Details

analyze3.6s (17.3%)

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
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample235.0ms (1.1%)

Algorithm

1×

intervals

Results

154.0ms	175×	body	1024	valid
25.0ms	50×	body	512	valid
19.0ms	9×	body	2048	valid
4.0ms	12×	body	256	valid
2.0ms	10×	body	128	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`*-commutative_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	17.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite93.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 1588 to 295 computations (81.4% saved)

series156.0ms (0.7%)

Error

16.6b

Counts

4 → 47

Calls

4 calls:

58.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
33.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
26.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
20.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2505 to 1636 computations (34.7% saved)

simplify119.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-l_binary64`
404×	`sub-neg_binary64`
385×	`distribute-rgt-neg-in_binary64`
378×	`distribute-lft-neg-in_binary64`
366×	`associate-r_binary64`

Counts

104 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2573
1	340	2327
2	823	2315
3	1977	2305
4	4040	2305
5	4963	2305

prune78.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	31	12	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	12	44

Error

2.7b

Counts

44 → 12

Alt Table

Status	Error	Program
	45.1b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
	17.9b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3)) R)
	17.8b	(.f64 (acos.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 phi2) (cbrt.f64 (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
	43.7b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) (sqrt.f64 R)) (sqrt.f64 R))
	17.9b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	18.3b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	49.0b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
	17.7b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	17.8b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	18.3b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
▶	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))

Compiler

Compiled 1910 to 702 computations (63.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite147.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

13×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
9×	`associate-r_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2725 to 392 computations (85.6% saved)

series329.0ms (1.6%)

Error

2.7b

Counts

4 → 58

Calls

4 calls:

129.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
91.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
46.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
27.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4855 to 2747 computations (43.4% saved)

simplify170.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

894×	`cancel-sign-sub-inv_binary64`
534×	`associate-r_binary64`
490×	`associate-l_binary64`
349×	`distribute-rgt-neg-in_binary64`
257×	`neg-mul-1_binary64`

Counts

130 → 95

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	278	5272
1	802	4608
2	3098	4608
3	4814	4608
4	5100	4608

prune132.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	82	13	95
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Error

2.5b

Counts

107 → 15

Alt Table

Status	Error	Program
	45.1b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
	36.8b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	3.2b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	3.8b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.7b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	3.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)))
	3.2b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))
	43.6b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R) 3))
	3.0b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)
	3.0b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
	3.2b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) 3)) R)
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))
	3.0b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
▶	3.0b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)

Compiler

Compiled 3773 to 1161 computations (69.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
0.6b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

rewrite117.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`exp-prod_binary64`
8×	`log-pow_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 2589 to 212 computations (91.8% saved)

series591.0ms (2.8%)

Error

2.5b

Counts

4 → 51

Calls

4 calls:

276.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
192.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
71.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
48.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 4017 to 2575 computations (35.9% saved)

simplify309.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
385×	`associate-/r/_binary64`
373×	`log-prod_binary64`
336×	`unswap-sqr_binary64`
302×	`distribute-rgt-out_binary64`

Counts

109 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	99	5909
1	159	4844
2	324	4844
3	448	4844
4	607	4838
5	1083	4838
6	2775	4838
7	4508	4838
8	4931	4838
9	4912	4838

prune80.0ms (0.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	88	16	104

Error

2.5b

Counts

104 → 16

Alt Table

Status	Error	Program
	3.7b	(.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (.f64 R (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))))
	45.1b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
	36.8b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	3.2b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	3.8b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)))
	3.2b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))
	43.6b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R) 3))
	3.0b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)
▶	3.0b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))) R)
	3.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) R)
	3.1b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) 3))) R)
	3.0b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
	3.2b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) 3)) R)
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))

Compiler

Compiled 2969 to 947 computations (68.1% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
0.5b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
0.6b	(log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))
1.0b	(exp.f64 PI.f64)

rewrite194.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

2.3b

Rules

37×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
23×	`log-prod_binary64`

Counts

4 → 95

Calls

4 calls:

7.0ms	(/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
6.0ms	(log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))
2.0ms	(exp.f64 PI.f64)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 4567 to 470 computations (89.7% saved)

series593.0ms (2.8%)

Error

2.5b

Counts

4 → 36

Calls

4 calls:

