Details

analyze3.6s (17%)

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)

sample10.4s (48.7%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

7.8s	5702×	body	1024	valid
1.2s	1446×	body	512	valid
732.0ms	246×	body	2048	valid
293.0ms	541×	body	256	valid
96.0ms	321×	body	128	valid
3.0ms	2×	body	1024	invalid
1.0ms	1×	body	512	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

17.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
▶	17.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Status

Error

Program

17.6b

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

▶

17.6b

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

Compiler

Compiled 136 to 86 computations (36.8% saved)

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)))
✓	0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
✓	1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	4.4b	(cos.f64 (-.f64 lambda1 lambda2))

series84.0ms (0.4%)

Counts

4 → 164

Calls

4 calls:

35.0ms	(.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)
35.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
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)))))
4.0ms	(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 (+.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)))))

simplify230.0ms (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

prune185.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	12	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

3.2b

Counts

164 → 12

Alt Table

Status	Error	Program
▶	3.4b	(.f64 (acos.f64 (+.f64 (.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)
	18.2b	(.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (*.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	17.7b	(.f64 (acos.f64 (+.f64 (.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)
	17.7b	(.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))))))))
	18.1b	(.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)))
	17.6b	(.f64 (-.f64 (/.f64 (PI.f64) 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	17.6b	(.f64 (exp.f64 (log.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)
	17.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	30.0b	(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)))
	36.6b	(.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))
	17.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) R)

Compiler

Compiled 5979 to 1613 computations (73% saved)

localize26.0ms (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 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
✓	0.3b	(.f64 (acos.f64 (+.f64 (.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)
✓	1.1b	(acos.f64 (+.f64 (.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))))))

series148.0ms (0.7%)

Counts

4 → 164

Calls

4 calls:

70.0ms	(.f64 (acos.f64 (+.f64 (.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)
47.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
21.0ms	(acos.f64 (+.f64 (.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))))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite17.0ms (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:

6.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
3.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.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)
1.0ms	(acos.f64 (+.f64 (.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))))))

simplify197.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-neg_binary64`
636×	`cancel-sign-sub-inv_binary64`
527×	`associate-r_binary64`
475×	`associate-l_binary64`
329×	`distribute-rgt-neg-in_binary64`

Counts

242 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	283	9323
1	788	7669
2	2620	7537
3	4304	7533
4	5044	7533

prune244.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	160	15	175

Error

3.1b

Counts

175 → 15

Alt Table

Status	Error	Program
	17.7b	(.f64 (acos.f64 (+.f64 (.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)
	17.7b	(.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))))))))
	18.2b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) (.f64 R (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
▶	3.4b	(.f64 (log.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)
	4.3b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.6b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (.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)))))))
	17.6b	(.f64 (exp.f64 (log.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)
	3.5b	(.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)
	28.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.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)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.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)))
	42.1b	(cbrt.f64 (.f64 (.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (.f64 (.f64 R R) R)))
	4.3b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	17.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	30.0b	(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)))
	28.9b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (sqrt.f64 R)) (sqrt.f64 R))
	3.5b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)

Compiler

Compiled 8554 to 2015 computations (76.4% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (.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)
✓	0.3b	(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)))))
✓	0.8b	(log.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))))))
✓	1.1b	(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))))

series79.0ms (0.4%)

Counts

4 → 108

Calls

4 calls:

34.0ms	(.f64 (log.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)
23.0ms	(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)))))
11.0ms	(log.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))))))
10.0ms	(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))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

3.0ms	(.f64 (log.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)
2.0ms	(log.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))))))
1.0ms	(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)))))
0.0ms	(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))))

simplify270.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

174 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	95	7290
1	129	6869
2	252	6869
3	399	6869
4	675	6863
5	1202	6863
6	2999	6863
7	4798	6863
8	5065	6863

