Details

analyze4.3s (20.6%)

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)

sample319.0ms (1.5%)

Algorithm

1×

intervals

Results

215.0ms	176×	body	1024	valid
39.0ms	14×	body	2048	valid
26.0ms	39×	body	512	valid
7.0ms	15×	body	256	valid
2.0ms	12×	body	128	valid

Compiler

Compiled 54 to 40 computations (25.9% saved)

simplify13.0ms (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

17.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	17.1b	(.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 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite71.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.6b

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 57

Calls

4 calls:

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

Compiler

Compiled 1588 to 295 computations (81.4% saved)

series118.0ms (0.6%)

Error

16.4b

Counts

4 → 48

Calls

4 calls:

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)
25.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
19.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2568 to 1669 computations (35% saved)

simplify115.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

424×	`sub-neg_binary64`
400×	`unsub-neg_binary64`
382×	`associate-l_binary64`
354×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`

Counts

105 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2635
1	366	2379
2	869	2356
3	2028	2348
4	4073	2348
5	5045	2348

prune59.0ms (0.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	31	13	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	13	45

Error

4.7b

Counts

45 → 13

Alt Table

Status	Error	Program
	41.3b	(.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))
	17.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))) R)
	17.8b	(.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))
▶	4.9b	(.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)
	41.3b	(.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 R)) (.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 R)))
	17.7b	(.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)))
	44.7b	(cbrt.f64 (pow.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) 3))
	17.2b	(.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)
	17.6b	(.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)
	17.3b	(.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)
	17.1b	(.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)
	17.1b	(.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)
	17.2b	(.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))))))))

Compiler

Compiled 2076 to 768 computations (63% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.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)
1.1b	(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))))))

rewrite122.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

Rules

13×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
9×	`associate-r_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
3.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2725 to 392 computations (85.6% saved)

series277.0ms (1.3%)

Error

4.6b

Counts

4 → 61

Calls

4 calls:

115.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
67.0ms	(.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)
35.0ms	(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))))))
23.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 5181 to 2971 computations (42.7% saved)

simplify140.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-r_binary64`
559×	`associate-l_binary64`
336×	`distribute-rgt-neg-in_binary64`
313×	`*-commutative_binary64`
313×	`distribute-lft-neg-in_binary64`

Counts

133 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	339	5820
1	983	5004
2	3435	4802
3	5035	4802

prune120.0ms (0.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	91	15	106
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	103	16	119

Error

4.5b

Counts

119 → 16

Alt Table

Status	Error	Program
	16.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (+.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi2 phi1))) (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) (.f64 2 (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (sin.f64 lambda2) (-.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) R)
	5.7b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	5.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.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 (.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 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
	39.2b	(cbrt.f64 (pow.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))
	5.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.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)
	5.1b	(.f64 (.f64 (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)))))))) (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))))))))) R)
	5.0b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)
	5.6b	(.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)
	17.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))) R)
	4.9b	(.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)
	5.1b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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))))))))))
	5.6b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.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))))))))))
	5.1b	(.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)
	4.9b	(.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)
▶	4.9b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	35.2b	(.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))

Compiler

Compiled 4198 to 1338 computations (68.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.3b	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
1.1b	(acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
29.4b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))

rewrite157.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

Rules

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

Counts

4 → 67

Calls

4 calls:

4.0ms	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
3.0ms	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))
1.0ms	(acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2483 to 655 computations (73.6% saved)

series215.0ms (1%)

Error

4.5b

Counts

4 → 47

Calls

4 calls:

75.0ms	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
50.0ms	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
38.0ms	(acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
23.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))

Compiler

Compiled 3765 to 2361 computations (37.3% saved)

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

516×	`cancel-sign-sub-inv_binary64`
502×	`unswap-sqr_binary64`
446×	`*-commutative_binary64`
303×	`distribute-rgt-neg-in_binary64`
250×	`log-prod_binary64`