334.0ms	(log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))
198.0ms	(/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
55.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))
0.0ms	(exp.f64 PI.f64)

Compiler

Compiled 3275 to 2218 computations (32.3% saved)

simplify324.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

461×	`prod-exp_binary64`
410×	`distribute-rgt-in_binary64`
379×	`div-exp_binary64`
301×	`times-frac_binary64`
284×	`distribute-lft-in_binary64`

Counts

131 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	9078
1	275	7939
2	529	7665
3	1075	7661
4	2305	7661
5	3795	7661
6	5025	7661

prune104.0ms (0.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	5	10	15
Picked	0	1	1
Done	0	0	0
Total	91	19	110

Error

2.4b

Counts

110 → 19

Alt Table

Status	Error	Program
	3.6b	(.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) (-.f64 (/.f64 PI.f64 2) (log.f64 (sqrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))))) R)
	4.1b	(.f64 (+.f64 (+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 PI.f64)))) (.f64 (log.f64 (cbrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))) -2)) (log.f64 (/.f64 (sqrt.f64 (sqrt.f64 (exp.f64 PI.f64))) (cbrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))))) R)
	3.7b	(.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (.f64 R (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))))
	3.7b	(.f64 (+.f64 (-.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (exp.f64 PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) (log.f64 (/.f64 (cbrt.f64 (sqrt.f64 (exp.f64 PI.f64))) (sqrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))))) R)
	4.0b	(.f64 (+.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 PI.f64)))) (-.f64 (log.f64 (sqrt.f64 (sqrt.f64 (exp.f64 PI.f64)))) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	45.1b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
	36.8b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	3.2b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)))
	3.2b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))
	43.6b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R) 3))
	3.0b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) R)
	3.8b	(.f64 (log.f64 (.f64 (fabs.f64 (cbrt.f64 (exp.f64 PI.f64))) (/.f64 (sqrt.f64 (cbrt.f64 (exp.f64 PI.f64))) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) R)
	3.0b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))) R)
	3.0b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (neg.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) R)
	3.6b	(.f64 (log.f64 (.f64 (/.f64 (fabs.f64 (cbrt.f64 (exp.f64 PI.f64))) (.f64 (cbrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) (cbrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) (/.f64 (sqrt.f64 (cbrt.f64 (exp.f64 PI.f64))) (cbrt.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))))) R)
	2.9b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (-.f64 (log.f64 (sqrt.f64 (exp.f64 PI.f64))) (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))))) R)
	3.2b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))) 3)) R)
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))))

Compiler

Compiled 3227 to 892 computations (72.4% saved)

regimes6.2s (29.1%)

Accuracy

Total 0.5b remaining (13.9%)

Threshold costs 0.5b (13.9%)

Compiler

Compiled 139268 to 75895 computations (45.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	53
1	33	53
2	33	53

end25.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 185 to 115 computations (37.8% saved)

sample7.4s (35%)

Algorithm

1×

intervals

Results

4.7s	5600×	body	1024	valid
705.0ms	1349×	body	512	valid
529.0ms	271×	body	2048	valid
178.0ms	491×	body	256	valid
47.0ms	289×	body	128	valid
3.0ms	4×	body	1024	invalid
1.0ms	2×	body	512	invalid

Compiler

Compiled 1098 to 576 computations (47.5% saved)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Details

analyze3.6s (17.3%)

sample235.0ms (1.1%)

simplify14.0ms (0.1%)

prune2.0ms (0%)

localize18.0ms (0.1%)

rewrite93.0ms (0.4%)

series156.0ms (0.7%)

simplify119.0ms (0.6%)

prune78.0ms (0.4%)

localize25.0ms (0.1%)

rewrite147.0ms (0.7%)

series329.0ms (1.6%)

simplify170.0ms (0.8%)

prune132.0ms (0.6%)

localize28.0ms (0.1%)

rewrite117.0ms (0.6%)

series591.0ms (2.8%)

simplify309.0ms (1.5%)

prune80.0ms (0.4%)

localize37.0ms (0.2%)

rewrite194.0ms (0.9%)

series593.0ms (2.8%)

simplify324.0ms (1.5%)

prune104.0ms (0.5%)

regimes6.2s (29.1%)

simplify3.0ms (0%)

end25.0ms (0.1%)

sample7.4s (35%)

Profiling

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31