Details

analyze3.7s (18%)

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 (52.2%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

8.0s	5646×	body	1024	valid
1.3s	1503×	body	512	valid
790.0ms	269×	body	2048	valid
313.0ms	542×	body	256	valid
92.0ms	296×	body	128	valid
2.0ms	2×	body	512	invalid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	256	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

17.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.4b	(.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)
▶	17.4b	(.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

17.4b

(*.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)

▶

17.4b

(*.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)

localize19.0ms (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 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
✓	0.8b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	3.0b	(cos.f64 (-.f64 lambda1 lambda2))

series59.0ms (0.3%)

Counts

4 → 124

Calls

4 calls:

36.0ms	(.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)
10.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
9.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`cos-sum_binary64`
9×	`prod-diff_binary64`

Counts

4 → 74

Calls

4 calls:

4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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)))))

simplify162.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-neg_binary64`
573×	`sub-neg_binary64`
382×	`fma-def_binary64`
356×	`*-commutative_binary64`
344×	`distribute-rgt-neg-in_binary64`

Counts

198 → 134

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	260	5438
1	463	4940
2	1251	4849
3	2498	4795
4	4511	4793
5	5051	4793

prune153.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	12	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	124	12	136

Error

3.1b

Counts

136 → 12

Alt Table

Status	Error	Program
	37.3b	(.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))
	17.4b	(.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)
	18.0b	(.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))
▶	3.3b	(.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)
	17.5b	(.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))))))))
	17.5b	(.f64 (expm1.f64 (log1p.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)
	37.2b	(.f64 (sqrt.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)) (sqrt.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)))
	18.0b	(.f64 (.f64 (.f64 (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)))))) (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))))))) (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))))))) R)
	18.0b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	17.6b	(.f64 (cbrt.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))))))) R)
	17.4b	(.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)
	17.4b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Compiler

Compiled 5078 to 1388 computations (72.7% saved)

localize25.0ms (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 (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)
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	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))))))

series98.0ms (0.5%)

Counts

3 → 116

Calls

3 calls:

69.0ms

(*.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)

19.0ms

(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))))))

9.0ms

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

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

3.0ms

(*.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))))))

simplify209.0ms (1%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-neg_binary64`
480×	`distribute-rgt-neg-in_binary64`
453×	`associate-l_binary64`
399×	`distribute-lft-neg-in_binary64`
355×	`associate-r_binary64`

Counts

167 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	7164
1	334	5781
2	899	5757
3	2083	5733
4	3428	5733
5	4950	5733
6	5018	5733

prune202.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	122	12	134
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	133	13	146

Error

3.0b

Counts

146 → 13

Alt Table

Status	Error	Program
	17.4b	(.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)
	4.2b	(.f64 (.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)))))))) (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)))))))) R)
▶	3.3b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
	28.8b	(.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))
	28.7b	(.f64 (sqrt.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)) (sqrt.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)))
	3.5b	(.f64 (cbrt.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)))))))) R)
	4.2b	(.f64 (.f64 (cbrt.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)))))) R)) (cbrt.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)))))) R))) (cbrt.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)))))) R)))
	3.4b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (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)
	3.5b	(.f64 (expm1.f64 (log1p.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)
	3.3b	(.f64 (acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
	4.2b	(.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))
	3.5b	(.f64 (.f64 (sqrt.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 (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)
	3.5b	(.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 (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))

Compiler

Compiled 6137 to 1497 computations (75.6% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.7b	(acos.f64 (+.f64 (log.f64 (exp.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))))))
✓	4.7b	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

series98.0ms (0.5%)

Counts

3 → 132

Calls

3 calls:

69.0ms

(*.f64 (acos.f64 (+.f64 (log.f64 (exp.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)

19.0ms

(acos.f64 (+.f64 (log.f64 (exp.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))))))

10.0ms

(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 46

Calls

3 calls:

4.0ms

(*.f64 (acos.f64 (+.f64 (log.f64 (exp.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)

2.0ms

(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

1.0ms

(acos.f64 (+.f64 (log.f64 (exp.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))))))

simplify209.0ms (1%)

Algorithm

1×	egg-herbie

Rules

510×	`fma-neg_binary64`
442×	`distribute-rgt-neg-in_binary64`
386×	`distribute-lft-neg-in_binary64`
312×	`associate-l_binary64`
300×	`fma-def_binary64`

