Details

analyze4.6s (23.2%)

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)

sample309.0ms (1.5%)

Algorithm

1×

intervals

Results

214.0ms	180×	body	1024	valid
27.0ms	10×	body	2048	valid
26.0ms	40×	body	512	valid
6.0ms	14×	body	256	valid
4.0ms	12×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`*-commutative_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	15.6b	(.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 48 to 34 computations (29.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite75.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.0ms	(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)))))

Compiler

Compiled 1696 to 307 computations (81.9% saved)

series165.0ms (0.8%)

Error

14.7b

Counts

4 → 59

Calls

4 calls:

60.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
45.0ms	(.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)
24.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3428 to 2103 computations (38.7% saved)

simplify200.0ms (1%)

Algorithm

1×	egg-herbie

Rules

446×	`distribute-rgt-neg-in_binary64`
399×	`distribute-lft-neg-in_binary64`
369×	`neg-mul-1_binary64`
359×	`cancel-sign-sub-inv_binary64`
270×	`associate-r_binary64`

Counts

118 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	3337
1	502	3030
2	1495	2930
3	2621	2908
4	4808	2908
5	4998	2908
6	4996	2908
7	4967	2908

prune75.0ms (0.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	47	15	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	15	63

Error

3.5b

Counts

63 → 15

Alt Table

Status	Error	Program
	15.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	16.3b	(.f64 (.f64 (acos.f64 (+.f64 (.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))
	3.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
▶	3.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	15.9b	(.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 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))))
	15.8b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) 3)) R)
	15.6b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	15.7b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) R)
	42.3b	(.f64 (.f64 (acos.f64 (+.f64 (.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))
	15.6b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) R)
	16.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	16.3b	(.f64 (.f64 (cbrt.f64 (.f64 (acos.f64 (+.f64 (.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 (+.f64 (.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 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	43.2b	(exp.f64 (log.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) R)))
	15.9b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	16.3b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)

Compiler

Compiled 2597 to 940 computations (63.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite117.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

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 → 70

Calls

4 calls:

6.0ms	(.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
4.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 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)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2879 to 360 computations (87.5% saved)

series229.0ms (1.1%)

Error

3.5b

Counts

4 → 53

Calls

4 calls:

73.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
73.0ms	(.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
35.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
22.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4561 to 2648 computations (41.9% saved)

simplify213.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

324×	`associate-l_binary64`
319×	`associate-r_binary64`
310×	`sub-neg_binary64`
274×	`cancel-sign-sub-inv_binary64`
246×	`distribute-rgt-neg-in_binary64`

Counts

123 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	4734
1	539	3630
2	1551	3575
3	2418	3555
4	4026	3555
5	4926	3555
6	4993	3555
7	4902	3555

prune88.0ms (0.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	99	13	112

Error

3.4b

Counts

112 → 13

Alt Table

Status	Error	Program
	3.7b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (+.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)
▶	3.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)
	15.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	35.4b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	15.9b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	3.9b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) 3)) R)
	3.7b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
	3.8b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
	4.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.0b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	16.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	34.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	4.5b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)

Compiler

Compiled 3142 to 954 computations (69.6% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (sin.f64 lambda2))))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))

rewrite101.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
13×	`add-sqr-sqrt_binary64`
9×	`associate-l_binary64`

Counts

4 → 66

Calls

4 calls:

7.0ms	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))

Compiler

Compiled 2712 to 327 computations (87.9% saved)

series222.0ms (1.1%)

Error

3.4b

Counts

4 → 53

Calls

4 calls:

72.0ms	(.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (sin.f64 lambda2))))
70.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)
37.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 phi1) (sin.f64 lambda2)))))))
23.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4561 to 2664 computations (41.6% saved)

simplify178.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

452×	`cancel-sign-sub-inv_binary64`
335×	`associate-r_binary64`
292×	`associate-l_binary64`
284×	`sub-neg_binary64`
251×	`neg-mul-1_binary64`

