Details

analyze3.6s (16.6%)

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)

sample10.6s (48.4%)

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Results

8.2s	5835×	body	1024	valid
1.1s	1386×	body	512	valid
798.0ms	269×	body	2048	valid
250.0ms	459×	body	256	valid
94.0ms	307×	body	128	valid
6.0ms	3×	body	1024	invalid

Compiler

Compiled 74 to 53 computations (28.4% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29

Stop Event

1×

saturated

Counts

1 → 2

prune6.0ms (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

18.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
	18.9b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Status

Error

Program

▶

18.9b

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

18.9b

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

Compiler

Compiled 136 to 89 computations (34.6% saved)

localize17.0ms (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 lambda2 lambda1)))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
✓	0.6b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))))
✓	3.1b	(cos.f64 (-.f64 lambda2 lambda1))

series72.0ms (0.3%)

Counts

4 → 164

Calls

4 calls:

34.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))
25.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
9.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))))
4.0ms	(cos.f64 (-.f64 lambda2 lambda1))

rewrite70.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

355×	`log1p-udef_binary64`
195×	`add-sqr-sqrt_binary64`
181×	`log1p-expm1-u_binary64`
181×	`expm1-log1p-u_binary64`
180×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	362	77
2	4849	77

Stop Event

1×	node limit

Counts

4 → 81

Calls

4 calls:

68.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))
68.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1))))) R)
68.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda2 lambda1)))))
68.0ms	(cos.f64 (-.f64 lambda2 lambda1))

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

573×	`cancel-sign-sub-inv_binary64`
568×	`fma-def_binary64`
442×	`*-commutative_binary64`
334×	`sub-neg_binary64`
248×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	4331
1	434	4272
2	1451	4154
3	4577	4154

Stop Event

1×	node limit

Counts

245 → 133

prune184.0ms (0.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	117	16	133
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	119	16	135

Error

3.5b

Counts

135 → 16

Alt Table

Status	Error	Program
	31.5b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
	19.1b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda2 lambda1))) 3)))) R)
	42.2b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 2)
	19.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) 1) R)
	19.5b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 3)
	18.9b	(.f64 (-.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	19.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	19.5b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 3) R)
	18.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda2 lambda1)) 3))))) R)
	19.0b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	19.1b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 2))) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	49.5b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
▶	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
	18.9b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	40.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (neg.f64 (sin.f64 lambda1)) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (-.f64 (.f64 1/6 (pow.f64 lambda2 3)) lambda2)) (.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 phi1)))) -1/2))))) R)

Compiler

Compiled 4654 to 1640 computations (64.8% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
✓	0.2b	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
✓	0.6b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))

series118.0ms (0.5%)

Counts

4 → 180

Calls

4 calls:

66.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
33.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
11.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))
8.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

226×	`add-sqr-sqrt_binary64`
207×	`log1p-expm1-u_binary64`
207×	`expm1-log1p-u_binary64`
206×	`add-log-exp_binary64`
205×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	109
1	427	79

Stop Event

1×	node limit

Counts

4 → 75

Calls

4 calls:

37.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
37.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))) R)
37.0ms	(*.f64 (sin.f64 lambda2) (sin.f64 lambda1))
37.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))

simplify97.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

401×	`fma-neg_binary64`
349×	`associate-r_binary64`
322×	`distribute-rgt-neg-in_binary64`
315×	`associate--l+_binary64`
304×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	6296
1	674	6240
2	2497	6059

Stop Event

1×	node limit

Counts

255 → 132

prune261.0ms (1.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	126	6	132
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	129	19	148

Error

3.5b

Counts

148 → 19

Alt Table

Status	Error	Program
	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))) 1))))) R)
	19.0b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	18.9b	(.f64 (exp.f64 (log.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)))))))) R)
	19.1b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2))))) 2))) R)
▶	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)
	42.2b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 2)
	19.1b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) 1) R)
	19.5b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)) 3)
	18.9b	(.f64 (-.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (log.f64 (pow.f64 (exp.f64 (sin.f64 lambda2)) (sin.f64 lambda1))))))) R)
	40.6b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (fma.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (neg.f64 (sin.f64 lambda1)) (.f64 (cos.f64 phi2) (cos.f64 phi1))) (-.f64 (.f64 1/6 (pow.f64 lambda2 3)) lambda2)) (.f64 (.f64 (.f64 lambda2 lambda2) (.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 phi1)))) -1/2))))) R)
	19.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))) 3))) R)
	19.5b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))))) 3) R)
	31.5b	(expm1.f64 (log1p.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R)))
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	49.5b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))) R) 3))
	19.0b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))) R)
	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
	18.9b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)

Compiler

Compiled 5497 to 2035 computations (63% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
✓	0.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.6b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))

series92.0ms (0.4%)

Counts

4 → 60

Calls

4 calls:

36.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)
35.0ms	(.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
10.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite44.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

222×	`add-sqr-sqrt_binary64`
202×	`add-log-exp_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
201×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	104
1	421	104

Stop Event

1×	node limit

Counts

4 → 73

Calls

4 calls:

42.0ms	(.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
42.0ms	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)
42.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
42.0ms	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary64`
648×	`cancel-sign-sub-inv_binary64`
630×	`associate-l_binary64`
623×	`associate-r_binary64`
211×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	1808
1	386	1780
2	1389	1697

