Details

analyze3.9s (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
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)

sample629.0ms (2.5%)

Algorithm

1×

intervals

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

220.0ms	174×	body	1024	valid
33.0ms	49×	body	512	valid
23.0ms	8×	body	2048	valid
5.0ms	12×	body	256	valid
3.0ms	13×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify12.0ms (0%)

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

prune6.0ms (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

18.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.4b	(.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)
	18.4b	(.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

▶

18.4b

(*.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)

18.4b

(*.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)

localize18.0ms (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)))))
✓	3.5b	(cos.f64 (-.f64 lambda1 lambda2))

series100.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

44.0ms	(.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)
41.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
10.0ms	(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))

rewrite18.0ms (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:

6.0ms	(.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 (0.9%)

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

prune184.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	146	15	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	15	163

Error

4.2b

Counts

163 → 15

Alt Table

Status	Error	Program
	18.4b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	44.2b	(.f64 (sqrt.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)) (sqrt.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)))
	19.0b	(.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)))
	4.5b	(.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)
	18.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2))) (.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	44.6b	(cbrt.f64 (.f64 (.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) (.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)) (.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)))
	44.2b	(.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))))) (sqrt.f64 R)) (sqrt.f64 R))
	18.4b	(.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)
	19.0b	(.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))
▶	4.5b	(.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)
	45.6b	(exp.f64 (+.f64 (log.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (log.f64 R)))
	18.4b	(.f64 (exp.f64 (log.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)
	18.4b	(.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)
	19.0b	(.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))
	18.6b	(.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))

Compiler

Compiled 6102 to 1702 computations (72.1% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
✓	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)))
✓	0.9b	(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))))))

series195.0ms (0.8%)

Counts

4 → 204

Calls

4 calls:

80.0ms	(.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)
49.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
49.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
17.0ms	(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))))))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64`
30×	`add-exp-log_binary64`
30×	`pow1_binary64`
17×	`cbrt-unprod_binary64`
17×	`prod-exp_binary64`

Counts

4 → 84

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
6.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
3.0ms	(.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)
0.0ms	(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))))))

simplify188.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

764×	`associate-r_binary64`
642×	`associate-l_binary64`
482×	`distribute-rgt-neg-in_binary64`
472×	`fma-neg_binary64`
350×	`*-commutative_binary64`

Counts

288 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	10922
1	1006	9047
2	3568	9037
3	5064	9037

prune303.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	172	13	185
Fresh	13	1	14
Picked	1	0	1
Done	0	0	0
Total	186	14	200

Error

4.1b

Counts

200 → 14

Alt Table

Status	Error	Program
	4.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2))))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	5.4b	(.f64 (.f64 (cbrt.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))))))) (cbrt.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)))))))) (.f64 (cbrt.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))
	5.3b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)))
	4.7b	(.f64 (cbrt.f64 (.f64 (.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)))))) (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))))))) (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)
	36.7b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)) (sqrt.f64 R))
	4.5b	(.f64 (log.f64 (exp.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)
	4.7b	(.f64 (sqrt.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))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))
	36.7b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)) (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)))
	45.6b	(exp.f64 (+.f64 (log.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (log.f64 R)))
	38.7b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R) 3))
	4.5b	(.f64 (exp.f64 (log.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)
▶	4.5b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) R)
	4.5b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
	5.4b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))

Compiler

Compiled 9694 to 2240 computations (76.9% saved)

localize27.0ms (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 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) R)
✓	0.4b	(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
✓	0.5b	(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
✓	0.9b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

series89.0ms (0.4%)

Counts

4 → 148

Calls

4 calls:

37.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) R)
29.0ms	(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
12.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
11.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

rewrite12.0ms (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 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) R)
2.0ms	(log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
1.0ms	(exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
0.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

simplify337.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

214 → 107

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	101	8770
1	133	8349
2	268	8349
3	431	8349
4	699	8343
5	1226	8343
6	2999	8343
7	4798	8343
8	5065	8343

prune171.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	108	13	121

Error

4.1b

Counts

121 → 13

Alt Table

Status	Error	Program
	4.6b	(.f64 (log.f64 (cbrt.f64 (.f64 (.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R)
	5.3b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)))
	4.6b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 (PI.f64))) (exp.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))) R)
▶	4.5b	(.f64 (exp.f64 (log.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)
	4.7b	(.f64 (sqrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.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 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))
	4.5b	(.f64 (log.f64 (exp.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)
	5.4b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))) (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))) R))
	5.2b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (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 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))) R)
	4.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2))))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	5.4b	(.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 (log.f64 (exp.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R))
	4.7b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R)
	45.6b	(exp.f64 (+.f64 (log.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (log.f64 R)))
	36.7b	(.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) (sqrt.f64 R)) (sqrt.f64 R))

