Details

analyze9.2s (15.8%)

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)

sample22.1s (38.1%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

16.2s	5384×	body	1024	valid
2.6s	455×	body	2048	valid
2.3s	1288×	body	512	valid
426.0ms	380×	body	256	valid
414.0ms	749×	body	128	valid
8.0ms	3×	body	1024	invalid

Compiler

Compiled 212 to 140 computations (34% saved)

simplify499.0ms (0.9%)

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

25.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

Status

Error

Program

▶

25.7b

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

25.7b

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

Compiler

Compiled 409 to 260 computations (36.4% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
✓	0.6b	(-.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)))
✓	3.7b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
✓	5.6b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

series126.0ms (0.2%)

Counts

4 → 120

Calls

4 calls:

105.0ms	(-.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)))
13.0ms	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
4.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
3.0ms	(-.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)))
3.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
3.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

simplify142.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

518×	`fma-neg_binary64`
365×	`distribute-rgt-neg-in_binary64`
350×	`sub-neg_binary64`
348×	`associate-r_binary64`
286×	`fma-def_binary64`

Counts

192 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	7168
1	985	6517
2	3328	6115
3	5144	6115

prune2.0s (3.4%)

Pruning

39 alts after pruning (39 fresh and 0 done)

	Pruned	Kept	Total
New	285	39	324
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	287	39	326

Error

23.9b

Counts

326 → 39

Alt Table

Status	Error	Program
	25.9b	(.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)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.3b	(.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 1/2 phi1)) 2)))))))
	33.9b	(.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 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.8b	(.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 (.f64 (neg.f64 (.f64 (cbrt.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))) (cbrt.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))))) (cbrt.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)))))))))
	26.4b	(.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))) (log.f64 (exp.f64 (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)))))))
	34.0b	(.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 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi1)) (pow.f64 (sin.f64 (*.f64 1/2 phi1)) 2)))))))
	35.0b	(.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 (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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.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)) (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)))) (+.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))))))))
	33.6b	(.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 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	37.2b	(.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 1/2 lambda1))) (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)))))))
	39.5b	(.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)) (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2)))) (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)))))))
	26.5b	(.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)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 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)))))))
	33.6b	(.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 (+.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2))))))))
	35.8b	(.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 1/2 lambda1))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.6b	(.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)) (log1p.f64 (expm1.f64 (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)))))))
	42.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 (fma.f64 lambda2 (.f64 (cos.f64 (.f64 1/2 lambda1)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1)))) (fma.f64 1/4 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)))) 1)) (fma.f64 1/4 (.f64 (pow.f64 (cos.f64 (.f64 1/2 lambda1)) 2) (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2))))))))
	36.0b	(.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 -1/2 phi2)) 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)))))))
▶	25.1b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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)))))))
	40.1b	(.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 (fma.f64 (cos.f64 phi2) (.f64 lambda2 (.f64 (cos.f64 (.f64 1/2 lambda1)) (.f64 (sin.f64 (.f64 1/2 lambda1)) (cos.f64 phi1)))) 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)))))))
	33.9b	(.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 -1/2 phi2)) 2)))))))
	25.1b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	35.1b	(.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 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.8b	(.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 (.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2)) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 phi1 phi2))) 2)))))))
	34.6b	(.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 (-.f64 (sin.f64 (.f64 1/2 phi1)) (fma.f64 1/2 (.f64 phi2 (cos.f64 (.f64 1/2 phi1))) (.f64 1/8 (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 phi2))))) 2))) (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)))))))
	39.8b	(.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))) (fma.f64 1/4 (.f64 (.f64 phi1 phi1) (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2)) (fma.f64 (sin.f64 (.f64 -1/2 phi2)) (+.f64 (sin.f64 (.f64 -1/2 phi2)) (.f64 phi1 (cos.f64 (.f64 -1/2 phi2)))) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2) (.f64 (*.f64 phi1 phi1) -1/4))))))))))
	25.9b	(.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))) (.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 4) (pow.f64 (cbrt.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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (expm1.f64 (log1p.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	37.6b	(.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))) (-.f64 (+.f64 (.f64 1/4 (.f64 (pow.f64 phi1 2) (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2))) (+.f64 (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 (.f64 -1/2 phi2)) (.f64 phi1 (sin.f64 (.f64 -1/2 phi2)))))) (.f64 1/4 (.f64 (pow.f64 phi1 2) (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 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)))))))
	36.4b	(.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 1/2 phi1)) 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)))))))
	26.2b	(.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 (cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) (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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	37.3b	(.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))) (-.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) phi2))))) (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)))))))
	41.5b	(.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 (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda1 lambda1) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)))) 1) (+.f64 (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda1 (.f64 lambda1 (cos.f64 phi1))) (pow.f64 (cos.f64 (.f64 -1/2 lambda2)) 2))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)) (.f64 (cos.f64 phi2) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (*.f64 lambda1 (cos.f64 phi1))))))))))))
	39.3b	(.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)) (-.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2))) (fma.f64 1/8 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 lambda1 lambda1)) (.f64 1/48 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (pow.f64 lambda1 3)))))) (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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 3)) 2)))))))

