Details

analyze3.5s (17.6%)

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
0.8%	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)

sample10.5s (52%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

7.8s	5680×	body	1024	valid
1.2s	1469×	body	512	valid
757.0ms	259×	body	2048	valid
290.0ms	539×	body	256	valid
90.0ms	309×	body	128	valid
4.0ms	3×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

47×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

14.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.6b	(.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)
▶	14.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Status

Error

Program

14.6b

(*.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)

▶

14.6b

(*.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Compiler

Compiled 136 to 86 computations (36.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	0.2b	(.f64 (acos.f64 (fma.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 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	4.4b	(cos.f64 (-.f64 lambda1 lambda2))

series75.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

34.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
29.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
8.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite78.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

355×	`log1p-udef_binary64`
195×	`add-sqr-sqrt_binary64`
181×	`log1p-expm1-u_binary64`
181×	`expm1-log1p-u_binary64`
179×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	362	77
2	4646	77
3	5227	77

Stop Event

1×	node limit

Counts

4 → 81

Calls

4 calls:

75.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
75.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
75.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
75.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify146.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

671×	`distribute-rgt-neg-in_binary64`
626×	`distribute-lft-neg-in_binary64`
581×	`cancel-sign-sub-inv_binary64`
508×	`fma-def_binary64`
455×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	139	4337
1	383	4311
2	1274	4176
3	3342	4172
4	4831	4172
5	4997	4172

Stop Event

1×	node limit

Counts

245 → 130

prune169.0ms (0.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	114	16	130
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	16	132

Error

3.1b

Counts

132 → 16

Alt Table

Status	Error	Program
	15.3b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 3)
	15.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 2)) R)
	14.8b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) 1) R)
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
	15.2b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 3) R)
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
▶	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	35.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) -1/2 (.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))) R)
	14.7b	(.f64 (/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	45.7b	(cbrt.f64 (.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3) (pow.f64 R 3)))
	40.5b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 2)
	14.6b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	14.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	14.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))))) R)
	14.6b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	14.8b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 2) R)

Compiler

Compiled 4579 to 1599 computations (65.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
✓	0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))

series134.0ms (0.7%)

Counts

4 → 164

Calls

4 calls:

61.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
46.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
18.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite40.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`add-sqr-sqrt_binary64`
238×	`log1p-expm1-u_binary64`
238×	`expm1-log1p-u_binary64`
235×	`add-log-exp_binary64`
234×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	105
1	488	81
2	5107	81

Stop Event

1×	node limit

Counts

4 → 58

Calls

4 calls:

38.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
38.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
38.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
38.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))

simplify155.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

771×	`fma-def_binary64`
639×	`distribute-rgt-neg-in_binary64`
634×	`cancel-sign-sub-inv_binary64`
345×	`sub-neg_binary64`
311×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	6712
1	512	6688
2	1638	6192
3	4036	6192
4	5036	6192

Stop Event

1×	node limit

Counts

222 → 110

prune202.0ms (1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	109	17	126

Error

3.0b

Counts

126 → 17

Alt Table

Status	Error	Program
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)))) R)
	15.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 2)) R)
	15.3b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 3)
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) 3) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	14.6b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	14.8b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 2) R)
▶	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
	14.7b	(.f64 (/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	45.7b	(cbrt.f64 (.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3) (pow.f64 R 3)))
	40.5b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 2)
	14.8b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) 1) R)
	14.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	14.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))))) R)
	14.6b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	15.2b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 3) R)
	35.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) -1/2 (.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))) R)

Compiler

Compiled 5095 to 1786 computations (64.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 lambda1))))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
✓	0.2b	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

series167.0ms (0.8%)

Counts

4 → 92

Calls

4 calls:

58.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
47.0ms	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
46.0ms	(.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 lambda1))))
15.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`add-sqr-sqrt_binary64`
245×	`log1p-expm1-u_binary64`
245×	`expm1-log1p-u_binary64`
243×	`add-log-exp_binary64`
242×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	131
1	504	131
2	5241	131

Stop Event

1×	node limit

Counts

4 → 54

Calls

4 calls:

41.0ms	(.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 lambda1))))
41.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
41.0ms	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
41.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-r_binary64`
478×	`distribute-rgt-neg-in_binary64`
464×	`fma-neg_binary64`
462×	`distribute-lft-neg-in_binary64`
367×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	4484
1	673	4390
2	2388	3962
3	4958	3962
4	5228	3962

Stop Event

1×	node limit

Counts

146 → 113

prune206.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	11	5	16
Picked	1	0	1
Done	0	0	0
Total	115	15	130

Error

3.0b

Counts

130 → 15

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)) 2)
	14.7b	(.f64 (/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	4.3b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)) 3)
	45.7b	(cbrt.f64 (.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3) (pow.f64 R 3)))
	3.6b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) 2) R)
	14.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))))) R)
	3.4b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
	4.1b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) 3) R)
▶	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)))) R)
	3.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) 3) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	3.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	4.1b	(.f64 (.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	3.5b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) 1) R)
	3.4b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) R)

Compiler

Compiled 5986 to 1910 computations (68.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)))) R)
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
✓	0.7b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1))))
✓	4.1b	(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)

series1.4s (6.8%)

Counts

4 → 204

Calls

4 calls:

1.2s	(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)
62.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)))) R)
47.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
16.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1))))

rewrite44.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`expm1-log1p-u_binary64`
265×	`log1p-expm1-u_binary64`
261×	`add-log-exp_binary64`
260×	`add-cbrt-cube_binary64`
259×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	131
1	549	131
2	5036	131

Stop Event

1×	node limit

Counts

4 → 70

Calls

4 calls:

42.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)))) R)
42.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
42.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1))))
42.0ms	(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)

simplify179.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

720×	`distribute-rgt-neg-in_binary64`
702×	`distribute-lft-neg-in_binary64`
625×	`*-commutative_binary64`
617×	`fma-def_binary64`
494×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	8624
1	444	8268
2	1390	7580
3	3597	7580
4	5028	7580

Stop Event

1×	node limit

Counts

274 → 87

prune143.0ms (0.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	87	15	102

Error

3.0b

Counts

102 → 15

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)) 2)
	14.7b	(.f64 (/.f64 (-.f64 (.f64 (/.f64 (PI.f64) 2) (/.f64 (PI.f64) 2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	4.3b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)) 3)
	45.7b	(cbrt.f64 (.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) 3) (pow.f64 R 3)))
	3.4b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
	4.1b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) 3) R)
✓	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 1)))) R)
	3.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	3.6b	(.f64 (pow.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))))))) 2) R)
	3.3b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) 3) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	3.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	14.6b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))))) R)
	4.1b	(.f64 (.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) 2) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	3.5b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) 1) R)
	3.4b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))) R)

Compiler

Compiled 4178 to 1181 computations (71.7% saved)

regimes2.1s (10.4%)

Accuracy

Total 0.3b remaining (7.8%)

Threshold costs 0.3b (7.8%)

Counts

153 → 1

Compiler

Compiled 54326 to 35448 computations (34.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	49
1	29	49
2	29	49

Stop Event

1×

saturated

end642.0ms (3.2%)

Compiler: Compiled 823 to 502 computations (39% saved)

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29

Details

analyze3.5s (17.6%)

sample10.5s (52%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series75.0ms (0.4%)

rewrite78.0ms (0.4%)

simplify146.0ms (0.7%)

prune169.0ms (0.8%)

localize24.0ms (0.1%)

series134.0ms (0.7%)

rewrite40.0ms (0.2%)

simplify155.0ms (0.8%)

prune202.0ms (1%)

localize26.0ms (0.1%)

series167.0ms (0.8%)

rewrite43.0ms (0.2%)

simplify118.0ms (0.6%)

prune206.0ms (1%)

localize29.0ms (0.1%)

series1.4s (6.8%)

rewrite44.0ms (0.2%)

simplify179.0ms (0.9%)

prune143.0ms (0.7%)

regimes2.1s (10.4%)

simplify3.0ms (0%)

end642.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	18	29
1	28	29
2	43	29
3	53	29
4	60	29
5	78	29
6	104	29
7	125	29
8	142	29
9	152	29
10	156	29
11	158	29
12	144	29