Compiler

Compiled 5954 to 1037 computations (82.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series4.0s (16.1%)

Counts

2 → 96

Calls

2 calls:

4.0s

(log.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)))))))

18.0ms

(exp.f64 (log.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))))))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms

(exp.f64 (log.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))))))))

1.0ms

(log.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)))))))

simplify342.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1093×	`fma-def_binary64`
620×	`unswap-sqr_binary64`
349×	`associate-/l*_binary64`
316×	`associate-l_binary64`
287×	`associate-/r*_binary64`

Counts

127 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	6200
1	106	4867
2	194	4867
3	262	4859
4	375	4859
5	447	4859
6	617	4859
7	1151	4859
8	2213	4859
9	3498	4859
10	4686	4859
11	4886	4859
12	4996	4859
13	4830	4859

prune260.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	138	15	153

Error

4.1b

Counts

153 → 15

Alt Table

Status	Error	Program
	4.7b	(.f64 (.f64 (sqrt.f64 (exp.f64 (log.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))))))))) (sqrt.f64 (exp.f64 (log.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)
	4.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2))))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	4.6b	(.f64 (log.f64 (cbrt.f64 (.f64 (.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R)
	4.9b	(.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.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)))))))) (cbrt.f64 (log.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)))))))))) (cbrt.f64 (log.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)
	4.5b	(.f64 (exp.f64 (log1p.f64 (expm1.f64 (log.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)
	5.3b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)))
	5.4b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))) (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))) R))
	5.2b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (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 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))) R)
	4.7b	(.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R)
	5.4b	(.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 (log.f64 (exp.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R))
	4.7b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))) R)
	45.6b	(exp.f64 (+.f64 (log.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (log.f64 R)))
	36.7b	(.f64 (.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))) (sqrt.f64 R)) (sqrt.f64 R))
	4.6b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 (PI.f64))) (exp.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))) R)
	4.7b	(.f64 (sqrt.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.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 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))

Compiler

Compiled 7456 to 1555 computations (79.1% saved)

regimes3.8s (15.4%)

Accuracy

Total 0.3b remaining (8.7%)

Threshold costs 0.3b (8.7%)

Counts

251 → 1

Compiler

Compiled 112512 to 59430 computations (47.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`exp-1-e_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	45
1	33	45
2	32	45

end31.0ms (0.1%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 224 to 161 computations (28.1% saved)

sample9.9s (39.9%)

Algorithm

1×

intervals

Results

6.9s	5536×	body	1024	valid
995.0ms	1420×	body	512	valid
674.0ms	242×	body	2048	valid
220.0ms	486×	body	256	valid
72.0ms	316×	body	128	valid
2.0ms	2×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 989 to 425 computations (57% 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

analyze3.9s (15.6%)

sample629.0ms (2.5%)

simplify12.0ms (0%)

prune6.0ms (0%)

localize18.0ms (0.1%)

series100.0ms (0.4%)

rewrite18.0ms (0.1%)

simplify231.0ms (0.9%)

prune184.0ms (0.7%)

localize25.0ms (0.1%)

series195.0ms (0.8%)

rewrite23.0ms (0.1%)

simplify188.0ms (0.8%)

prune303.0ms (1.2%)

localize27.0ms (0.1%)

series89.0ms (0.4%)

rewrite12.0ms (0%)

simplify337.0ms (1.4%)

prune171.0ms (0.7%)

localize29.0ms (0.1%)

series4.0s (16.1%)

rewrite5.0ms (0%)

simplify342.0ms (1.4%)

prune260.0ms (1.1%)

regimes3.8s (15.4%)

simplify3.0ms (0%)

end31.0ms (0.1%)

sample9.9s (39.9%)

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