Details

analyze3.7s (15.8%)

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)

sample617.0ms (2.7%)

Algorithm

1×

intervals

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

215.0ms	174×	body	1024	valid
28.0ms	44×	body	512	valid
15.0ms	6×	body	2048	valid
9.0ms	23×	body	256	valid
2.0ms	9×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify13.0ms (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

13.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.9b	(.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)
	13.9b	(.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

▶

13.9b

(*.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)

13.9b

(*.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 (.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)
✓	1.3b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	1.9b	(cos.f64 (-.f64 lambda1 lambda2))

series86.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

39.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
31.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
9.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
6.0ms	(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:

6.0ms	(.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 (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)))))

simplify243.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

240 → 161

Iterations

Useful iterations: 3 (0.0ms)

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

prune208.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	144	17	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	146	17	163

Error

3.2b

Counts

163 → 17

Alt Table

Status	Error	Program
	3.4b	(.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)
	3.5b	(.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)
	14.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))) 3)))) R)
	14.6b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	14.0b	(.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)
	33.7b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (-.f64 (fma.f64 (pow.f64 lambda1 3) (.f64 -1/6 (sin.f64 lambda2)) (cos.f64 lambda2)) (.f64 lambda1 (-.f64 (.f64 (*.f64 (cos.f64 lambda2) 1/2) lambda1) (sin.f64 lambda2))))))) R)
	14.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) R)
	14.1b	(.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))
	39.9b	(exp.f64 (log.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)))
▶	3.4b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	14.6b	(.f64 (.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))))))) (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)
	14.0b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	14.6b	(.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))
	38.6b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (sqrt.f64 R)))
	45.3b	(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))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (*.f64 R R) R)))
	14.6b	(.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)))
	45.2b	(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)))

Compiler

Compiled 6362 to 1804 computations (71.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
✓	1.3b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series147.0ms (0.6%)

Counts

4 → 164

Calls

4 calls:

66.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
52.0ms	(.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
18.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
11.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64`

Counts

4 → 78

Calls

4 calls:

7.0ms	(.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 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)
0.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify211.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

987×	`fma-neg_binary64`
636×	`cancel-sign-sub-inv_binary64`
529×	`associate-r_binary64`
462×	`associate-l_binary64`
326×	`distribute-rgt-neg-in_binary64`

Counts

242 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	277	9603
1	761	7949
2	2538	7777
3	4291	7775
4	4955	7775

prune279.0ms (1.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	151	11	162
Fresh	11	5	16
Picked	1	0	1
Done	0	0	0
Total	163	16	179

Error

3.1b

Counts

179 → 16

Alt Table

Status	Error	Program
	14.6b	(.f64 (.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))))))) (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)
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	14.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))) 3)))) R)
	42.6b	(cbrt.f64 (.f64 (.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R) (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	14.6b	(.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))
	3.5b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2)))))))) R)
	45.3b	(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))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (*.f64 R R) R)))
	4.4b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.7b	(.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))
	3.5b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
	39.9b	(exp.f64 (log.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)))
	32.6b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)))
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R))) (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
▶	3.4b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
	3.7b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) 3)) R)
	3.5b	(.f64 (exp.f64 (log.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)

Compiler

Compiled 8685 to 2047 computations (76.4% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))
✓	0.2b	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
✓	1.3b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

series165.0ms (0.7%)

Counts

4 → 88

Calls

4 calls:

67.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
53.0ms	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
26.0ms	(.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))
18.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

4 → 75

Calls

4 calls:

7.0ms	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))
4.0ms	(.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))
3.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1))))))) R)
0.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))

simplify171.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

831×	`cancel-sign-sub-inv_binary64`
521×	`associate-r_binary64`
388×	`associate-l_binary64`
388×	`fma-neg_binary64`
361×	`distribute-rgt-neg-in_binary64`

Counts

163 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	7066
1	763	6470
2	2520	6021
3	4466	6021
4	5003	6021

prune281.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	170	14	184

Error

3.1b

Counts

184 → 14

Alt Table

Status	Error	Program
▶	3.5b	(.f64 (exp.f64 (log.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)
	14.6b	(.f64 (.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))))))) (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)
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	14.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))) 3)))) R)
	42.6b	(cbrt.f64 (.f64 (.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R) (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	14.6b	(.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))
	3.5b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2)))))))) R)
	45.3b	(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))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (*.f64 R R) R)))
	4.4b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	39.9b	(exp.f64 (log.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)))
	32.6b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)))
	3.5b	(.f64 (log.f64 (exp.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)
	3.5b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))) R)
	3.7b	(.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))

