Details

analyze3.7s (16.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample10.8s (48.5%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

8.0s	5647×	body	1024	valid
1.2s	1460×	body	512	valid
872.0ms	288×	body	2048	valid
326.0ms	592×	body	256	valid
81.0ms	269×	body	128	valid
3.0ms	2×	body	1024	invalid
1.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 74 to 53 computations (28.4% 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

16.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.2b	(.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)
▶	16.2b	(.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

16.2b

(*.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)

▶

16.2b

(*.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 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
✓	0.6b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	3.8b	(cos.f64 (-.f64 lambda1 lambda2))

series93.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

40.0ms	(.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)
37.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
11.0ms	(acos.f64 (+.f64 (.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))

rewrite19.0ms (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)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

simplify237.0ms (1.1%)

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

prune201.0ms (0.9%)

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

3.7b

Counts

164 → 15

Alt Table

Status	Error	Program
	16.9b	(.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)))
	16.2b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1)))))) R)
	40.5b	(.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))
	47.9b	(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))))) R) (.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)) (.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)))
	29.5b	(expm1.f64 (log1p.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)))
	16.4b	(.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)
	16.8b	(.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))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
▶	4.0b	(.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)
	16.4b	(.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))))))))
	4.0b	(.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)
	16.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	16.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	16.8b	(.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 (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))
	40.6b	(.f64 (.f64 (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)))))) (sqrt.f64 R)) (.f64 (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)))))) (sqrt.f64 R)))
	16.2b	(.f64 (log.f64 (exp.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)

Compiler

Compiled 6305 to 1729 computations (72.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series116.0ms (0.5%)

Counts

4 → 124

Calls

4 calls:

75.0ms	(.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)
22.0ms	(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))))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

4.0ms	(.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)
4.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(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))))))

simplify198.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-neg_binary64`
585×	`sub-neg_binary64`
523×	`fma-def_binary64`
420×	`*-commutative_binary64`
312×	`cancel-sign-sub-inv_binary64`

Counts

196 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	7980
1	512	6473
2	1439	6143
3	2812	6107
4	4783	6107
5	5244	6107

prune245.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	122	14	136
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	131	20	151

Error

3.6b

Counts

151 → 20

Alt Table

Status	Error	Program
	4.2b	(.f64 (sqrt.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))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	4.8b	(.f64 (.f64 (.f64 (cbrt.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))))))) (cbrt.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)))))))) (cbrt.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)
	29.5b	(expm1.f64 (log1p.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)))
	16.4b	(.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)
	16.4b	(.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))))))))
▶	4.0b	(.f64 (log.f64 (exp.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 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	4.0b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
	4.1b	(.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 (.f64 (sin.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2))))))) R)
	4.8b	(.f64 (.f64 (cbrt.f64 (.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)) (cbrt.f64 (.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))) (cbrt.f64 (.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)))
	16.8b	(.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 (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))
	4.0b	(.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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2))))))) R)
	4.1b	(.f64 (acos.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2))) (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (cbrt.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)
	59.9b	(log.f64 (pow.f64 (exp.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) R))
	4.8b	(.f64 (.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (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))
	33.6b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (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)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (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)))
	16.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	33.2b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	43.5b	(cbrt.f64 (.f64 (.f64 (.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) (.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)) (.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)))
	33.5b	(.f64 (.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)))))) (sqrt.f64 R)) (sqrt.f64 R))

Compiler

Compiled 7732 to 1843 computations (76.2% 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 (+.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)
✓	0.4b	(exp.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)))))))
✓	0.4b	(log.f64 (exp.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))))))))
	0.6b	(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))))))

series158.0ms (0.7%)

Counts

3 → 156

Calls

3 calls:

77.0ms

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

59.0ms

(exp.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)))))))

22.0ms

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`exp-prod_binary64`
9×	`add-cube-cbrt_binary64`
8×	`log-pow_binary64`

Counts

3 → 56

Calls

3 calls:

4.0ms

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

2.0ms

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

2.0ms

(exp.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)))))))

simplify341.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

212 → 102

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	10857
1	188	8699
2	368	8269
3	546	8269
4	743	8263
5	1226	8263
6	2999	8263
7	4798	8263
8	5065	8263

prune211.0ms (0.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	108	15	123
Fresh	14	5	19
Picked	1	0	1
Done	0	0	0
Total	123	20	143

