Details

analyze10.2s (15.4%)

Algorithm

1×

Search

True	Other	False	Iter
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)

sample25.5s (38.3%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

18.9s	5402×	body	1024	valid
3.0s	457×	body	2048	valid
2.5s	1271×	body	512	valid
490.0ms	403×	body	256	valid
487.0ms	723×	body	128	valid
12.0ms	3×	body	1024	invalid

Compiler

Compiled 212 to 140 computations (34% saved)

simplify164.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
571×	`fma-neg_binary64`
563×	`sub-neg_binary64`
520×	`distribute-rgt-neg-in_binary64`
460×	`sqr-pow_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	103
1	59	99
2	123	99
3	247	99
4	552	99
5	1018	99
6	1698	99
7	2589	99
8	3560	99
9	3893	99
10	4414	99
11	4607	99
12	4426	99
13	4413	99
14	4778	99
15	4761	99

prune9.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

22.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	22.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
▶	22.7b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Status

Error

Program

22.7b

(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

▶

22.7b

(*.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Compiler

Compiled 409 to 260 computations (36.4% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(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)))))
✓	0.6b	(-.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)))))
✓	2.8b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
✓	3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series402.0ms (0.6%)

Counts

4 → 144

Calls

4 calls:

246.0ms	(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)))))
144.0ms	(-.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)))))
7.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
9×	`add-log-exp_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(-.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)))))
7.0ms	(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)))))
3.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

simplify249.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
268×	`*-commutative_binary64`
262×	`+-commutative_binary64`
257×	`fma-neg_binary64`
188×	`associate-r_binary64`

Counts

214 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	617	12951
1	1909	11907
2	4550	11900
3	5006	11900

prune1.6s (2.4%)

Pruning

39 alts after pruning (39 fresh and 0 done)

	Pruned	Kept	Total
New	271	38	309
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	272	39	311

Error

20.7b

Counts

311 → 39

Alt Table

Status	Error	Program
	22.7b	(.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)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	30.9b	(.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 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1)))))))
	34.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 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)))))))))
	31.4b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	26.1b	(.f64 R (.f64 2 (atan2.f64 (log.f64 (exp.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)))))))))
	36.0b	(.f64 R (.f64 2 (atan2.f64 (fma.f64 1/2 (.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (.f64 lambda1 (cos.f64 phi1))))) (sqrt.f64 (/.f64 1 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2))))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 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)))))))))
	22.7b	(.f64 R (.f64 2 (atan2.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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)))))))))
	35.5b	(.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))) (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.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)))))))))
	22.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.1b	(.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 (fma.f64 1/48 (.f64 (cos.f64 (.f64 1/2 lambda1)) (pow.f64 lambda2 3)) (sin.f64 (.f64 1/2 lambda1))) (fma.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 1/8 (.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 lambda2 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)))))))))
	23.2b	(.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))) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 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)))))))))
	33.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 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)))))))))
	22.8b	(.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 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2)))))))))))
	31.1b	(.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 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	22.8b	(.f64 R (.f64 2 (atan2.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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)))))))))
	22.7b	(.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 (expm1.f64 (log1p.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	32.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.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)))))))))
	22.9b	(.f64 R (.f64 2 (atan2.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) (sqrt.f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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)))))))))
	34.1b	(.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 -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)))))))))
	33.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 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)))))))))
	22.9b	(.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 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)))) (cbrt.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)))))))))
	22.7b	(.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))) (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
	36.8b	(.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 (fma.f64 lambda2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (.f64 1/2 lambda1)) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1)))) (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)))) 1)) (fma.f64 1/4 (.f64 (pow.f64 (cos.f64 (.f64 1/2 lambda1)) 2) (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2))))))))
	31.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (sin.f64 (.f64 1/2 phi1)) (fma.f64 1/2 (.f64 phi2 (cos.f64 (.f64 1/2 phi1))) (.f64 1/8 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2))))) 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)))))))))
▶	22.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	22.7b	(.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 (exp.f64 (log.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)))))))))))
	22.1b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	31.0b	(.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 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)))))))
	34.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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)))))))))
	34.0b	(.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 1/2 lambda1))))) (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)))))))))
	32.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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)))))))))
	31.2b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	31.3b	(.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 1/2 lambda1)))))))))
	23.1b	(.f64 R (.f64 2 (atan2.f64 (.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)))))))))
	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 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2))) (fma.f64 1/8 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 lambda1 lambda1)) (.f64 1/48 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (pow.f64 lambda1 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)))))))))
	22.7b	(.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))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	22.8b	(.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 (log.f64 (/.f64 (exp.f64 1) (.f64 (exp.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)) (exp.f64 (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
	32.2b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1))) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2)))))))
	37.2b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 (.f64 phi1 (cos.f64 (.f64 -1/2 phi2))) (sin.f64 (.f64 -1/2 phi2))) 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 35812 to 22188 computations (38% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))
	0.6b	(-.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)))))
	2.8b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
	3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series594.0ms (0.9%)

