Details

analyze8.5s (13.6%)

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)

sample29.1s (46.4%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

21.6s	5356×	body	1024	valid
3.2s	427×	body	2048	valid
2.9s	1343×	body	512	valid
744.0ms	414×	body	256	valid
484.0ms	716×	body	128	valid
2.0ms	1×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 212 to 140 computations (34% saved)

simplify160.0ms (0.3%)

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

21.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	21.6b	(.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)))))))
▶	21.5b	(.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))) (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

21.6b

(*.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)))))))

▶

21.5b

(*.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))) (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)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
✓	0.7b	(-.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)))))
✓	3.1b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
✓	3.1b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

series143.0ms (0.2%)

Counts

4 → 120

Calls

4 calls:

119.0ms	(-.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)))))
13.0ms	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
6.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite84.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

261×	`prod-diff_binary64`
242×	`add-sqr-sqrt_binary64`
233×	`log1p-expm1-u_binary64`
233×	`expm1-log1p-u_binary64`
225×	`add-log-exp_binary64`

Counts

4 → 83

Calls

4 calls:

80.0ms	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
80.0ms	(-.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)))))
80.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
80.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	77
1	478	67
2	4866	67
3	5270	67
0	0	0
1	0	0

simplify116.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-neg_binary64`
333×	`sub-neg_binary64`
321×	`distribute-rgt-neg-in_binary64`
318×	`associate-r_binary64`
299×	`neg-mul-1_binary64`

Counts

203 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	3880
1	796	3828
2	2837	3714
3	4916	3714
4	5102	3714

prune2.1s (3.3%)

Pruning

38 alts after pruning (38 fresh and 0 done)

	Pruned	Kept	Total
New	289	38	327
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	291	38	329

Error

20.0b

Counts

329 → 38

Alt Table

Status	Error	Program
	37.6b	(.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 (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (.f64 (cos.f64 phi1) (pow.f64 lambda1 2))))) 1) (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 phi1) lambda1)))) (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (cos.f64 (.f64 -1/2 lambda2)) 2) (.f64 (cos.f64 phi1) (pow.f64 lambda1 2))))) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2)))))))))
	32.0b	(.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 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	34.8b	(.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)))))))))
	35.6b	(.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)))))))))
	22.2b	(.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)))))))))
	21.7b	(.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 (pow.f64 (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) 2) (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	21.7b	(.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 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2)))))))))))
	21.1b	(.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)))))))))
	21.5b	(.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))) (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)))))))))))
	31.5b	(.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))) (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)))))))
	21.5b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (expm1.f64 (log1p.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	21.0b	(.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 (-.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)))))))))
	31.9b	(.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 (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)))))))
	37.7b	(.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 (+.f64 1 (.f64 (cos.f64 phi2) (+.f64 (.f64 1/4 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)))) (.f64 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1)))))) (+.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2) (.f64 1/4 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 lambda1)) 2)))))))))))
	21.6b	(.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 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 3)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	21.6b	(.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 (sqrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (fma.f64 (neg.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 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 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 (fma.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 (sin.f64 (.f64 1/2 phi1))) 1) (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)))))))
	21.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	21.7b	(.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 (fma.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2) (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 (cos.f64 phi2) (-.f64 (.f64 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1))) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2))))))
	33.8b	(.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)))))))))
	21.6b	(.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 (log.f64 (+.f64 1 (expm1.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)))))))))
▶	21.0b	(.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 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)) (-.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))))) (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)))))))))
	21.6b	(.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 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (fma.f64 (neg.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))))))))
	30.7b	(.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 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1)))))))
	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 (+.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)))))))))
	21.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 3) 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)))))))))
	23.0b	(.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))) (log.f64 (exp.f64 (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)))))))))
	31.8b	(.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))) (sin.f64 (*.f64 -1/2 lambda2)))))))))
	37.9b	(.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 (+.f64 1 (+.f64 (.f64 1/4 (.f64 (pow.f64 phi1 2) (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2))) (.f64 1/2 (.f64 (cos.f64 phi2) (.f64 (pow.f64 phi1 2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))) (+.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2) (+.f64 (.f64 1/4 (.f64 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (pow.f64 phi1 2))) (+.f64 (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)) (.f64 (cos.f64 (.f64 -1/2 phi2)) (.f64 phi1 (sin.f64 (.f64 -1/2 phi2))))))))))))
	38.4b	(.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 (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)))))))))
	21.5b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	32.0b	(.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))) (sin.f64 (*.f64 1/2 lambda1)))))))))
	49.5b	(.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))) (pow.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 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)))))))))
	21.5b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 6)) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	33.6b	(.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)))))))))
	32.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.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))))) (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 31941 to 19592 computations (38.7% saved)