Counts

114 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	3891
1	383	3232
2	1177	3173
3	2500	3155
4	4639	3152
5	4948	3152

prune132.0ms (0.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	98	16	114

Error

4.5b

Counts

114 → 16

Alt Table

Status	Error	Program
	16.7b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (/.f64 (.f64 (+.f64 (cos.f64 (-.f64 phi1 phi2)) (cos.f64 (+.f64 phi2 phi1))) (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) (.f64 2 (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (sin.f64 lambda1) (.f64 (sin.f64 lambda2) (-.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))) R)
	5.7b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	5.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.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 (.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 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
	39.2b	(cbrt.f64 (pow.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))
	5.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.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)
	5.1b	(.f64 (.f64 (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)))))))) (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))))))))) R)
	5.0b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)
	5.6b	(.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)
	17.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))) R)
	4.9b	(.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)
	5.1b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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))))))))))
	5.7b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi2) (sin.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))
	5.1b	(.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)
▶	4.9b	(.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)
✓	4.9b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
	35.2b	(.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))

Compiler

Compiled 3521 to 1213 computations (65.5% saved)

localize31.0ms (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 (cos.f64 phi2) (.f64 (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 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
0.6b	(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)))))))))
1.1b	(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)))))))

rewrite109.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

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 (cos.f64 phi2) (.f64 (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 (cos.f64 phi2) (.f64 (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 (cos.f64 phi2) (.f64 (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 (cos.f64 phi2) (.f64 (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)

series478.0ms (2.3%)

Error

4.5b

Counts

4 → 51

Calls

4 calls:

218.0ms	(.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)
156.0ms	(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)))))))))
58.0ms	(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))))))))
40.0ms	(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)))))))

Compiler

Compiled 4051 to 2684 computations (33.7% saved)

simplify283.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

109 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	5909
1	175	4844
2	323	4844
3	450	4844
4	609	4838
5	1085	4838
6	2777	4838
7	4510	4838
8	4933	4838
9	4912	4838

prune70.0ms (0.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	89	16	105

Error

4.5b

Counts

105 → 16

Alt Table

Status	Error	Program
	5.4b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.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 (.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 (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
	39.2b	(cbrt.f64 (pow.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))
	5.0b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (cos.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))) R)
	5.6b	(.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)
	17.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))) R)
	4.9b	(.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)
	35.2b	(.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))
	5.0b	(.f64 (log.f64 (/.f64 (sqrt.f64 (exp.f64 PI.f64)) (exp.f64 (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)
	5.0b	(.f64 (log.f64 (pow.f64 E.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)
	4.9b	(.f64 (exp.f64 (log.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)
	5.1b	(.f64 (sqrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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))))))))))
	5.5b	(.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)
	5.7b	(.f64 (.f64 (cbrt.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) (.f64 R (cbrt.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi2) (sin.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))))
	5.7b	(.f64 (.f64 (cbrt.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)) (cbrt.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))) (cbrt.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)))
	5.1b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.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)
	4.9b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)

Compiler

Compiled 2173 to 557 computations (74.4% saved)

regimes3.9s (18.2%)

Accuracy

Total 0.3b remaining (9%)

Threshold costs 0.3b (9%)

Compiler

Compiled 106390 to 59399 computations (44.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	53
1	35	53
2	35	53

end35.0ms (0.2%)

Compiler: Compiled 185 to 120 computations (35.1% saved)

sample9.8s (46.5%)

Algorithm

1×

intervals

Results

6.5s	5467×	body	1024	valid
943.0ms	1441×	body	512	valid
754.0ms	274×	body	2048	valid
213.0ms	507×	body	256	valid
64.0ms	311×	body	128	valid
5.0ms	3×	body	1024	invalid
1.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 857 to 466 computations (45.6% 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

analyze4.3s (20.6%)

sample319.0ms (1.5%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize20.0ms (0.1%)

rewrite71.0ms (0.3%)

series118.0ms (0.6%)

simplify115.0ms (0.5%)

prune59.0ms (0.3%)

localize26.0ms (0.1%)

rewrite122.0ms (0.6%)

series277.0ms (1.3%)

simplify140.0ms (0.7%)

prune120.0ms (0.6%)

localize34.0ms (0.2%)

rewrite157.0ms (0.7%)

series215.0ms (1%)

simplify142.0ms (0.7%)

prune132.0ms (0.6%)

localize31.0ms (0.1%)

rewrite109.0ms (0.5%)

series478.0ms (2.3%)

simplify283.0ms (1.3%)

prune70.0ms (0.3%)

regimes3.9s (18.2%)

simplify4.0ms (0%)

end35.0ms (0.2%)

sample9.8s (46.5%)

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