Stop Event

1×	node limit

Counts

133 → 119

prune258.0ms (1.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	105	14	119
Fresh	15	3	18
Picked	1	0	1
Done	0	0	0
Total	121	17	138

Error

3.4b

Counts

138 → 17

Alt Table

Status	Error	Program
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))) R)
	4.0b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) 3)) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
▶	3.8b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))) R)
	4.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) 3)))) R)
	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
	4.6b	(.f64 (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) 3) R)
	18.9b	(.f64 (log.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 (-.f64 lambda2 lambda1)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))) R)
	43.0b	(cbrt.f64 (pow.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R) 3))
	3.9b	(.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))) R)
	4.6b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)) 3)
	4.1b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) 2))) R)
	4.0b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))) 1) R)
	3.8b	(.f64 (-.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	36.6b	(exp.f64 (log.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)))
	34.4b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)) 2)

Compiler

Compiled 5131 to 1877 computations (63.4% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.5b	(expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
✓	0.6b	(log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))
	0.6b	(acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))

series2.1s (9.7%)

Counts

2 → 96

Calls

2 calls:

2.1s

(log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))

30.0ms

(expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

228×	`add-sqr-sqrt_binary64`
210×	`log1p-expm1-u_binary64`
210×	`expm1-log1p-u_binary64`
208×	`add-cbrt-cube_binary64`
208×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	74
1	448	74

Stop Event

1×	node limit

Counts

2 → 48

Calls

2 calls:

37.0ms

(expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))

37.0ms

(log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (*.f64 (cos.f64 phi2) (*.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

122×	`fma-def_binary64`
42×	`*-commutative_binary64`
42×	`associate-l_binary64`
26×	`associate-r_binary64`
10×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	3552
1	47	3552
2	76	3552
3	186	3552
4	330	3552
5	376	3552

Stop Event

1×

saturated

Counts

144 → 51

prune249.0ms (1.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	110	17	127

Error

3.4b

Counts

127 → 17

Alt Table

Status	Error	Program
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
	4.0b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (/.f64 (-.f64 (.f64 (.f64 (PI.f64) 1/2) (.f64 (PI.f64) 1/2)) (.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))) (+.f64 (.f64 (PI.f64) 1/2) (asin.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))))) R)
	3.9b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))) R)
	4.0b	(.f64 (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) 3)) R)
	4.2b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) 3)))) R)
	3.8b	(.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)))))) R)
	4.6b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) (pow.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) 2)) R)
	36.6b	(exp.f64 (log.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)))
	54.8b	(.f64 (-.f64 (log.f64 (-.f64 1 (pow.f64 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) 2))) (log.f64 (-.f64 1 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))) R)
	34.4b	(pow.f64 (sqrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)) 2)
	3.9b	(.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))) (log.f64 (sqrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))) R)
	4.6b	(pow.f64 (cbrt.f64 (.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) R)) 3)
	4.1b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) (cbrt.f64 (pow.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) 2))) R)
	4.4b	(.f64 (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))) R)
	4.0b	(.f64 (-.f64 (exp.f64 (log1p.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))) 1) R)
	3.8b	(.f64 (log.f64 (+.f64 1 (expm1.f64 (acos.f64 (fma.f64 (cos.f64 phi1) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))))) R)
	4.1b	(.f64 (-.f64 (log.f64 (+.f64 1 (pow.f64 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) 2) (expm1.f64 (acos.f64 (fma.f64 (sin.f64 phi1) (sin.f64 phi2) (.f64 (cos.f64 phi2) (.f64 (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))))))) R)

Compiler

Compiled 5066 to 1543 computations (69.5% saved)

regimes3.0s (13.7%)

Accuracy

Total 0.3b remaining (7.9%)

Threshold costs 0.3b (7.9%)

Counts

188 → 1

Compiler

Compiled 63078 to 41512 computations (34.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	25	39

Stop Event

1×

saturated

end640.0ms (2.9%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 1063 to 599 computations (43.7% saved)

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29

Details

analyze3.6s (16.6%)

sample10.6s (48.4%)

simplify11.0ms (0%)

prune6.0ms (0%)

localize17.0ms (0.1%)

series72.0ms (0.3%)

rewrite70.0ms (0.3%)

simplify94.0ms (0.4%)

prune184.0ms (0.8%)

localize22.0ms (0.1%)

series118.0ms (0.5%)

rewrite38.0ms (0.2%)

simplify97.0ms (0.4%)

prune261.0ms (1.2%)

localize24.0ms (0.1%)

series92.0ms (0.4%)

rewrite44.0ms (0.2%)

simplify42.0ms (0.2%)

prune258.0ms (1.2%)

localize28.0ms (0.1%)

series2.1s (9.7%)

rewrite39.0ms (0.2%)

simplify120.0ms (0.6%)

prune249.0ms (1.1%)

regimes3.0s (13.7%)

simplify3.0ms (0%)

end640.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	18	29
1	28	29
2	44	29
3	57	29
4	67	29
5	85	29
6	123	29
7	160	29
8	206	29
9	243	29
10	269	29
11	271	29