localize72.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 1 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))
	3.1b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
	3.1b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
✓	29.4b	(fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))

series535.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

465.0ms

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

69.0ms

(fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))

rewrite56.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

323×	`log1p-expm1-u_binary64`
323×	`expm1-log1p-u_binary64`
315×	`add-log-exp_binary64`
314×	`add-cbrt-cube_binary64`
314×	`add-exp-log_binary64`

Counts

2 → 33

Calls

2 calls:

54.0ms

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

54.0ms

(fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	130
1	670	120
2	5212	120
0	0	0
1	0	0

simplify133.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

972×	`cancel-sign-sub-inv_binary64`
724×	`fma-neg_binary64`
327×	`sub-neg_binary64`
265×	`associate-r_binary64`
234×	`fma-def_binary64`

Counts

105 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	5102
1	659	5011
2	2491	5010
3	4824	5010
4	5014	5010

prune1.8s (2.8%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	222	10	232
Fresh	12	25	37
Picked	1	0	1
Done	0	0	0
Total	235	35	270

Error

11.7b

Counts

270 → 35

Alt Table

Status	Error	Program
	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 (+.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 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2)) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))))))))
▶	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	21.5b	(.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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 6)) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	37.6b	(.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 (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (.f64 (cos.f64 phi1) (pow.f64 lambda1 2))))) 1) (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 phi1) lambda1)))) (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (cos.f64 (.f64 -1/2 lambda2)) 2) (.f64 (cos.f64 phi1) (pow.f64 lambda1 2))))) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2)))))))))
	32.0b	(.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 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	34.8b	(.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)))))))))
	35.6b	(.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)))))))))
	22.2b	(.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)))))))))
	12.4b	(.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 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	21.7b	(.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 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 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 (+.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)))))))))
	21.5b	(.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))) (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)))))))))))
	37.7b	(.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 (+.f64 1 (.f64 (cos.f64 phi2) (+.f64 (.f64 1/4 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)))) (.f64 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1)))))) (+.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2) (.f64 1/4 (.f64 (.f64 lambda2 lambda2) (pow.f64 (cos.f64 (.f64 1/2 lambda1)) 2)))))))))))
	21.6b	(.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 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 3)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	21.6b	(.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 (sqrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (fma.f64 (neg.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 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 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 (fma.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 (sin.f64 (.f64 1/2 phi1))) 1) (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)))))))
	21.7b	(.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 (fma.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2) (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 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))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 (+.f64 1 (.f64 (cos.f64 phi2) (-.f64 (.f64 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1))) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2))))))
	34.3b	(.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 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	21.6b	(.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 (log.f64 (+.f64 1 (expm1.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)))))))))
	35.1b	(.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)) (-.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))))) (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)))))))))
	21.6b	(.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 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (fma.f64 (neg.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))))))))
	30.7b	(.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 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1)))))))
	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 (+.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)))))))))
	21.1b	(.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 (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))) 2) (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	21.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 3) 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)))))))))
	23.0b	(.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))) (log.f64 (exp.f64 (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)))))))))
	31.6b	(.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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 1/2 lambda1)))))))))
	21.0b	(.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 (expm1.f64 (log1p.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	21.2b	(.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 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))))
	49.5b	(.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))) (pow.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 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)))))))))
	21.0b	(.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 (-.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)))))))))
	21.0b	(.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 (-.f64 1 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)) 3)) (+.f64 1 (+.f64 (pow.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)) 2) (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	33.6b	(.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)))))))))
	31.8b	(.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))) (sin.f64 (*.f64 -1/2 lambda2)))))))))

