Details

analyze4.6s (21.7%)

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)

sample319.0ms (1.5%)

Algorithm

1×

intervals

Results

233.0ms	189×	body	1024	valid
25.0ms	8×	body	2048	valid
24.0ms	37×	body	512	valid
5.0ms	13×	body	256	valid
2.0ms	9×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify16.0ms (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

16.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	16.1b	(.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)

localize22.0ms (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)
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite71.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

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:

4.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(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)

series128.0ms (0.6%)

Error

15.0b

Counts

4 → 47

Calls

4 calls:

49.0ms	(.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)
26.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
20.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
18.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2524 to 1652 computations (34.5% saved)

simplify138.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

668×	`distribute-rgt-neg-in_binary64`
582×	`distribute-lft-neg-in_binary64`
420×	`neg-mul-1_binary64`
378×	`neg-sub0_binary64`
347×	`sub-neg_binary64`

Counts

104 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	2592
1	348	2338
2	805	2320
3	1799	2315
4	3324	2315
5	4658	2315
6	4884	2315

prune59.0ms (0.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	29	14	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	14	44

Error

1.6b

Counts

44 → 14

Alt Table

Status	Error	Program
	16.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
▶	1.9b	(.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)
	16.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	33.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (cos.f64 lambda2) (.f64 lambda1 (-.f64 (.f64 lambda1 (*.f64 (cos.f64 lambda2) 1/2)) (sin.f64 lambda2))))))) R)
	16.1b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
	16.3b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) 3)) R)
	16.3b	(.f64 (sqrt.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 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	16.7b	(.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 phi2) (cos.f64 phi1))))))))
	42.0b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	43.4b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	16.3b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	16.1b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	16.1b	(.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 phi2) (cos.f64 phi1)))))) R)
	42.2b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) (sqrt.f64 R)) (sqrt.f64 R))

Compiler

Compiled 2102 to 806 computations (61.7% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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)
0.7b	(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))))))

rewrite97.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(.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)
1.0ms	(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 2199 to 333 computations (84.9% saved)

series182.0ms (0.9%)

Error

1.6b

Counts

4 → 48

Calls

4 calls:

74.0ms	(.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)
36.0ms	(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))))))
28.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
23.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3667 to 2260 computations (38.4% saved)

simplify187.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

514×	`cancel-sign-sub-inv_binary64`
509×	`sub-neg_binary64`
430×	`distribute-rgt-neg-in_binary64`
374×	`*-commutative_binary64`
318×	`distribute-lft-neg-in_binary64`

Counts

112 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	3801
1	433	3158
2	1153	3108
3	1891	3088
4	3296	3088
5	4533	3088
6	4986	3088
7	4927	3088

prune84.0ms (0.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	63	12	75
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	75	14	89

Error

1.5b

Counts

89 → 14

Alt Table

Status	Error	Program
	43.4b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	35.3b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	1.9b	(.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)
	2.1b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) 3)) R)
	42.2b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) (sqrt.f64 R)) (sqrt.f64 R))
	1.9b	(.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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1)))))))) R)
	35.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	2.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	2.1b	(.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 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	2.7b	(.f64 (.f64 (cbrt.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))))))) (cbrt.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 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	2.1b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
▶	1.9b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
	1.9b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)

Compiler

Compiled 2880 to 1011 computations (64.9% saved)

localize30.0ms (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 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.6b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

rewrite81.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

1.4b

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:

6.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
2.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 2589 to 212 computations (91.8% saved)

series498.0ms (2.4%)

Error

1.5b

Counts

4 → 51

Calls

4 calls:

235.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
160.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
58.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
39.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 4051 to 2684 computations (33.7% saved)

simplify281.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

109 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	5909
1	175	4844
2	323	4844
3	450	4844
4	609	4838
5	1085	4838
6	2777	4838
7	4510	4838
8	4933	4838
9	4912	4838

prune56.0ms (0.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	88	15	103

Error

1.5b

Counts

103 → 15

Alt Table

Status	Error	Program
	2.1b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) 3))) R)
	2.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	2.5b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) R)
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
▶	1.9b	(.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)
	2.1b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) 3)) R)
	42.2b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) (sqrt.f64 R)) (sqrt.f64 R))
	1.9b	(.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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1)))))))) R)
	37.4b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	35.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	1.9b	(.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 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) R)
	2.1b	(.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 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	2.7b	(.f64 (.f64 (cbrt.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))))))) (cbrt.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 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	35.3b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	1.9b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)

Compiler

Compiled 2791 to 910 computations (67.4% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.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)
0.3b	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
0.7b	(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))))))
26.1b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))

rewrite115.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

10×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`

Counts

4 → 67

Calls

4 calls:

4.0ms	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
3.0ms	(.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)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))
1.0ms	(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))))))

Compiler

Compiled 2483 to 655 computations (73.6% saved)

series182.0ms (0.9%)

Error

1.5b

Counts

4 → 45

Calls

4 calls:

72.0ms	(.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)
38.0ms	(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))))))
36.0ms	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
22.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))

Compiler

Compiled 3585 to 2260 computations (37% saved)

simplify164.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

476×	`unswap-sqr_binary64`
456×	`cancel-sign-sub-inv_binary64`
396×	`*-commutative_binary64`
321×	`log-prod_binary64`
248×	`exp-prod_binary64`

Counts

112 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	165	3842
1	358	3183
2	1068	3137
3	2219	3119
4	4559	3116
5	4971	3116
6	4954	3116

prune82.0ms (0.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	95	15	110

Error

1.5b

Counts

110 → 15

Alt Table

Status	Error	Program
	1.9b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	2.1b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) 3))) R)
	2.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	2.5b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) R)
	2.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R))) (cbrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	2.1b	(.f64 (sqrt.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))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi2) (sin.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))
	42.2b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) (sqrt.f64 R)) (sqrt.f64 R))
	1.9b	(.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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1)))))))) R)
	37.4b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	35.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	1.9b	(.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 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) R)
	2.7b	(.f64 (.f64 (cbrt.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))))))) (cbrt.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 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	35.3b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	2.1b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) 3)) R)
	1.9b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)

Compiler

Compiled 2528 to 748 computations (70.4% saved)

regimes3.7s (17.4%)

Accuracy

Total 0.3b remaining (9.1%)

Threshold costs 0.3b (9.1%)

Compiler

Compiled 96976 to 57176 computations (41% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	53
1	35	53
2	35	53

end42.0ms (0.2%)

Remove: (sort phi1 phi2)
Compiler: Compiled 259 to 168 computations (35.1% saved)

sample9.9s (47.2%)

Algorithm

1×

intervals

Results

6.9s	5452×	body	1024	valid
977.0ms	1465×	body	512	valid
718.0ms	266×	body	2048	valid
229.0ms	511×	body	256	valid
72.0ms	306×	body	128	valid
5.0ms	4×	body	1024	invalid

Compiler

Compiled 773 to 435 computations (43.7% 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

analyze4.6s (21.7%)

sample319.0ms (1.5%)

simplify16.0ms (0.1%)

prune2.0ms (0%)

localize22.0ms (0.1%)

rewrite71.0ms (0.3%)

series128.0ms (0.6%)

simplify138.0ms (0.7%)

prune59.0ms (0.3%)

localize27.0ms (0.1%)

rewrite97.0ms (0.5%)

series182.0ms (0.9%)

simplify187.0ms (0.9%)

prune84.0ms (0.4%)

localize30.0ms (0.1%)

rewrite81.0ms (0.4%)

series498.0ms (2.4%)

simplify281.0ms (1.3%)

prune56.0ms (0.3%)

localize30.0ms (0.1%)

rewrite115.0ms (0.5%)

series182.0ms (0.9%)

simplify164.0ms (0.8%)

prune82.0ms (0.4%)

regimes3.7s (17.4%)

simplify4.0ms (0%)

end42.0ms (0.2%)

sample9.9s (47.2%)

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