Counts

1 → 48

Calls

1 calls:

594.0ms

(sqrt.f64 (+.f64 (pow.f64 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))

rewrite14.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`sqrt-div_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

7.0ms

(sqrt.f64 (+.f64 (pow.f64 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))

simplify252.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

516×	`*-commutative_binary64`
372×	`cancel-sign-sub-inv_binary64`
342×	`fma-def_binary64`
319×	`unswap-sqr_binary64`
214×	`sub-neg_binary64`

Counts

65 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	11139
1	1393	10550
2	3199	10547
3	4991	10547
4	5002	10547

prune2.1s (3.2%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	263	18	281
Fresh	19	19	38
Picked	1	0	1
Done	0	0	0
Total	283	37	320

Error

12.6b

Counts

320 → 37

Alt Table

Status	Error	Program
	33.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 1/2 lambda1))))) (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)))))))))
	22.1b	(.f64 R (.f64 2 (atan2.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 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)))))))))
	22.7b	(.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)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
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	31.0b	(.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 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)))))))
	32.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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)))))))))
	31.2b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	31.3b	(.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 1/2 lambda1)))))))))
	25.5b	(.f64 R (.f64 2 (atan2.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 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)))))))))
	22.7b	(.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))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	22.8b	(.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 (log.f64 (/.f64 (exp.f64 1) (.f64 (exp.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)) (exp.f64 (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
	25.5b	(.f64 R (.f64 2 (atan2.f64 (log.f64 (exp.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	30.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 1/2 lambda1)))))))))
	22.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 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)))))))))
▶	13.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 40157 to 26852 computations (33.1% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)
	0.4b	(sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))
✓	0.7b	(-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))
	3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series369.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

325.0ms

(-.f64 1 (+.f64 (pow.f64 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))

43.0ms

(pow.f64 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 53

Calls

2 calls:

10.0ms

(-.f64 1 (+.f64 (pow.f64 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))

5.0ms

(pow.f64 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)

simplify241.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
398×	`sub-neg_binary64`
318×	`associate-r_binary64`
300×	`fma-def_binary64`
249×	`associate-l_binary64`

Counts

125 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	307	10864
1	928	9803
2	3391	9217
3	4945	9217
4	4951	9217

prune2.6s (3.9%)

Pruning

39 alts after pruning (39 fresh and 0 done)

	Pruned	Kept	Total
New	309	22	331
Fresh	19	17	36
Picked	1	0	1
Done	0	0	0
Total	329	39	368