Compiler

Compiled 31631 to 21476 computations (32.1% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2)
	0.8b	(-.f64 1 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))
	3.1b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
	29.4b	(fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))

series49.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

49.0ms

(pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2)

rewrite132.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

303×	`expm1-udef_binary64`
303×	`log1p-udef_binary64`
189×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`

Counts

1 → 30

Calls

1 calls:

130.0ms

(pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65
1	374	31
2	4279	31
3	5025	31
0	0	0
1	0	0

simplify49.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-neg_binary64`
488×	`unswap-sqr_binary64`
318×	`associate-r_binary64`
315×	`associate-l_binary64`
281×	`fma-def_binary64`

Counts

54 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	910
1	179	900
2	564	866
3	2226	840
4	5060	840

prune2.9s (4.6%)

Pruning

37 alts after pruning (37 fresh and 0 done)

	Pruned	Kept	Total
New	288	20	308
Fresh	17	17	34
Picked	1	0	1
Done	0	0	0
Total	306	37	343

Error

11.5b

Counts

343 → 37

Alt Table

Status	Error	Program
	37.6b	(.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 (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (.f64 (cos.f64 phi1) (pow.f64 lambda1 2))))) 1) (+.f64 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 phi1) lambda1)))) (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 (cos.f64 (.f64 -1/2 lambda2)) 2) (.f64 (cos.f64 phi1) (pow.f64 lambda1 2))))) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2)))))))))
	34.8b	(.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)))))))))
	31.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (.f64 lambda2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 (.f64 1/2 lambda1)) (.f64 (cos.f64 phi1) (sin.f64 (.f64 1/2 lambda1)))))) (+.f64 1 (+.f64 (.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (pow.f64 lambda2 2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 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))))))))) (+.f64 (.f64 1/4 (.f64 (pow.f64 (cos.f64 (.f64 1/2 lambda1)) 2) (.f64 (pow.f64 lambda2 2) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))) (+.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))))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 0) 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	35.6b	(.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)))))))))
	21.7b	(.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 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2)))))))))))
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	30.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2))) 3))))))
	21.1b	(.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 (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))) 2) (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
▶	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	21.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 3) 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)))))))))
	31.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))
	13.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (log.f64 (exp.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	25.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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) (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)))))))))
	27.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	25.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 -1/2 lambda2)))))))))
	49.5b	(.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))) (pow.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 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)))))))))
	29.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (cos.f64 (.f64 1/2 lambda1)) (.f64 lambda2 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 (.f64 1/2 lambda1))))) (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)))))))))
	26.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 1/2 lambda1)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
	30.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))

Compiler

Compiled 51038 to 36256 computations (29% saved)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)
✓	0.8b	(-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))
	3.1b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
	29.4b	(fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))

series291.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

239.0ms

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

52.0ms

(pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)

rewrite79.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

304×	`log1p-expm1-u_binary64`
304×	`expm1-log1p-u_binary64`
297×	`add-log-exp_binary64`
296×	`add-cbrt-cube_binary64`
296×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

77.0ms

(pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (*.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)

77.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	155
1	634	155
2	4919	155
3	5127	155
0	0	0
1	0	0

simplify182.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-neg_binary64`
375×	`sub-neg_binary64`
271×	`fma-def_binary64`
269×	`associate-r_binary64`
202×	`distribute-rgt-neg-in_binary64`

Counts

102 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	5988
1	724	5887
2	2738	5775
3	4993	5775
4	4990	5775
5	4992	5775

prune2.1s (3.4%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	199	14	213
Fresh	15	21	36
Picked	1	0	1
Done	0	0	0
Total	215	35	250