Compiler

Compiled 32234 to 19255 computations (40.3% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
	0.6b	(-.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)))
	3.7b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
	5.6b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

prune1.6s (2.8%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	245	12	257
Fresh	14	24	38
Picked	1	0	1
Done	0	0	0
Total	260	36	296

Error

13.0b

Counts

296 → 36

Alt Table

Status	Error	Program
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.8b	(.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 (.f64 (neg.f64 (.f64 (cbrt.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))) (cbrt.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))))) (cbrt.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)))))))))
	33.4b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	26.4b	(.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))) (log.f64 (exp.f64 (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)))))))
	36.8b	(.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 1/2 lambda1))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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)))))))
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	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))))
	37.2b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (.f64 (sin.f64 (.f64 -1/2 phi2)) (+.f64 (sin.f64 (.f64 -1/2 phi2)) (.f64 phi1 (cos.f64 (*.f64 -1/2 phi2)))))))))))
	25.9b	(.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)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.0b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	39.5b	(.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)) (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2)))) (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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	40.5b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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 (-.f64 (sin.f64 (.f64 1/2 phi1)) (fma.f64 1/2 (.f64 phi2 (cos.f64 (.f64 1/2 phi1))) (.f64 1/8 (.f64 (sin.f64 (.f64 1/2 phi1)) (*.f64 phi2 phi2))))) 2)))))))
▶	13.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))

Compiler

Compiled 30414 to 19361 computations (36.3% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))
✓	0.4b	(pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)
✓	0.6b	(-.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))
	3.7b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series486.0ms (0.8%)

Counts

3 → 120

Calls

3 calls:

292.0ms

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

163.0ms

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

31.0ms

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

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`pow1_binary64`

Counts

3 → 67

Calls

3 calls:

5.0ms

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

3.0ms

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

2.0ms

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

simplify347.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

559×	`*-commutative_binary64`
558×	`fma-def_binary64`
372×	`fma-neg_binary64`
227×	`associate-+r+_binary64`
220×	`associate--r+_binary64`

Counts

187 → 183

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	571	21409
1	1847	19921
2	4886	19921
3	5189	19921

prune2.3s (4%)

Pruning

42 alts after pruning (42 fresh and 0 done)

	Pruned	Kept	Total
New	304	21	325
Fresh	14	21	35
Picked	1	0	1
Done	0	0	0
Total	319	42	361

Error

12.8b

Counts

361 → 42

Alt Table

Status	Error	Program
	45.1b	(.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 (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)))) (sqrt.f64 2)) (sqrt.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	25.9b	(.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)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	35.4b	(.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 1/2 phi2)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 (+.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)))))))))
	33.4b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.8b	(.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 (.f64 (neg.f64 (.f64 (cbrt.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))) (cbrt.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))))) (cbrt.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)))))))))
	35.0b	(.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 (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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.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)) (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)))) (+.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))))))))
	35.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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)))))))
	29.0b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 1/2 lambda1))) (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)))))))
	30.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (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 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 (cos.f64 (.f64 1/2 phi2)) (sin.f64 (.f64 1/2 phi2)))))))) (sqrt.f64 (-.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
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	13.8b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (.f64 (.f64 (cbrt.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (cbrt.f64 (-.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))) (cbrt.f64 (-.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
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	13.8b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))))
	25.8b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 -1/2 lambda2))) (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)))))))
	26.0b	(.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)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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)))))))
	41.5b	(.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 (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda1 lambda1) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)))) 1) (+.f64 (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda1 (.f64 lambda1 (cos.f64 phi1))) (pow.f64 (cos.f64 (.f64 -1/2 lambda2)) 2))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)) (.f64 (cos.f64 phi2) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (*.f64 lambda1 (cos.f64 phi1))))))))))))
	39.3b	(.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)) (-.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2))) (fma.f64 1/8 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 lambda1 lambda1)) (.f64 1/48 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (pow.f64 lambda1 3)))))) (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)))))))
	26.2b	(.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 (cbrt.f64 (.f64 (.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) (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)))))))
	37.2b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (.f64 (sin.f64 (.f64 -1/2 phi2)) (+.f64 (sin.f64 (.f64 -1/2 phi2)) (.f64 phi1 (cos.f64 (*.f64 -1/2 phi2)))))))))))
	30.3b	(.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 1/2 lambda1))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	33.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (sqrt.f64 (-.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	39.5b	(.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)) (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2)))) (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)))))))
	14.5b	(.f64 R (.f64 2 (atan2.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) 3)) (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))

Compiler

Compiled 50761 to 35121 computations (30.8% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(sqrt.f64 (fma.f64 (log1p.f64 (expm1.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))
	0.4b	(pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)
	0.6b	(-.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))
	3.7b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series284.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