Error

3.5b

Counts

143 → 20

Alt Table

Status	Error	Program
	4.1b	(.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	4.1b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) 3))) R)
	33.2b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (exp.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)) (cbrt.f64 (.f64 (log.f64 (exp.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))) (cbrt.f64 (.f64 (log.f64 (exp.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)))
	16.8b	(.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 (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))
▶	4.0b	(.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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2))))))) R)
	4.1b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.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))))))))) (log.f64 (sqrt.f64 (exp.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)
	43.5b	(cbrt.f64 (.f64 (.f64 (.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) (.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)) (.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)))
	4.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (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 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	59.9b	(log.f64 (pow.f64 (exp.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) R))
	33.5b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (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))
	19.9b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	4.6b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.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)))))))) (cbrt.f64 (exp.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)))))))))) (log.f64 (cbrt.f64 (exp.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)
	4.8b	(.f64 (.f64 (log.f64 (exp.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)))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.1b	(.f64 (-.f64 (log.f64 (exp.f64 (/.f64 (PI.f64) 2))) (log.f64 (exp.f64 (asin.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)
	4.5b	(.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	4.2b	(.f64 (sqrt.f64 (log.f64 (exp.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))))))))) (.f64 (sqrt.f64 (log.f64 (exp.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))
	4.8b	(.f64 (.f64 (cbrt.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))))))) (log.f64 (exp.f64 (.f64 (cbrt.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))))))) (cbrt.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)
	4.1b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 (PI.f64))) (exp.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	4.1b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (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 phi2) (.f64 (cos.f64 phi1) (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 8379 to 1462 computations (82.6% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
✓	0.6b	(cbrt.f64 (sin.f64 lambda1))
✓	0.6b	(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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))))))

series441.0ms (2%)

Counts

4 → 96

Calls

4 calls:

233.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
176.0ms	(cbrt.f64 (sin.f64 lambda1))
21.0ms	(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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))))))
12.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`pow1_binary64`
21×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
18×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 89

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))
5.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
1.0ms	(cbrt.f64 (sin.f64 lambda1))
1.0ms	(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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))))))

simplify169.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
531×	`*-commutative_binary64`
518×	`cancel-sign-sub-inv_binary64`
450×	`fma-def_binary64`
283×	`unswap-sqr_binary64`

Counts

185 → 154

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	201	4369
1	492	3623
2	1480	3441
3	3086	3413
4	4583	3291
5	4881	3291
6	4870	3291

prune398.0ms (1.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	19	19
Picked	0	1	1
Done	0	0	0
Total	202	20	222

Error

3.5b

Counts

222 → 20

Alt Table

Status	Error	Program
	4.1b	(.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	4.1b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) 3))) R)
	33.2b	(.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 (log.f64 (exp.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)) (cbrt.f64 (.f64 (log.f64 (exp.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))) (cbrt.f64 (.f64 (log.f64 (exp.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)))
	16.8b	(.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 (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))
✓	4.0b	(.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 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2))))))) R)
	4.1b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.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))))))))) (log.f64 (sqrt.f64 (exp.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)
	43.5b	(cbrt.f64 (.f64 (.f64 (.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) (.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)) (.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)))
	4.6b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (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 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	59.9b	(log.f64 (pow.f64 (exp.f64 (acos.f64 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 phi1) (sin.f64 phi2))))) R))
	33.5b	(.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (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))
	19.9b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) R)))
	4.6b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.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)))))))) (cbrt.f64 (exp.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)))))))))) (log.f64 (cbrt.f64 (exp.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)
	4.8b	(.f64 (.f64 (log.f64 (exp.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)))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.1b	(.f64 (-.f64 (log.f64 (exp.f64 (/.f64 (PI.f64) 2))) (log.f64 (exp.f64 (asin.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)
	4.5b	(.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))) R)
	4.2b	(.f64 (sqrt.f64 (log.f64 (exp.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))))))))) (.f64 (sqrt.f64 (log.f64 (exp.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))
	4.8b	(.f64 (.f64 (cbrt.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))))))) (log.f64 (exp.f64 (.f64 (cbrt.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))))))) (cbrt.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)
	4.1b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 (PI.f64))) (exp.f64 (asin.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	4.1b	(.f64 (log.f64 (.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (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 phi2) (.f64 (cos.f64 phi1) (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 10583 to 2467 computations (76.7% saved)

regimes4.2s (18.7%)

Accuracy

Total 0.4b remaining (10.4%)

Threshold costs 0.4b (10.4%)

Counts

277 → 1

Compiler

Compiled 128574 to 70070 computations (45.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	57
1	35	57
2	35	57

end636.0ms (2.8%)

Remove: (sort phi1 phi2)
Compiler: Compiled 1541 to 710 computations (53.9% 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

analyze3.7s (16.5%)

sample10.8s (48.5%)

simplify12.0ms (0.1%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series93.0ms (0.4%)

rewrite19.0ms (0.1%)

simplify237.0ms (1.1%)

prune201.0ms (0.9%)

localize26.0ms (0.1%)

series116.0ms (0.5%)

rewrite16.0ms (0.1%)

simplify198.0ms (0.9%)

prune245.0ms (1.1%)

localize28.0ms (0.1%)

series158.0ms (0.7%)

rewrite14.0ms (0.1%)

simplify341.0ms (1.5%)

prune211.0ms (0.9%)

localize30.0ms (0.1%)

series441.0ms (2%)

rewrite20.0ms (0.1%)

simplify169.0ms (0.8%)

prune398.0ms (1.8%)

regimes4.2s (18.7%)

simplify3.0ms (0%)

end636.0ms (2.8%)

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