Error

11.4b

Counts

250 → 35

Alt Table

Status	Error	Program
	31.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2))) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	34.8b	(.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)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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))))))) (sqrt.f64 (expm1.f64 (log1p.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	25.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 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 (+.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)))))))))
	21.5b	(.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))) (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)))))))))))
	21.6b	(.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 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 3)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	21.6b	(.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 (sqrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (fma.f64 (neg.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 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 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 (fma.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 (sin.f64 (.f64 1/2 phi1))) 1) (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)))))))
	13.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (expm1.f64 (log1p.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	29.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (+.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 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 (.f64 1/2 lambda1)))) (-.f64 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (.f64 1/2 lambda1))))) (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))))))))))
	12.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (pow.f64 (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))) 3)))))
	21.7b	(.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 (fma.f64 (.f64 (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))) (cbrt.f64 (-.f64 1 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (neg.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2)))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2) (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) (pow.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2))) 2))))))))
	12.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2)))) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	12.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	21.6b	(.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 (log.f64 (+.f64 1 (expm1.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)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (exp.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 0) 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 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 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)) (-.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))))) (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)))))))))
	30.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1)))))))))
	30.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (cbrt.f64 (pow.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2))) 3))))))
	21.1b	(.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 (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))) 2) (cbrt.f64 (-.f64 1 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	21.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 3) 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)))))))))
	12.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (*.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))))
	27.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	31.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (sin.f64 (*.f64 1/2 phi2)) 2)))))))))
	25.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 -1/2 lambda2)))))))))
	49.5b	(.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))) (pow.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 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)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 2) (pow.f64 (-.f64 (.f64 (sin.f64 (.f64 1/2 phi1)) (cos.f64 (.f64 1/2 phi2))) (.f64 (cos.f64 (.f64 1/2 phi1)) (sin.f64 (.f64 1/2 phi2)))) 2)))))))))
	26.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 1/2 lambda1)))))))))
	31.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 phi1) (cos.f64 phi2)) (pow.f64 (-.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))))) 2) (pow.f64 (+.f64 (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2)))) (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2))))) 2)))))))))
	12.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 2) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))))
	31.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (fma.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 2))))) (fma.f64 (neg.f64 (sin.f64 (/.f64 phi2 2))) (cos.f64 (/.f64 phi1 2)) (.f64 (sin.f64 (/.f64 phi2 2)) (cos.f64 (/.f64 phi1 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 (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))))

Compiler

Compiled 33186 to 24109 computations (27.4% saved)

regimes11.3s (18.1%)

Accuracy

Total 0.5b remaining (3.7%)

Threshold costs 0.5b (3.7%)

Counts

272 → 1

Compiler

Compiled 401509 to 290028 computations (27.8% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
14×	`+-commutative_binary64`
11×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	224
1	79	224
2	100	224
3	114	224
4	121	224
5	122	224
6	121	224

end2.7s (4.3%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 5291 to 3949 computations (25.4% saved)

Details

analyze8.5s (13.6%)

sample29.1s (46.4%)

simplify160.0ms (0.3%)

prune9.0ms (0%)

localize26.0ms (0%)

series143.0ms (0.2%)

rewrite84.0ms (0.1%)

simplify116.0ms (0.2%)

prune2.1s (3.3%)

localize72.0ms (0.1%)

series535.0ms (0.9%)

rewrite56.0ms (0.1%)

simplify133.0ms (0.2%)

prune1.8s (2.8%)

localize36.0ms (0.1%)

series49.0ms (0.1%)

rewrite132.0ms (0.2%)

simplify49.0ms (0.1%)

prune2.9s (4.6%)

localize52.0ms (0.1%)

series291.0ms (0.5%)

rewrite79.0ms (0.1%)

simplify182.0ms (0.3%)

prune2.1s (3.4%)

regimes11.3s (18.1%)

simplify8.0ms (0%)

end2.7s (4.3%)

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