Details

analyze5.5s (15.6%)

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
1.6%	98.2%	0.2%	11
1.6%	98.2%	0.2%	12
2.3%	97.4%	0.2%	13
2.7%	97%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample13.4s (38%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

10.1s	5731×	body	1024	valid
1.5s	1441×	body	512	valid
979.0ms	255×	body	2048	valid
333.0ms	512×	body	256	valid
121.0ms	317×	body	128	valid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify24.0ms (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

prune11.0ms (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

15.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.6b	(.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)
▶	15.6b	(.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)

Status

Error

Program

15.6b

(*.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)

▶

15.6b

(*.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)

Compiler

Compiled 136 to 86 computations (36.8% saved)

localize37.0ms (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)))
✓	0.3b	(.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)))))
✓	3.9b	(cos.f64 (-.f64 lambda1 lambda2))

series191.0ms (0.5%)

Counts

4 → 164

Calls

4 calls:

82.0ms	(.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)
77.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
22.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
8.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite39.0ms (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:

12.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
8.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(.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)
3.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

simplify333.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

240 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	319	6712
1	634	6151
2	2059	5962
3	4105	5897
4	4875	5897
5	4991	5897
6	4905	5897

prune226.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	147	15	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	15	164

Error

2.6b

Counts

164 → 15

Alt Table

Status	Error	Program
	15.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	43.6b	(cbrt.f64 (.f64 (.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (.f64 R R) R)))
	15.6b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	36.8b	(.f64 (.f64 (acos.f64 (fma.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))
	15.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (.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)
	16.2b	(.f64 (.f64 (acos.f64 (fma.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))
	15.8b	(.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 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	16.2b	(.f64 (.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))))))) (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))))))) R)
	16.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	15.6b	(.f64 (log.f64 (exp.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)
	36.5b	(.f64 (sqrt.f64 (.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)) (sqrt.f64 (.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)))
	16.2b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.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 (fma.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 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	15.7b	(.f64 (expm1.f64 (log1p.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)
▶	2.8b	(.f64 (acos.f64 (+.f64 (.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 6365 to 1749 computations (72.5% saved)

localize27.0ms (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 (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 lambda1) (cos.f64 lambda2)) (.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 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series239.0ms (0.7%)

Counts

4 → 164

Calls

4 calls:

126.0ms	(.f64 (acos.f64 (+.f64 (.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)
76.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
25.0ms	(acos.f64 (+.f64 (.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))))))
11.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite29.0ms (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:

9.0ms	(.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 (+.f64 (.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)
1.0ms	(acos.f64 (+.f64 (.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))))))

simplify376.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-r_binary64`
575×	`associate-l_binary64`
485×	`fma-neg_binary64`
362×	`distribute-rgt-neg-in_binary64`
315×	`*-commutative_binary64`

Counts

244 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	350	10179
1	1037	8619
2	3801	8607
3	5027	8607

prune557.0ms (1.6%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	159	17	176
Fresh	13	1	14
Picked	1	0	1
Done	0	0	0
Total	173	18	191

Error

2.4b

Counts

191 → 18

Alt Table

Status	Error	Program
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.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 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.f64 (.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 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 (acos.f64 (+.f64 (.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)
	15.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	30.3b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (sqrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	30.5b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (sqrt.f64 R)) (sqrt.f64 R))
▶	2.8b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	3.6b	(.f64 (.f64 (acos.f64 (+.f64 (.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))
	2.8b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
	3.6b	(.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 lambda1) (cos.f64 lambda2)) (.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 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (+.f64 (.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)
	3.6b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
	38.0b	(cbrt.f64 (.f64 (.f64 (.f64 (acos.f64 (+.f64 (.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)))))) (acos.f64 (+.f64 (.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))))))) (acos.f64 (+.f64 (.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 (.f64 R R) R)))

Compiler

Compiled 8952 to 2298 computations (74.3% saved)

localize52.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
✓	0.4b	(exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
✓	0.5b	(log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
✓	0.7b	(acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

series140.0ms (0.4%)

Counts

4 → 108

Calls

4 calls:

50.0ms	(exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
45.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)
23.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
21.0ms	(acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite13.0ms (0%)

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

simplify350.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

174 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	7290
1	129	6869
2	252	6869
3	391	6869
4	659	6863
5	1226	6863
6	2999	6863
7	4798	6863
8	5065	6863

prune170.0ms (0.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	9	8	17
Picked	1	0	1
Done	0	0	0
Total	89	18	107