Error

12.4b

Counts

368 → 39

Alt Table

Status	Error	Program
	28.1b	(.f64 R (.f64 2 (atan2.f64 (-.f64 (sqrt.f64 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (.f64 (sin.f64 (.f64 1/2 phi2)) (cos.f64 (.f64 1/2 phi2))) (sin.f64 (.f64 1/2 phi1))))))) (.f64 1/2 (.f64 (.f64 (cos.f64 phi2) (.f64 lambda2 (.f64 (cos.f64 (.f64 1/2 lambda1)) (.f64 (cos.f64 phi1) (sin.f64 (.f64 1/2 lambda1)))))) (sqrt.f64 (/.f64 1 (-.f64 (fma.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (.f64 (sin.f64 (.f64 1/2 phi2)) (cos.f64 (.f64 1/2 phi2))) (sin.f64 (.f64 1/2 phi1))))))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	30.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 1/2 lambda1)))))))))
	27.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	22.7b	(.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)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	34.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	13.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 4) (pow.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	33.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	36.0b	(.f64 R (.f64 2 (atan2.f64 (fma.f64 1/2 (.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (.f64 lambda1 (cos.f64 phi1))))) (sqrt.f64 (/.f64 1 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2))))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 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)))))))))
	14.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	35.1b	(.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 (fma.f64 1/48 (.f64 (cos.f64 (.f64 1/2 lambda1)) (pow.f64 lambda2 3)) (sin.f64 (.f64 1/2 lambda1))) (fma.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 1/8 (.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 lambda2 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)))))))))
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	28.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 lambda2 -1/2)) 2)) (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (.f64 (sin.f64 (.f64 1/2 phi2)) (cos.f64 (.f64 1/2 phi2))) (sin.f64 (.f64 1/2 phi1))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	13.6b	(.f64 R (.f64 2 (atan2.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (sqrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	32.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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)))))))))
	31.3b	(.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 1/2 lambda1)))))))))
	13.8b	(.f64 R (.f64 2 (atan2.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	22.7b	(.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))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	13.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (+.f64 1 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (-.f64 1 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))))
	25.5b	(.f64 R (.f64 2 (atan2.f64 (log.f64 (exp.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	46.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 2) (pow.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	31.1b	(.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 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	32.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	26.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 1/2 lambda1))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 52259 to 36455 computations (30.2% saved)

localize138.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (*.f64 1/2 phi2))))))))
	0.7b	(-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))
	3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
✓	3.8b	(sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2)))

series733.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

727.0ms

(sqrt.f64 (-.f64 (+.f64 (*.f64 (cos.f64 phi2) (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1))) (+.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 2)) (*.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (*.f64 1/2 phi2)) 2)))) (*.f64 2 (*.f64 (cos.f64 (*.f64 1/2 phi1)) (*.f64 (sin.f64 (*.f64 1/2 phi1)) (*.f64 (cos.f64 (*.f64 1/2 phi2)) (sin.f64 (*.f64 1/2 phi2))))))))

5.0ms

(sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2)))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sin-sum_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 52

Calls

2 calls:

17.0ms

(sqrt.f64 (-.f64 (+.f64 (*.f64 (cos.f64 phi2) (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1))) (+.f64 (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (*.f64 1/2 phi2)) 2)) (*.f64 (pow.f64 (cos.f64 (*.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (*.f64 1/2 phi2)) 2)))) (*.f64 2 (*.f64 (cos.f64 (*.f64 1/2 phi1)) (*.f64 (sin.f64 (*.f64 1/2 phi1)) (*.f64 (cos.f64 (*.f64 1/2 phi2)) (sin.f64 (*.f64 1/2 phi2))))))))

5.0ms

(sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2)))

simplify230.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

628×	`*-commutative_binary64`
451×	`cancel-sign-sub-inv_binary64`
363×	`fma-def_binary64`
346×	`unswap-sqr_binary64`
234×	`sub-neg_binary64`

Counts

100 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	617	12583
1	1547	11453
2	3582	11231
3	5261	11231

prune2.8s (4.2%)

Pruning

42 alts after pruning (42 fresh and 0 done)

	Pruned	Kept	Total
New	240	12	252
Fresh	8	30	38
Picked	1	0	1
Done	0	0	0
Total	249	42	291