Counts

178 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	7313
1	292	5854
2	764	5828
3	1816	5810
4	3223	5810
5	4858	5810
6	4999	5810

prune226.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	137	13	150

Error

3.0b

Counts

150 → 13

Alt Table

Status	Error	Program
	3.4b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (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)
	4.2b	(.f64 (.f64 (.f64 (cbrt.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 phi2) (sin.f64 phi1))))) (cbrt.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 phi2) (sin.f64 phi1)))))) (cbrt.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 phi2) (sin.f64 phi1)))))) R)
✓	3.3b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
	28.8b	(.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))
	28.7b	(.f64 (sqrt.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)) (sqrt.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)))
	3.5b	(.f64 (cbrt.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)))))))) R)
	4.2b	(.f64 (.f64 (cbrt.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)))))) R)) (cbrt.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)))))) R))) (cbrt.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)))))) R)))
	3.5b	(.f64 (expm1.f64 (log1p.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)
	3.3b	(.f64 (log.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 phi2) (sin.f64 phi1)))))) R)
▶	3.3b	(.f64 (acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
	4.2b	(.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))
	3.5b	(.f64 (.f64 (sqrt.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 (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)
	3.5b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (log.f64 (exp.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 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi2) (sin.f64 phi1)))))))

Compiler

Compiled 6404 to 1509 computations (76.4% saved)

localize28.0ms (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) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
✓	0.2b	(.f64 (acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
✓	0.7b	(acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

series139.0ms (0.7%)

Counts

3 → 100

Calls

3 calls:

73.0ms

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

48.0ms

(*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))

18.0ms

(acos.f64 (+.f64 (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`cbrt-unprod_binary64`

Counts

3 → 54

Calls

3 calls:

6.0ms

(*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))

3.0ms

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

1.0ms

(acos.f64 (+.f64 (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 lambda1) (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

simplify227.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
496×	`cancel-sign-sub-inv_binary64`
446×	`associate-r_binary64`
348×	`associate-l_binary64`
261×	`sub-neg_binary64`

Counts

154 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	7274
1	644	6819
2	2044	6343
3	4213	6343
4	4996	6343
5	4995	6343
6	4943	6343

prune241.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	157	11	168

Error

3.0b

Counts

168 → 11

Alt Table

Status	Error	Program
	3.4b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (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)
	4.2b	(.f64 (.f64 (.f64 (cbrt.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 phi2) (sin.f64 phi1))))) (cbrt.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 phi2) (sin.f64 phi1)))))) (cbrt.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 phi2) (sin.f64 phi1)))))) R)
✓	3.3b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
	28.8b	(.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))
	28.7b	(.f64 (sqrt.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)) (sqrt.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)))
	3.5b	(.f64 (cbrt.f64 (.f64 (.f64 (acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) (acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))) (acos.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1))))))))) R)
	4.2b	(.f64 (.f64 (cbrt.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)))))) R)) (cbrt.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)))))) R))) (cbrt.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)))))) R)))
	3.5b	(.f64 (expm1.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))))) R)
	3.3b	(.f64 (log.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 phi2) (sin.f64 phi1)))))) R)
	4.2b	(.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))
	3.5b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (log.f64 (exp.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 phi2) (.f64 (cos.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (sin.f64 phi2) (sin.f64 phi1)))))))

Compiler

Compiled 7488 to 1501 computations (80% saved)

regimes3.7s (17.8%)

Accuracy

Total 0.3b remaining (8.6%)

Threshold costs 0.3b (8.6%)

Counts

213 → 1

Compiler

Compiled 91504 to 52617 computations (42.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	43
1	36	43
2	35	43

end283.0ms (1.4%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 769 to 402 computations (47.7% 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 (18%)

sample10.8s (52.2%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series59.0ms (0.3%)

rewrite14.0ms (0.1%)

simplify162.0ms (0.8%)

prune153.0ms (0.7%)

localize25.0ms (0.1%)

series98.0ms (0.5%)

rewrite9.0ms (0%)

simplify209.0ms (1%)

prune202.0ms (1%)

localize28.0ms (0.1%)

series98.0ms (0.5%)

rewrite9.0ms (0%)

simplify209.0ms (1%)

prune226.0ms (1.1%)

localize28.0ms (0.1%)

series139.0ms (0.7%)

rewrite14.0ms (0.1%)

simplify227.0ms (1.1%)

prune241.0ms (1.2%)

regimes3.7s (17.8%)

simplify2.0ms (0%)

end283.0ms (1.4%)

Profiling

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