Counts

119 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	4599
1	512	4082
2	1524	3477
3	2292	3457
4	3677	3457
5	4896	3457
6	4955	3457

prune77.0ms (0.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	85	13	98

Error

3.4b

Counts

98 → 13

Alt Table

Status	Error	Program
	3.7b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (+.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)
✓	3.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)
	15.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	35.4b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	15.9b	(.f64 (.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))))) (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	3.9b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) 3)) R)
	3.8b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
	4.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.0b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	16.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	34.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
▶	3.7b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
	4.5b	(.f64 (.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)

Compiler

Compiled 2828 to 882 computations (68.8% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
0.9b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.4b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))

rewrite89.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

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 → 58

Calls

4 calls:

4.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
2.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))

Compiler

Compiled 2589 to 212 computations (91.8% saved)

series472.0ms (2.4%)

Error

3.4b

Counts

4 → 51

Calls

4 calls:

225.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
152.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
56.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
36.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))

Compiler

Compiled 4051 to 2684 computations (33.7% saved)

simplify290.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
385×	`associate-/r/_binary64`
373×	`log-prod_binary64`
336×	`unswap-sqr_binary64`
307×	`distribute-rgt-out_binary64`

Counts

109 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	5909
1	175	4844
2	340	4844
3	446	4844
4	609	4838
5	1085	4838
6	2777	4838
7	4510	4838
8	4933	4838
9	4912	4838

prune61.0ms (0.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	96	15	111

Error

3.3b

Counts

111 → 15

Alt Table

Status	Error	Program
	3.8b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) R)
	3.9b	(.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) 3))) R)
	3.7b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (+.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)
	3.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (sin.f64 lambda2))))))) R)
	15.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))))) R)
	35.4b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (sqrt.f64 R)) (sqrt.f64 R))
	4.6b	(.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) (.f64 (cbrt.f64 R) (cbrt.f64 R))) (cbrt.f64 R))
	4.5b	(.f64 (log.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
	4.0b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (.f64 R (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	4.4b	(.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) R)
	4.4b	(.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) (cbrt.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))) R)
	16.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))) (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (cos.f64 phi1))))))) R)
	34.8b	(.f64 (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)) (sqrt.f64 (.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)))
	4.5b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) (cbrt.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))))
	3.9b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) 3)) R)

Compiler

Compiled 2750 to 565 computations (79.5% saved)

regimes2.8s (14%)

Accuracy

Total 0.3b remaining (8.9%)

Threshold costs 0.3b (8.9%)

Compiler

Compiled 82749 to 46756 computations (43.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	53
1	33	53
2	33	53

end23.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 185 to 115 computations (37.8% saved)

sample9.5s (47.3%)

Algorithm

1×

intervals

Results

6.7s	5502×	body	1024	valid
935.0ms	1412×	body	512	valid
748.0ms	271×	body	2048	valid
220.0ms	499×	body	256	valid
78.0ms	316×	body	128	valid
5.0ms	4×	body	1024	invalid

Compiler

Compiled 858 to 438 computations (49% saved)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Details

analyze4.6s (23.2%)

sample309.0ms (1.5%)

simplify14.0ms (0.1%)

prune2.0ms (0%)

localize20.0ms (0.1%)

rewrite75.0ms (0.4%)

series165.0ms (0.8%)

simplify200.0ms (1%)

prune75.0ms (0.4%)

localize28.0ms (0.1%)

rewrite117.0ms (0.6%)

series229.0ms (1.1%)

simplify213.0ms (1.1%)

prune88.0ms (0.4%)

localize29.0ms (0.1%)

rewrite101.0ms (0.5%)

series222.0ms (1.1%)

simplify178.0ms (0.9%)

prune77.0ms (0.4%)

localize30.0ms (0.1%)

rewrite89.0ms (0.4%)

series472.0ms (2.4%)

simplify290.0ms (1.5%)

prune61.0ms (0.3%)

regimes2.8s (14%)

simplify4.0ms (0%)

end23.0ms (0.1%)

sample9.5s (47.3%)

Profiling

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31