284.0ms

(sqrt.f64 (fma.f64 (log1p.f64 (expm1.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 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (fma.f64 (log1p.f64 (expm1.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 (-.f64 (*.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))

simplify176.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

502×	`*-commutative_binary64`
341×	`cancel-sign-sub-inv_binary64`
320×	`fma-def_binary64`
309×	`unswap-sqr_binary64`
273×	`distribute-rgt-in_binary64`

Counts

63 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	405	10734
1	1325	10185
2	3008	9607
3	5273	9607

prune2.6s (4.4%)

Pruning

41 alts after pruning (41 fresh and 0 done)

	Pruned	Kept	Total
New	317	8	325
Fresh	8	33	41
Picked	1	0	1
Done	0	0	0
Total	326	41	367

Error

12.8b

Counts

367 → 41

Alt Table

Status	Error	Program
	45.1b	(.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 (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)))) (sqrt.f64 2)) (sqrt.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	25.9b	(.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)) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	35.4b	(.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 1/2 phi2)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	35.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (log1p.f64 (expm1.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 1/2 phi1)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.8b	(.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 (.f64 (neg.f64 (.f64 (cbrt.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))) (cbrt.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))))) (cbrt.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)))))))))
	33.4b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))
	35.0b	(.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 (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)))))))
	25.7b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (/.f64 (-.f64 (.f64 1 1) (.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)) (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)))) (+.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))))))))
	35.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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)))))))
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	41.5b	(.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 (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda1 lambda1) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)))) 1) (+.f64 (fma.f64 1/4 (.f64 (cos.f64 phi2) (.f64 (.f64 lambda1 (.f64 lambda1 (cos.f64 phi1))) (pow.f64 (cos.f64 (.f64 -1/2 lambda2)) 2))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)) (.f64 (cos.f64 phi2) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 (.f64 -1/2 lambda2)) (*.f64 lambda1 (cos.f64 phi1))))))))))))
	39.3b	(.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)) (-.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2))) (fma.f64 1/8 (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 lambda1 lambda1)) (.f64 1/48 (.f64 (cos.f64 (.f64 -1/2 lambda2)) (pow.f64 lambda1 3)))))) (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)))))))
	25.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (log1p.f64 (expm1.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 -1/2 lambda2))) (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)))))))
	27.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (fma.f64 (cos.f64 phi2) (.f64 (pow.f64 (sin.f64 (.f64 -1/2 lambda2)) 2) (cos.f64 phi1)) (fma.f64 (pow.f64 (sin.f64 (.f64 phi1 1/2)) 2) (pow.f64 (cos.f64 (.f64 phi2 1/2)) 2) (.f64 (pow.f64 (cos.f64 (.f64 phi1 1/2)) 2) (pow.f64 (sin.f64 (.f64 phi2 1/2)) 2)))) (.f64 2 (.f64 (cos.f64 (.f64 phi1 1/2)) (.f64 (sin.f64 (.f64 phi1 1/2)) (.f64 (cos.f64 (.f64 phi2 1/2)) (sin.f64 (.f64 phi2 1/2)))))))) (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	37.2b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (.f64 (sin.f64 (.f64 -1/2 phi2)) (+.f64 (sin.f64 (.f64 -1/2 phi2)) (.f64 phi1 (cos.f64 (*.f64 -1/2 phi2)))))))))))
	30.3b	(.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 1/2 lambda1))) (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	33.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2))) (sqrt.f64 (-.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	39.5b	(.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)) (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (sin.f64 (.f64 -1/2 lambda2)))) (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)))))))
	34.5b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (*.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	13.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (log1p.f64 (expm1.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.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))))) (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)))))))

Compiler

Compiled 46841 to 32486 computations (30.6% saved)

regimes13.6s (23.4%)

Accuracy

Total 0.8b remaining (6%)

Threshold costs 0.8b (6%)

Counts

349 → 1

Compiler

Compiled 407920 to 285496 computations (30% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	148
1	53	148
2	66	148
3	75	148
4	80	148
5	81	148
6	81	148

end2.5s (4.3%)

Remove: (sort phi1 phi2)
Compiler: Compiled 4751 to 3390 computations (28.6% saved)

Details

analyze9.2s (15.8%)

sample22.1s (38.1%)

simplify499.0ms (0.9%)

prune9.0ms (0%)

localize26.0ms (0%)

series126.0ms (0.2%)

rewrite19.0ms (0%)

simplify142.0ms (0.2%)

prune2.0s (3.4%)

localize41.0ms (0.1%)

prune1.6s (2.8%)

localize34.0ms (0.1%)

series486.0ms (0.8%)

rewrite17.0ms (0%)

simplify347.0ms (0.6%)

prune2.3s (4%)

localize38.0ms (0.1%)

series284.0ms (0.5%)

rewrite2.0ms (0%)

simplify176.0ms (0.3%)

prune2.6s (4.4%)

regimes13.6s (23.4%)

simplify6.0ms (0%)

end2.5s (4.3%)

Profiling