Compiler

Compiled 8871 to 2050 computations (76.9% 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 (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)))))))))
✓	0.2b	(.f64 (exp.f64 (log.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)
✓	0.7b	(log.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))))))))
✓	1.3b	(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)))))))

series3.6s (15.5%)

Counts

4 → 204

Calls

4 calls:

3.5s	(log.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))))))))
57.0ms	(.f64 (exp.f64 (log.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)
16.0ms	(exp.f64 (log.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)))))))))
16.0ms	(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)))))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`log-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`

Counts

4 → 65

Calls

4 calls:

4.0ms	(.f64 (exp.f64 (log.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)
2.0ms	(exp.f64 (log.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)))))))))
1.0ms	(log.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))))))))
0.0ms	(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)))))))

simplify494.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-def_binary64`
435×	`unswap-sqr_binary64`
278×	`*-commutative_binary64`
269×	`log-div_binary64`
251×	`associate-l_binary64`

Counts

269 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	12350
1	137	11763
2	291	10944
3	458	10386
4	671	10386
5	1013	10386
6	1325	10386
7	2784	10386
8	3670	10386
9	4793	10386
10	4926	10386

prune166.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	108	15	123

Error

3.1b

Counts

123 → 15

Alt Table

Status	Error	Program
	3.5b	(.f64 (log.f64 (exp.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)
	4.4b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.9b	(.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (log.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))))))))) (cbrt.f64 (log.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)))))))))) (cbrt.f64 (log.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)
	14.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))) 3)))) R)
	42.6b	(cbrt.f64 (.f64 (.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R) (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)) (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	3.5b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi1) (cos.f64 lambda1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) (cos.f64 phi1)))))))) R)
	3.7b	(.f64 (sqrt.f64 (exp.f64 (log.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)))))))))) (.f64 (sqrt.f64 (exp.f64 (log.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))
	3.7b	(.f64 (exp.f64 (+.f64 (log.f64 (sqrt.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))))))))) (log.f64 (sqrt.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)
	14.6b	(.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))
	3.5b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda1)) (sin.f64 lambda1)) (.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (sin.f64 lambda2)))))))) R)
	39.9b	(exp.f64 (log.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)))
	32.6b	(.f64 (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)) (.f64 (sqrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (sqrt.f64 R)))
	4.4b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.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 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)))
	4.3b	(.f64 (exp.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) 2)) (log.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) R)
	45.3b	(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))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (*.f64 R R) R)))

Compiler

Compiled 5822 to 751 computations (87.1% saved)

regimes3.0s (13%)

Accuracy

Total 0.3b remaining (8.5%)

Threshold costs 0.3b (8.5%)

Counts

212 → 1

Compiler

Compiled 84790 to 49380 computations (41.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	46
1	30	46
2	30	46

end30.0ms (0.1%)

Compiler: Compiled 165 to 110 computations (33.3% saved)

sample9.6s (41.6%)

Algorithm

1×

intervals

Results

6.6s	5535×	body	1024	valid
917.0ms	1394×	body	512	valid
798.0ms	295×	body	2048	valid
212.0ms	494×	body	256	valid
63.0ms	282×	body	128	valid
2.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 938 to 404 computations (56.9% 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 (15.8%)

sample617.0ms (2.7%)

simplify13.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series86.0ms (0.4%)

rewrite19.0ms (0.1%)

simplify243.0ms (1%)

prune208.0ms (0.9%)

localize25.0ms (0.1%)

series147.0ms (0.6%)

rewrite19.0ms (0.1%)

simplify211.0ms (0.9%)

prune279.0ms (1.2%)

localize26.0ms (0.1%)

series165.0ms (0.7%)

rewrite20.0ms (0.1%)

simplify171.0ms (0.7%)

prune281.0ms (1.2%)

localize29.0ms (0.1%)

series3.6s (15.5%)

rewrite13.0ms (0.1%)

simplify494.0ms (2.1%)

prune166.0ms (0.7%)

regimes3.0s (13%)

simplify3.0ms (0%)

end30.0ms (0.1%)

sample9.6s (41.6%)

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