Details

analyze3.7s (18.1%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 29 to 18 computations (37.9% saved)

sample12.0s (59.4%)

Results

9.2s	5472×	body	1024	valid
1.3s	1324×	body	512	valid
741.0ms	203×	body	2048	valid
342.0ms	438×	body	256	valid
249.0ms	819×	body	128	valid

Compiler

Compiled 86 to 53 computations (38.4% saved)

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary64`
194×	`fma-neg_binary64`
83×	`cancel-sign-sub-inv_binary64`
59×	`distribute-rgt-neg-in_binary64`
47×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

13.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 108 to 55 computations (49.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	5.1b	(sin.f64 (-.f64 lambda1 lambda2))
✓	5.1b	(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms (0.2%)

Counts

4 → 88

Calls

4 calls:

34.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
8.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite61.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

315×	`expm1-udef_binary64`
315×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	321	36
2	4161	36
3	5098	36

Stop Event

1×	node limit

Counts

4 → 86

Calls

4 calls:

59.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
59.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
59.0ms	(sin.f64 (-.f64 lambda1 lambda2))
59.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify70.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

866×	`cancel-sign-sub-inv_binary64`
560×	`sub-neg_binary64`
358×	`distribute-rgt-neg-in_binary64`
356×	`fma-neg_binary64`
336×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	1845
1	574	1774
2	1893	1605
3	4137	1597
4	5132	1597

Stop Event

1×	node limit

Counts

174 → 163

prune317.0ms (1.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	144	19	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	19	164

Error

6.9b

Counts

164 → 19

Alt Table

Status	Error	Program
	13.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	7.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.3b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.5b	(atan2.f64 (.f64 (-.f64 (sin.f64 lambda1) (.f64 lambda2 (cos.f64 lambda1))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	27.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (cos.f64 lambda2) (.f64 lambda1 (-.f64 (.f64 (*.f64 (cos.f64 lambda2) 1/2) lambda1) (sin.f64 lambda2)))))))
	13.2b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))))
	25.4b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (.f64 (.f64 lambda1 lambda1) (-.f64 (.f64 1/2 (sin.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) 1/6) lambda1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.2b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)))
	13.4b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	25.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)) (.f64 1/2 (.f64 (cos.f64 lambda1) (*.f64 lambda2 lambda2)))))))
	13.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	26.6b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	42.1b	(atan2.f64 (.f64 (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	43.0b	(atan2.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) 1/3) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	9.9b	(atan2.f64 (.f64 (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.7b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.6b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))))

Compiler

Compiled 6762 to 2065 computations (69.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	5.1b	(cos.f64 (-.f64 lambda1 lambda2))

series10.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

10.0ms

(*.f64 (sin.f64 phi1) (cos.f64 phi2))

rewrite59.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

608×	`log1p-expm1-u_binary64`
608×	`expm1-log1p-u_binary64`
299×	`prod-diff_binary64`
131×	`fma-def_binary64`
120×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	123	8
2	1536	8
3	4952	8
4	5064	8

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

59.0ms

(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

612×	`cancel-sign-sub-inv_binary64`
589×	`distribute-rgt-neg-in_binary64`
488×	`fma-neg_binary64`
468×	`sub-neg_binary64`
460×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	196
1	135	176
2	386	154
3	1211	147
4	2622	143
5	4490	143
6	4966	143
7	4911	143

Stop Event

1×	node limit

Counts

26 → 32

prune322.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	147	9	156
Fresh	14	4	18
Picked	1	0	1
Done	0	0	0
Total	162	13	175

Error

0.0b

Counts

175 → 13

Alt Table

Status	Error	Program
	7.5b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	42.1b	(atan2.f64 (.f64 (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	35.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.4b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.4b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) 3)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.8b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (cos.f64 phi2))) (cos.f64 (-.f64 lambda1 lambda2)))))
	26.6b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	8.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.4b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	43.0b	(atan2.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) 1/3) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 7185 to 1895 computations (73.6% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series74.0ms (0.4%)

Counts

2 → 56

Calls

2 calls:

65.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
8.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite54.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

698×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`
148×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	306	24
2	3817	24
3	5180	24

Stop Event

1×	node limit

Counts

2 → 39

Calls

2 calls:

54.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
54.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

413×	`fma-neg_binary64`
372×	`associate-r_binary64`
320×	`associate--l+_binary64`
315×	`distribute-rgt-neg-in_binary64`
297×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2127
1	643	2042
2	2268	1864
3	5012	1864

Stop Event

1×	node limit

Counts

95 → 88

prune326.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	154	11	165

Error

0.0b

Counts

165 → 11

Alt Table

Status	Error	Program
	7.5b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	43.0b	(atan2.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) 1/3) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	26.6b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	8.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	42.1b	(atan2.f64 (.f64 (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.6b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (cos.f64 phi2))) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) 3)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	13.4b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 7924 to 2056 computations (74.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
✓	0.2b	(log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series9.0ms (0%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

rewrite60.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

589×	`expm1-log1p-u_binary64`
588×	`log1p-expm1-u_binary64`
324×	`log-prod_binary64`
140×	`prod-diff_binary64`
124×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	135	8
2	1531	8
3	4940	8
4	5009	8

Stop Event

1×	node limit

Counts

1 → 34

Calls

1 calls:

60.0ms

(log1p.f64 (expm1.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

624×	`cancel-sign-sub-inv_binary64`
531×	`distribute-rgt-neg-in_binary64`
518×	`fma-neg_binary64`
456×	`sub-neg_binary64`
453×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	324
1	135	298
2	391	273
3	1219	269
4	2725	269
5	4517	269
6	4968	269
7	4907	269

Stop Event

1×	node limit

Counts

58 → 49

prune311.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	169	11	180

Error

0.0b

Counts

180 → 11

Alt Table

Status	Error	Program
	7.5b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	43.0b	(atan2.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) 1/3) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	26.6b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	8.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	42.1b	(atan2.f64 (.f64 (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.6b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 phi1)) (cos.f64 phi2))) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) 3)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	13.4b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 8492 to 1908 computations (77.5% saved)

regimes2.2s (10.9%)

Accuracy

Total 0.1b remaining (54.6%)

Threshold costs 0.1b (54.6%)

Counts

204 → 1

Compiler

Compiled 48276 to 30010 computations (37.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
10×	`+-commutative_binary64`
10×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	61
1	46	61
2	69	61
3	85	61
4	97	61
5	101	61
6	100	61

Stop Event

1×

saturated

end305.0ms (1.5%)

Compiler: Compiled 513 to 309 computations (39.8% saved)

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Details

analyze3.7s (18.1%)

sample12.0s (59.4%)

simplify26.0ms (0.1%)

prune3.0ms (0%)

localize18.0ms (0.1%)

series51.0ms (0.2%)

rewrite61.0ms (0.3%)

simplify70.0ms (0.3%)

prune317.0ms (1.6%)

localize26.0ms (0.1%)

series10.0ms (0.1%)

rewrite59.0ms (0.3%)

simplify67.0ms (0.3%)

prune322.0ms (1.6%)

localize27.0ms (0.1%)

series74.0ms (0.4%)

rewrite54.0ms (0.3%)

simplify56.0ms (0.3%)

prune326.0ms (1.6%)

localize29.0ms (0.1%)

series9.0ms (0%)

rewrite60.0ms (0.3%)

simplify69.0ms (0.3%)

prune311.0ms (1.5%)

regimes2.2s (10.9%)

simplify4.0ms (0%)

end305.0ms (1.5%)

Profiling

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39