Error

2.4b

Counts

107 → 18

Alt Table

Status	Error	Program
	3.0b	(.f64 (.f64 (sqrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (sqrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	3.0b	(.f64 (expm1.f64 (log1p.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	30.3b	(.f64 (sqrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)) (sqrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)))
	2.8b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.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 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	3.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
▶	2.8b	(.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	3.7b	(.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.6b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (log.f64 (exp.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) R)
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2))))))) R)
	30.5b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (sqrt.f64 R)) (sqrt.f64 R))
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)) (cbrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R))) (cbrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)))
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.0b	(.f64 (log.f64 (cbrt.f64 (.f64 (.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.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 5548 to 1200 computations (78.4% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
✓	0.4b	(asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))
✓	0.5b	(log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
✓	0.7b	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))

series89.0ms (0.3%)

Counts

4 → 144

Calls

4 calls:

40.0ms	(exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
19.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
18.0ms	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
11.0ms	(asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite91.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

134×	`add-sqr-sqrt_binary64`
125×	`*-un-lft-identity_binary64`
119×	`add-cube-cbrt_binary64`
117×	`prod-diff_binary64`
93×	`times-frac_binary64`

Counts

4 → 209

Calls

4 calls:

9.0ms	(exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))
9.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
7.0ms	(-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))
0.0ms	(asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

simplify585.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
423×	`distribute-rgt-in_binary64`
383×	`fma-def_binary64`
292×	`times-frac_binary64`
290×	`associate-l_binary64`

Counts

353 → 250

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	269	23449
1	304	20110
2	762	16135
3	2185	16081
4	4752	16081
5	4877	16081

prune404.0ms (1.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	241	9	250
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	250	18	268

Error

2.3b

Counts

268 → 18

Alt Table

Status	Error	Program
	30.5b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) (sqrt.f64 R)) (sqrt.f64 R))
	35.4b	(.f64 (+.f64 (log.f64 (exp.f64 (fma.f64 1 (/.f64 (PI.f64) 2) (neg.f64 (.f64 (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) (log.f64 (exp.f64 (fma.f64 (neg.f64 (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) R)
	30.3b	(.f64 (sqrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)) (sqrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)))
	3.0b	(.f64 (log.f64 (expm1.f64 (log1p.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) R)
	5.5b	(.f64 (log.f64 (.f64 (exp.f64 (fma.f64 (/.f64 (.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) (exp.f64 (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))))) R)
	3.0b	(.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 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	3.7b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)) (cbrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R))) (cbrt.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) R)))
	5.2b	(.f64 (log.f64 (exp.f64 (+.f64 (fma.f64 (/.f64 (sqrt.f64 (PI.f64)) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (/.f64 (sqrt.f64 (PI.f64)) (cbrt.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))))) R)
	2.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log1p.f64 (expm1.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	4.1b	(.f64 (log.f64 (exp.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	3.0b	(.f64 (log.f64 (cbrt.f64 (.f64 (.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	35.3b	(.f64 (.f64 (-.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (+.f64 (sqrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (sqrt.f64 (*.f64 1/2 (PI.f64))))) R)
	3.7b	(.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	2.8b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2))))))) R)
	4.0b	(.f64 (+.f64 (log.f64 (exp.f64 (fma.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))))) (log.f64 (exp.f64 (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) (cbrt.f64 (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))))))))) R)
	3.5b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (-.f64 (.f64 1/2 (PI.f64)) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (.f64 1/2 (PI.f64)) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))))) R)
	3.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (log.f64 (exp.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (cbrt.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))))) R)

Compiler

Compiled 26761 to 3556 computations (86.7% saved)

regimes11.4s (32.3%)

Accuracy

Total 0.5b remaining (13.8%)

Threshold costs 0.5b (13.8%)

Counts

331 → 1

Compiler

Compiled 192742 to 90107 computations (53.2% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	43
1	32	43
2	31	43

end949.0ms (2.7%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 1840 to 677 computations (63.2% 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

analyze5.5s (15.6%)

sample13.4s (38%)

simplify24.0ms (0.1%)

prune11.0ms (0%)

localize37.0ms (0.1%)

series191.0ms (0.5%)

rewrite39.0ms (0.1%)

simplify333.0ms (0.9%)

prune226.0ms (0.6%)

localize27.0ms (0.1%)

series239.0ms (0.7%)

rewrite29.0ms (0.1%)

simplify376.0ms (1.1%)

prune557.0ms (1.6%)

localize52.0ms (0.1%)

series140.0ms (0.4%)

rewrite13.0ms (0%)

simplify350.0ms (1%)

prune170.0ms (0.5%)

localize31.0ms (0.1%)

series89.0ms (0.3%)

rewrite91.0ms (0.3%)

simplify585.0ms (1.7%)

prune404.0ms (1.1%)

regimes11.4s (32.3%)

simplify8.0ms (0%)

end949.0ms (2.7%)

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