prune130.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	89	14	103

Error

3.0b

Counts

103 → 14

Alt Table

Status	Error	Program
	4.3b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	18.5b	(expm1.f64 (log1p.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)))
	17.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	3.5b	(.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 (.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)
	4.1b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.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)))))))) (log.f64 (cbrt.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)
	28.9b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (sqrt.f64 R)) (sqrt.f64 R))
	4.3b	(.f64 (.f64 (log.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)))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	3.6b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (.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)))))))
	4.2b	(.f64 (cbrt.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 R (.f64 (cbrt.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))))) (cbrt.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))))))))
	3.7b	(.f64 (cbrt.f64 (.f64 (.f64 (log.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)))))) (log.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))))))) (log.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)
	42.1b	(cbrt.f64 (.f64 (.f64 (.f64 (log.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)))))) (log.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))))))) (log.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))))))) (.f64 (.f64 R R) R)))
	4.1b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.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)))))) (cbrt.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)))))))) (log.f64 (cbrt.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)
▶	3.5b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)

Compiler

Compiled 5404 to 1005 computations (81.4% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
✓	0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
✓	1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))
✓	27.3b	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series123.0ms (0.6%)

Counts

4 → 156

Calls

4 calls:

70.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
22.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
20.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))
10.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`pow1_binary64`
18×	`pow-prod-down_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`sin-mult_binary64`

Counts

4 → 88

Calls

4 calls:

11.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
6.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
2.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))

simplify225.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-neg_binary64`
564×	`fma-def_binary64`
549×	`*-commutative_binary64`
333×	`distribute-rgt-neg-in_binary64`
298×	`cancel-sign-sub-inv_binary64`

Counts

244 → 160

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	222	9477
1	524	8309
2	1578	7668
3	3453	7640
4	4842	7550
5	5071	7550

prune253.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	160	14	174

Error

3.0b

Counts

174 → 14

Alt Table

Status	Error	Program
	3.6b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (.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 lambda2) (sin.f64 lambda1)))) (.f64 (sin.f64 phi1) (sin.f64 phi2)))))))
	3.5b	(.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 lambda2) (sin.f64 lambda1)))) (.f64 (sin.f64 phi1) (sin.f64 phi2))))) R)
	4.3b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	18.5b	(expm1.f64 (log1p.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)))
	4.1b	(.f64 (log.f64 (.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (cbrt.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)
	4.1b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.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)))))))) (log.f64 (cbrt.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)
	3.6b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (.f64 R (sqrt.f64 (acos.f64 (fma.f64 (.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)))))))
	28.9b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (sqrt.f64 R)) (sqrt.f64 R))
	4.2b	(.f64 (cbrt.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 R (.f64 (cbrt.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))))) (cbrt.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))))))))
	3.7b	(.f64 (cbrt.f64 (.f64 (.f64 (log.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)))))) (log.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))))))) (log.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)
	42.1b	(cbrt.f64 (.f64 (.f64 (.f64 (log.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)))))) (log.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))))))) (log.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))))))) (.f64 (.f64 R R) R)))
	17.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))) R)
	4.1b	(.f64 (+.f64 (log.f64 (.f64 (cbrt.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)))))) (cbrt.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)))))))) (log.f64 (cbrt.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)
	4.3b	(.f64 (.f64 (log.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)))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))

Compiler

Compiled 9131 to 1774 computations (80.6% saved)

regimes4.6s (21.4%)

Accuracy

Total 0.4b remaining (9.7%)

Threshold costs 0.4b (9.7%)

Counts

301 → 1

Compiler

Compiled 142353 to 76576 computations (46.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end378.0ms (1.8%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 1058 to 489 computations (53.8% 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

analyze3.6s (17%)

sample10.4s (48.7%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series84.0ms (0.4%)

rewrite19.0ms (0.1%)

simplify230.0ms (1.1%)

prune185.0ms (0.9%)

localize26.0ms (0.1%)

series148.0ms (0.7%)

rewrite17.0ms (0.1%)

simplify197.0ms (0.9%)

prune244.0ms (1.1%)

localize27.0ms (0.1%)

series79.0ms (0.4%)

rewrite11.0ms (0.1%)

simplify270.0ms (1.3%)

prune130.0ms (0.6%)

localize29.0ms (0.1%)

series123.0ms (0.6%)

rewrite27.0ms (0.1%)

simplify225.0ms (1.1%)

prune253.0ms (1.2%)

regimes4.6s (21.4%)

simplify2.0ms (0%)

end378.0ms (1.8%)

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