Details

analyze3.8s (17.7%)

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)

sample645.0ms (3%)

Algorithm

1×

intervals

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

225.0ms	181×	body	1024	valid
34.0ms	45×	body	512	valid
10.0ms	4×	body	2048	valid
8.0ms	20×	body	256	valid
1.0ms	6×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify12.0ms (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`

Counts

1 → 2

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

prune5.0ms (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

17.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.5b	(.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)
	17.5b	(.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)

Status

Error

Program

▶

17.5b

(*.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)

17.5b

(*.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 136 to 86 computations (36.8% saved)

localize20.0ms (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)
✓	0.9b	(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))

series83.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

38.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
31.0ms	(.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)
9.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`cos-sum_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 76

Calls

4 calls:

7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.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)
0.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

simplify231.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
594×	`cancel-sign-sub-inv_binary64`
339×	`associate-r_binary64`
327×	`associate-l_binary64`
325×	`neg-mul-1_binary64`

Counts

240 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	319	6712
1	632	6151
2	2054	5962
3	4105	5897
4	4875	5897
5	4991	5897
6	4905	5897

prune194.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	147	14	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	14	163

Error

4.7b

Counts

163 → 14

Alt Table

Status	Error	Program
	4.9b	(.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)
	17.7b	(.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (sqrt.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))
▶	4.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	37.7b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.f64 R)))
	17.5b	(.f64 (log.f64 (exp.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)
	17.6b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	37.6b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 R)) (sqrt.f64 R))
	18.2b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 (cbrt.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))
	18.1b	(.f64 (.f64 (cbrt.f64 (.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)) (cbrt.f64 (.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))) (cbrt.f64 (.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)))
	17.7b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.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)
	17.6b	(.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 phi2) (cos.f64 phi1)))))) R)
	17.7b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) 3)) R)

Compiler

Compiled 6000 to 1668 computations (72.2% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.9b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series153.0ms (0.7%)

Counts

4 → 164

Calls

4 calls:

86.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
43.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
14.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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 → 80

Calls

4 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify234.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-r_binary64`
569×	`associate-l_binary64`
488×	`fma-neg_binary64`
363×	`distribute-rgt-neg-in_binary64`
314×	`*-commutative_binary64`

Counts

244 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	9069
1	1009	8619
2	3766	8607
3	4988	8607

prune295.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	164	11	175
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	175	14	189

Error

4.6b

Counts

189 → 14

Alt Table

Status	Error	Program
	5.1b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) 3)) R)
	33.3b	(exp.f64 (log.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) R)))
	5.8b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)))))) R)
	5.1b	(.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 (cbrt.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))
	17.6b	(.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 phi2) (cos.f64 phi1)))))) R)
	5.7b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) R)
	30.9b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) (sqrt.f64 R)) (sqrt.f64 R))
▶	4.9b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) R)
	4.9b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) R)
	37.7b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.f64 R)))
	30.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	5.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))

Compiler

Compiled 8216 to 2026 computations (75.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) R)
✓	0.3b	(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
✓	0.6b	(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))
✓	0.9b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))

series91.0ms (0.4%)

Counts

4 → 144

Calls

4 calls:

38.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) R)
28.0ms	(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
13.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))
12.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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 → 66

Calls

4 calls:

4.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) R)
2.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))
1.0ms	(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
0.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))

simplify323.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
666×	`times-frac_binary64`
336×	`unswap-sqr_binary64`
322×	`log-prod_binary64`
269×	`associate-l_binary64`

Counts

210 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	101	8602
1	143	8181
2	268	8181
3	445	8181
4	699	8175
5	1226	8175
6	2999	8175
7	4798	8175
8	5065	8175

prune188.0ms (0.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	8	109
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Error

4.5b

Counts

123 → 15

Alt Table

Status	Error	Program
	5.1b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) 3)) R)
	5.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))) (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	5.2b	(.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.0b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))) (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.8b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
▶	4.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)))))) R)
	5.6b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.1b	(.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))
	5.7b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (log.f64 (exp.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))))) R)
	5.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	5.1b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.1b	(.f64 (log.f64 (cbrt.f64 (.f64 (.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.0b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 (PI.f64))) (exp.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))))) R)
	30.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	17.6b	(.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 phi2) (cos.f64 phi1)))))) R)

Compiler

Compiled 6250 to 1131 computations (81.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.3b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
✓	0.9b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))
✓	24.7b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

series59.0ms (0.3%)

Counts

3 → 96

Calls

3 calls:

33.0ms

(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)

15.0ms

(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))

10.0ms

(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`

Counts

3 → 55

Calls

3 calls:

4.0ms

(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)

2.0ms

(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

0.0ms

(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))

simplify111.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
466×	`fma-def_binary64`
433×	`*-commutative_binary64`
290×	`cancel-sign-sub-inv_binary64`

Counts

151 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	3634
1	381	3493
2	1278	3401
3	3202	3377
4	5093	3377

prune358.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	156	15	171

Error

4.5b

Counts

171 → 15

Alt Table

Status	Error	Program
	5.1b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) 3)) R)
	5.7b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))) (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	5.0b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))))) (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.8b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	5.6b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.7b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda2) (sin.f64 lambda1) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) R)
	5.1b	(.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))
	5.0b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))) R)
	17.6b	(.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 phi2) (cos.f64 phi1)))))) R)
	5.1b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.1b	(.f64 (log.f64 (cbrt.f64 (.f64 (.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))))) R)
	5.0b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 (PI.f64))) (exp.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))))) R)
	30.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	5.0b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)))))))) R)
	5.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))

Compiler

Compiled 6449 to 2323 computations (64% saved)

regimes4.7s (21.9%)

Accuracy

Total 0.3b remaining (9.3%)

Threshold costs 0.3b (9.3%)

Counts

291 → 1

Compiler

Compiled 113018 to 68596 computations (39.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	41
1	28	41
2	28	41

end26.0ms (0.1%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 210 to 147 computations (30% saved)

sample9.6s (45.4%)

Algorithm

1×

intervals

Results

6.7s	5507×	body	1024	valid
1.0s	1450×	body	512	valid
725.0ms	266×	body	2048	valid
204.0ms	477×	body	256	valid
65.0ms	300×	body	128	valid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 897 to 418 computations (53.4% 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

analyze3.8s (17.7%)

sample645.0ms (3%)

simplify12.0ms (0.1%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series83.0ms (0.4%)

rewrite20.0ms (0.1%)

simplify231.0ms (1.1%)

prune194.0ms (0.9%)

localize24.0ms (0.1%)

series153.0ms (0.7%)

rewrite22.0ms (0.1%)

simplify234.0ms (1.1%)

prune295.0ms (1.4%)

localize28.0ms (0.1%)

series91.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify323.0ms (1.5%)

prune188.0ms (0.9%)

localize29.0ms (0.1%)

series59.0ms (0.3%)

rewrite9.0ms (0%)

simplify111.0ms (0.5%)

prune358.0ms (1.7%)

regimes4.7s (21.9%)

simplify4.0ms (0%)

end26.0ms (0.1%)

sample9.6s (45.4%)

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