42.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
41.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
Compiler

Compiled 7573 to 5038 computations (33.5% saved)

simplify168.0ms (0.5%)

Algorithm
egg-herbie
Rules
637×distribute-rgt-neg-in_binary64
614×cancel-sign-sub-inv_binary64
486×distribute-lft-neg-in_binary64
468×sub-neg_binary64
324×neg-mul-1_binary64
Counts
85 → 42
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01041600
11841512
24111435
310371407
424001407
542301407
647551407
749341407
849401407

prune226.0ms (0.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New40242
Fresh11011
Picked011
Done000
Total411354
Error
24.4b
Counts
54 → 13
Alt Table
StatusErrorProgram
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
37.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 (sin.f64 (*.f64 -1/2 lambda2)) (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8))) (*.f64 lambda1 (*.f64 (cos.f64 (*.f64 -1/2 lambda2)) (+.f64 1/2 (*.f64 lambda1 (*.f64 lambda1 -1/48))))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
36.5b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (sin.f64 (*.f64 1/2 lambda1)) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1)))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.2b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
50.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))) (*.f64 (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8)) (sin.f64 (*.f64 lambda2 1/2)))))))))))
38.7b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2))))))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
24.9b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (*.f64 1/2 lambda1)))))))))))
36.4b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
Compiler

Compiled 4900 to 3097 computations (36.8% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.3b
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
9.1b
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
9.1b
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

rewrite386.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
24.3b
Rules
24×cbrt-prod_binary64
10×add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
unpow-prod-down_binary64 cube-prod_binary64
pow1_binary64 add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1/3_binary64 unpow3_binary64 cube-mult_binary64 sqr-pow_binary64 rem-cbrt-cube_binary64 div-sub_binary64 sin-diff_binary64
Counts
4 → 58
Calls

4 calls:

8.0ms
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
6.0ms
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
Compiler

Compiled 4173 to 2542 computations (39.1% saved)

series373.0ms (1.1%)

Error
24.1b
Counts
4 → 44
Calls

4 calls:

45.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
45.0ms
(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
43.0ms
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
42.0ms
(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
Compiler

Compiled 7991 to 5377 computations (32.7% saved)

simplify197.0ms (0.6%)

Algorithm
egg-herbie
Rules
641×cancel-sign-sub-inv_binary64
498×unswap-sqr_binary64
365×fabs-mul_binary64
328×unsub-neg_binary64
323×distribute-rgt-neg-in_binary64
Counts
102 → 58
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0841842
11621758
23901694
39701666
419711638
542451638
648411638
749491638
849981638
949021638

prune229.0ms (0.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New58058
Fresh01111
Picked011
Done011
Total581371
Error
24.4b
Counts
71 → 13
Alt Table
StatusErrorProgram
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
37.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 (sin.f64 (*.f64 -1/2 lambda2)) (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8))) (*.f64 lambda1 (*.f64 (cos.f64 (*.f64 -1/2 lambda2)) (+.f64 1/2 (*.f64 lambda1 (*.f64 lambda1 -1/48))))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
36.5b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (sin.f64 (*.f64 1/2 lambda1)) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1)))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.2b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
50.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.8b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))) (*.f64 (+.f64 1 (*.f64 (*.f64 lambda1 lambda1) -1/8)) (sin.f64 (*.f64 lambda2 1/2)))))))))))
38.7b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2))))))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
24.9b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
38.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (+.f64 (*.f64 -1/2 (*.f64 lambda2 (cos.f64 (*.f64 1/2 lambda1)))) (*.f64 (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (*.f64 1/2 lambda1)))))))))))
36.4b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (*.f64 -1/2 lambda2)) (*.f64 1/2 (*.f64 lambda1 (cos.f64 (*.f64 -1/2 lambda2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
25.0b
(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 2 (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
Compiler

Compiled 3955 to 2487 computations (37.1% saved)

regimes6.2s (18.8%)

Accuracy

Total 0.5b remaining (1.9%)

Threshold costs 0.5b (1.9%)

Compiler

Compiled 158188 to 107860 computations (31.8% saved)

simplify8.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
031103
143103
257103
375103
495103
5108103
6116103
7121103
8123103
9121103

end28.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 350 to 230 computations (34.3% saved)

sample14.6s (44.5%)

Algorithm
intervals
Results
9.7s5265×body1024valid
1.5s1255×body512valid
1.3s413×body2048valid
316.0ms414×body256valid
230.0ms653×body128valid
3.0msbody1024invalid
2.0msbody512invalid
Compiler

Compiled 1201 to 819 computations (31.8% saved)

Profiling

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