Error

12.3b

Counts

291 → 42

Alt Table

Status	Error	Program
	24.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (+.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1))) 1/2)) (cos.f64 (.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)) 1/2))) (.f64 (cos.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1))) 1/2)) (sin.f64 (.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)) 1/2)))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	30.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 1/2 lambda1)))))))))
	15.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (log.f64 (exp.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	22.7b	(.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)) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	27.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	41.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (+.f64 (.f64 (sin.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))) 1/2)) (cos.f64 (.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))) 1/2))) (.f64 (cos.f64 (.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))) 1/2)) (sin.f64 (.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))) 1/2)))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
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	23.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 (fma.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (.f64 (sin.f64 (.f64 1/2 phi2)) (cos.f64 (.f64 1/2 phi2))) (sin.f64 (.f64 1/2 phi1)))) 1) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (pow.f64 (sin.f64 (*.f64 1/2 phi1)) 2)))))))))
	22.4b	(.f64 R (.f64 2 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))) (cbrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 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)))))))))
	36.8b	(.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 (fma.f64 lambda2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (.f64 1/2 lambda1)) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1)))) (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)))) 1)) (fma.f64 1/4 (.f64 (pow.f64 (cos.f64 (.f64 1/2 lambda1)) 2) (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2))))))))
	13.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (expm1.f64 (log1p.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	30.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (fma.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (.f64 (sin.f64 (.f64 1/2 phi2)) (cos.f64 (.f64 1/2 phi2))) (sin.f64 (.f64 1/2 phi1)))) 1) (+.f64 (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2))) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 lambda2 -1/2)) 2)) (.f64 (sin.f64 (.f64 lambda2 -1/2)) (.f64 (cos.f64 (.f64 lambda2 -1/2)) (*.f64 lambda1 (cos.f64 phi1))))))))))))
	26.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (+.f64 1 (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2))))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))))))))
	13.6b	(.f64 R (.f64 2 (atan2.f64 (.f64 (sqrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (sqrt.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	32.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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)))))))))
	26.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (-.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	31.3b	(.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 1/2 lambda1)))))))))
	13.8b	(.f64 R (.f64 2 (atan2.f64 (.f64 (fabs.f64 (cbrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	22.7b	(.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))) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)))))))))
	23.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (+.f64 (.f64 (sin.f64 (.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))) 1/2)) (cos.f64 (.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)))) 1/2))) (.f64 (cos.f64 (.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))) 1/2)) (sin.f64 (.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)))) 1/2)))) 2) (cos.f64 phi1))) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	46.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 2) (pow.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	32.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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)))))))))
	31.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)))))))
	26.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 1/2 lambda1))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 46979 to 34088 computations (27.4% saved)

regimes15.3s (23%)

Accuracy

Total 0.7b remaining (4.8%)

Threshold costs 0.7b (4.8%)

Counts

343 → 1

Compiler

Compiled 512565 to 367777 computations (28.2% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

41×	`*-commutative_binary64`
28×	`+-commutative_binary64`
24×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	202
1	108	202
2	133	202
3	165	202
4	197	202
5	227	202
6	245	202
7	256	202
8	260	202
9	258	202

end2.7s (4.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 5476 to 4034 computations (26.3% saved)

Iter	Nodes	Cost
0	66	202
1	108	202
2	133	202
3	165	202
4	197	202
5	227	202
6	245	202
7	256	202
8	260	202
9	258	202

Iter	Nodes	Cost
0	66	202
1	108	202
2	133	202
3	165	202
4	197	202
5	227	202
6	245	202
7	256	202
8	260	202
9	258	202

Details

analyze10.2s (15.4%)

sample25.5s (38.3%)

simplify164.0ms (0.2%)

prune9.0ms (0%)

localize28.0ms (0%)

series402.0ms (0.6%)

rewrite32.0ms (0%)

simplify249.0ms (0.4%)

prune1.6s (2.4%)

localize43.0ms (0.1%)

series594.0ms (0.9%)

rewrite14.0ms (0%)

simplify252.0ms (0.4%)

prune2.1s (3.2%)

localize41.0ms (0.1%)

series369.0ms (0.6%)

rewrite23.0ms (0%)

simplify241.0ms (0.4%)

prune2.6s (3.9%)

localize138.0ms (0.2%)

series733.0ms (1.1%)

rewrite28.0ms (0%)

simplify230.0ms (0.3%)

prune2.8s (4.2%)

regimes15.3s (23%)

simplify14.0ms (0%)

end2.7s (4.1%)

Profiling

Iter	Nodes	Cost
0	66	202
1	108	202
2	133	202
3	165	202
4	197	202
5	227	202
6	245	202
7	256	202
8	260	202
9	258	202