Details

analyze10.2s (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)

sample24.6s (33%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

18.2s	5473×	body	1024	valid
2.9s	1288×	body	512	valid
2.6s	431×	body	2048	valid
477.0ms	389×	body	256	valid
402.0ms	675×	body	128	valid
9.0ms	3×	body	1024	invalid
1.0ms	1×	body	256	invalid
1.0ms	1×	body	128	invalid

Compiler

Compiled 212 to 140 computations (34% saved)

simplify173.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

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

prune9.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

25.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	25.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
▶	25.3b	(.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 (-.f64 phi1 phi2) 2)) 2)))))))

Status

Error

Program

25.3b

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

▶

25.3b

(*.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 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 409 to 260 computations (36.4% saved)

localize30.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)
✓	0.7b	(-.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)))
✓	2.9b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
✓	4.6b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

series187.0ms (0.3%)

Counts

4 → 120

Calls

4 calls:

158.0ms	(-.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)
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 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:

4.0ms	(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))

simplify144.0ms (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

prune1.6s (2.1%)

Pruning

36 alts after pruning (36 fresh and 0 done)

	Pruned	Kept	Total
New	288	36	324
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	290	36	326

Error

23.2b

Counts

326 → 36

Alt Table

Status	Error	Program
	25.3b	(.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 (-.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))))))))
	33.8b	(.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 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)))))))
	37.8b	(.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 (fma.f64 1/2 (.f64 (.f64 phi1 phi1) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 lambda1 lambda2))) 2))) (.f64 1/4 (.f64 (.f64 phi1 phi1) (pow.f64 (sin.f64 (.f64 -1/2 phi2)) 2)))) (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2)) (fma.f64 1/4 (.f64 (.f64 phi1 phi1) (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2)) (fma.f64 phi1 (.f64 (sin.f64 (.f64 -1/2 phi2)) (cos.f64 (.f64 -1/2 phi2))) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 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)) (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)))))))
	32.7b	(.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 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.5b	(.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 (sin.f64 (.f64 1/2 lambda1)) (fma.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (.f64 1/8 (.f64 (sin.f64 (.f64 1/2 lambda1)) (.f64 lambda2 lambda2)))))) (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)))))))
	25.4b	(.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 (-.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)))))))))
	36.6b	(.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 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)))))))
	25.3b	(.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)) (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.3b	(.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 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (cbrt.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)))))))
	32.3b	(.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 (pow.f64 (cos.f64 (.f64 -1/2 phi2)) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 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 lambda1))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.5b	(.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)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 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)))))))
	38.4b	(.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)))))))
	39.0b	(.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 (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)))))))))
	35.2b	(.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 (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)))))))
▶	24.5b	(.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 (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)) (-.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)))))))
	24.6b	(.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))))))
	34.7b	(.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 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (.f64 1/2 lambda1)) 2))) (pow.f64 (sin.f64 (.f64 1/2 (-.f64 phi1 phi2))) 2)))))))
	25.3b	(.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)) (-.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)))))))
	25.3b	(.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 (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)))) 2)))))))
	37.9b	(.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))) (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))))))))))
	25.3b	(.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 (-.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)))))))
	39.0b	(.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))) (-.f64 (fma.f64 1/4 (.f64 (.f64 phi2 phi2) (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2)) (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2)) (fma.f64 (cos.f64 (.f64 1/2 phi1)) (.f64 phi2 (sin.f64 (.f64 1/2 phi1))) (.f64 1/4 (.f64 (.f64 phi2 phi2) (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)))))))
	25.4b	(.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 (-.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)))))))))
	25.3b	(.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 (fma.f64 1 1 (neg.f64 (.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 (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 (neg.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 (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 (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 (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))))))))))
	51.5b	(.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 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 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2))))))))
	25.5b	(.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 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 2) (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)))))))
	34.9b	(.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 -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)))))))
	32.7b	(.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 -1/2 phi2)) 2)))))))
	32.6b	(.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 (.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)))))))
	50.0b	(.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 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	25.5b	(.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 (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)))))))
	36.5b	(.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 1 (+.f64 (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))))))))))))
	34.8b	(.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 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (.f64 (cos.f64 phi1) (pow.f64 (sin.f64 (*.f64 1/2 (-.f64 lambda1 lambda2))) 2)))))))

Compiler

Compiled 32086 to 19099 computations (40.5% saved)

localize43.0ms (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)
	0.7b	(-.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)))
	2.9b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
	4.6b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

prune1.5s (2%)

Pruning

34 alts after pruning (34 fresh and 0 done)

	Pruned	Kept	Total
New	248	9	257
Fresh	10	25	35
Picked	1	0	1
Done	0	0	0
Total	259	34	293

Error

13.0b

Counts

293 → 34

Alt Table

Status	Error	Program
	25.3b	(.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 (-.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))))))))
	33.8b	(.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 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)))))))
	32.7b	(.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 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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)) (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)))))))
	33.5b	(.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 -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))) (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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	51.5b	(.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 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 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 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 (-.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)))))))
	25.5b	(.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 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 2) (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)))))))
	34.9b	(.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 -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)))))))
	38.7b	(.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))) (-.f64 (pow.f64 (sin.f64 (.f64 1/2 phi1)) 2) (.f64 (sin.f64 (.f64 1/2 phi1)) (.f64 phi2 (cos.f64 (*.f64 1/2 phi1)))))))))))
	36.5b	(.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 1 (+.f64 (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))))))))))))
	32.6b	(.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 (.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)))))))

Compiler

Compiled 30246 to 19191 computations (36.6% saved)

localize34.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(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)
✓	0.7b	(-.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)))
	2.9b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series712.0ms (1%)

Counts

3 → 120

Calls

3 calls:

452.0ms

(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)))

216.0ms

(-.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)))

42.0ms

(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)

rewrite67.0ms (0.1%)

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:

52.0ms

(-.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)))

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)

1.0ms

(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)))

simplify725.0ms (1%)

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

prune2.6s (3.5%)

Pruning

40 alts after pruning (40 fresh and 0 done)

	Pruned	Kept	Total
New	299	26	325
Fresh	19	14	33
Picked	1	0	1
Done	0	0	0
Total	319	40	359

Error

12.7b

Counts

359 → 40

Alt Table

Status	Error	Program
	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))) (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 (fma.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))))) 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 phi1)) 2) (pow.f64 (cos.f64 (.f64 1/2 phi2)) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/2 phi1)) 2) (pow.f64 (sin.f64 (.f64 1/2 phi2)) 2)))))))))
	13.9b	(.f64 R (.f64 2 (atan2.f64 (expm1.f64 (log1p.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)))))))
	33.8b	(.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 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)))))))
	32.7b	(.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 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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)) (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)))))))
	25.0b	(.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)))))))
	27.8b	(.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 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))) (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)))))))
	50.0b	(.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 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sqrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	32.0b	(.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 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (*.f64 -1/2 phi2)) 2)))))))
	14.0b	(.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 (.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)))))))))
	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 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)))))))
	25.5b	(.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 (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)))))))
	13.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (cbrt.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)))))))
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	30.7b	(.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 (fma.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))))) 1) (+.f64 (.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 (cos.f64 phi1) lambda1))))) (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)))))))))
	14.0b	(.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))) (exp.f64 (log.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))))) (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)))))))
	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 (-.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)))))))
	25.5b	(.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 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2))) 2) (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)))))))
	26.9b	(.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 (-.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)))))))
	14.0b	(.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)) (-.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)))))))
	27.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.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)))) (.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)))))))
	14.2b	(.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 (pow.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 4) (pow.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 2))))))))
	36.6b	(.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 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)))))))
	13.9b	(.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 (-.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 (fma.f64 1 1 (neg.f64 (.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 (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)))))) (fma.f64 (neg.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 (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))) (.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 (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))))))))))
	16.4b	(.f64 R (.f64 2 (atan2.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 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 51471 to 35679 computations (30.7% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)
✓	0.5b	(.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)) (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)))
✓	0.5b	(-.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))
	2.9b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

series1.9s (2.5%)

Counts

2 → 96

Calls

2 calls:

1.2s

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

609.0ms

(*.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)) (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)))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`fma-udef_binary64`

Counts

2 → 48

Calls

2 calls:

4.0ms

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

simplify782.0ms (1%)

Algorithm

1×	egg-herbie

Rules

544×	`*-commutative_binary64`
478×	`associate-r_binary64`
394×	`+-commutative_binary64`
370×	`fma-def_binary64`
351×	`associate-+r+_binary64`

Counts

144 → 159

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1121	40955
1	3953	39030
2	4993	39030
3	4989	39030

prune7.2s (9.6%)

Pruning

51 alts after pruning (51 fresh and 0 done)

	Pruned	Kept	Total
New	504	15	519
Fresh	3	36	39
Picked	1	0	1
Done	0	0	0
Total	508	51	559

Error

12.6b

Counts

559 → 51

Alt Table

Status	Error	Program
	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))) (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 (fma.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))))) 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 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)))))))))
	31.0b	(.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 (-.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (+.f64 1 (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))))))))
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	13.9b	(.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 (-.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 (.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2)))) (+.f64 1 (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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 4) (pow.f64 (cbrt.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))) 2)))))))))
	26.9b	(.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 (-.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)))))))
	30.9b	(.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 (-.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 (.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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 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 1/2 phi2)) 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 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (*.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2))))))))
	27.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (-.f64 (+.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)))) (.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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Compiler

Compiled 125823 to 85670 computations (31.9% saved)

regimes18.3s (24.5%)

Accuracy

Total 1.0b remaining (6.8%)

Threshold costs 1.0b (6.8%)

Counts

389 → 1

Compiler

Compiled 640002 to 451184 computations (29.5% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative_binary64`
19×	`+-commutative_binary64`
17×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	179
1	93	179
2	114	179
3	134	179
4	153	179
5	169	179
6	179	179
7	185	179
8	187	179
9	185	179

end3.9s (5.2%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 8080 to 5832 computations (27.8% saved)

Iter	Nodes	Cost
0	57	179
1	93	179
2	114	179
3	134	179
4	153	179
5	169	179
6	179	179
7	185	179
8	187	179
9	185	179

Iter	Nodes	Cost
0	57	179
1	93	179
2	114	179
3	134	179
4	153	179
5	169	179
6	179	179
7	185	179
8	187	179
9	185	179

Details

analyze10.2s (13.6%)

sample24.6s (33%)

simplify173.0ms (0.2%)

prune9.0ms (0%)

localize30.0ms (0%)

series187.0ms (0.3%)

rewrite19.0ms (0%)

simplify144.0ms (0.2%)

prune1.6s (2.1%)

localize43.0ms (0.1%)

prune1.5s (2%)

localize34.0ms (0%)

series712.0ms (1%)

rewrite67.0ms (0.1%)

simplify725.0ms (1%)

prune2.6s (3.5%)

localize59.0ms (0.1%)

series1.9s (2.5%)

rewrite16.0ms (0%)

simplify782.0ms (1%)

prune7.2s (9.6%)

regimes18.3s (24.5%)

simplify14.0ms (0%)

end3.9s (5.2%)

Profiling

Iter	Nodes	Cost
0	57	179
1	93	179
2	114	179
3	134	179
4	153	179
5	169	179
6	179	179
7	185	179
8	187	179
9	185	179