Details

analyze2.8s (15.3%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 25 to 15 computations (40% saved)

sample8.4s (46.3%)

Results

6.0s	4643×	body	1024	valid
1.4s	1756×	body	512	valid
384.0ms	745×	body	256	valid
307.0ms	118×	body	2048	valid
250.0ms	994×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

284×	`fma-def_binary64`
141×	`fma-neg_binary64`
44×	`distribute-rgt-in_binary64`
38×	`cancel-sign-sub-inv_binary64`
37×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Status

Error

Program

0.5b

(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))

▶

0.5b

(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 137 to 71 computations (48.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
✓	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	3.9b	(sin.f64 (-.f64 lambda1 lambda2))
✓	4.0b	(cos.f64 (-.f64 lambda1 lambda2))

series55.0ms (0.3%)

Counts

4 → 76

Calls

4 calls:

30.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
16.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite218.0ms (1.2%)

Algorithm

4×	egg-rewrite

Rules

52×	`egg`
50×	`egg`
30×	`egg`
26×	`egg`

Counts

4 → 158

Calls

4 calls:

65.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
53.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
49.0ms	(cos.f64 (-.f64 lambda1 lambda2))
47.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	116	6
2	1576	6
3	5053	6
0	5	6
1	116	6
2	1566	6
3	5003	6
0	11	16
1	249	14
2	3433	14
3	5002	14
0	8	11
1	174	11
2	2249	11
3	6499	11

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

857×	`cancel-sign-sub-inv_binary64`
740×	`fma-def_binary64`
563×	`sub-neg_binary64`
293×	`distribute-rgt-neg-in_binary64`
269×	`distribute-lft-neg-in_binary64`

Counts

234 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1717
1	512	1606
2	1658	1470
3	4218	1466
4	5088	1466

prune363.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	228	11	239
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	11	241

Error

0.4b

Counts

241 → 11

Alt Table

Status	Error	Program
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	1.5b	(+.f64 lambda1 (atan2.f64 (+.f64 (.f64 (cos.f64 phi2) (sin.f64 (neg.f64 lambda2))) (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) lambda1))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log1p.f64 (expm1.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	3.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2)) (/.f64 1 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	6.5b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (/.f64 1 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (-.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi1)) (pow.f64 (cos.f64 phi1) 2))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (pow.f64 (cbrt.f64 (cos.f64 phi2)) 2)) (cbrt.f64 (cos.f64 phi2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	30.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (sin.f64 (-.f64 lambda1 lambda2)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 8225 to 2112 computations (74.3% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.6b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
	3.9b	(sin.f64 (-.f64 lambda1 lambda2))

series78.0ms (0.4%)

Counts

3 → 104

Calls

3 calls:

57.0ms

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

11.0ms

(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

9.0ms

(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite225.0ms (1.2%)

Algorithm

3×	egg-rewrite

Rules

40×	`egg`
35×	`egg`
19×	`egg`

Counts

3 → 94

Calls

3 calls:

78.0ms

(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

78.0ms

(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

66.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	309	14
2	3876	14
3	5011	14
0	6	8
1	123	8
2	1544	8
3	4889	8
4	5061	8
0	19	39
1	399	27
2	4862	27
3	6762	27

simplify139.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
733×	`cancel-sign-sub-inv_binary64`
638×	`associate-r_binary64`
614×	`associate-l_binary64`
207×	`distribute-rgt-neg-in_binary64`

Counts

198 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	3693
1	483	3419
2	1573	3344
3	4226	3342
4	4992	3342
5	4976	3342

prune379.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	208	10	218

Error

0.1b

Counts

218 → 10

Alt Table

Status	Error	Program
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	3.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2)) (/.f64 1 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	30.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (sin.f64 (-.f64 lambda1 lambda2)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.9b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (/.f64 1 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (-.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi1)) (pow.f64 (cos.f64 phi1) 2))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (pow.f64 (cbrt.f64 (cos.f64 phi2)) 2)) (cbrt.f64 (cos.f64 phi2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 8079 to 2029 computations (74.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
	0.6b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series51.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

37.0ms

(*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))

15.0ms

(atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite170.0ms (0.9%)

Algorithm

2×	egg-rewrite

Rules

35×	`egg`
19×	`egg`

Counts

2 → 54

Calls

2 calls:

89.0ms

(*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))

79.0ms

(atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	416	37
2	4766	37
3	6416	37
0	13	23
1	260	21
2	2896	11
3	4828	11
4	5627	11

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-def_binary64`
537×	`distribute-rgt-neg-in_binary64`
503×	`distribute-lft-neg-in_binary64`
484×	`associate-l_binary64`
474×	`associate-r_binary64`

Counts

138 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	3417
1	302	3413
2	974	3372
3	3730	3372
4	5138	3372

prune424.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	206	9	215

Error

0.1b

Counts

215 → 9

Alt Table

Status	Error	Program
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.9b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
	3.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2)) (/.f64 1 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (/.f64 1 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (-.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi1)) (pow.f64 (cos.f64 phi1) 2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (pow.f64 (cbrt.f64 (cos.f64 phi2)) 2)) (cbrt.f64 (cos.f64 phi2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	30.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (sin.f64 (-.f64 lambda1 lambda2)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 8471 to 2053 computations (75.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.6b	(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

series108.0ms (0.6%)

Counts

3 → 84

Calls

3 calls:

58.0ms

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

37.0ms

(*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))

13.0ms

(atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))

rewrite189.0ms (1%)

Algorithm

3×	egg-rewrite

Rules

39×	`egg`
25×	`egg`
19×	`egg`

Counts

3 → 83

Calls

3 calls:

73.0ms

(atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))

57.0ms

(*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))

57.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	279	14
2	3339	14
3	5235	14
0	19	49
1	392	47
2	4733	47
3	5285	47
0	13	23
1	267	11
2	3071	11
3	5729	11

simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

532×	`associate--l+_binary64`
329×	`associate-+r+_binary64`
316×	`associate--r+_binary64`
273×	`fma-neg_binary64`
242×	`distribute-rgt-neg-in_binary64`

Counts

167 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2778
1	577	2679
2	1990	2488
3	5021	2488

prune482.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	189	9	198

Error

0.1b

Counts

198 → 9

Alt Table

Status	Error	Program
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.9b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	0.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
	3.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 2)) (/.f64 1 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (/.f64 1 (fma.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (-.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi1)) (pow.f64 (cos.f64 phi1) 2))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (pow.f64 (cbrt.f64 (cos.f64 phi2)) 2)) (cbrt.f64 (cos.f64 phi2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	30.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (sin.f64 (-.f64 lambda1 lambda2)) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 7542 to 1693 computations (77.6% saved)

regimes3.5s (19.1%)

Accuracy

Total 0.1b remaining (49.3%)

Threshold costs 0.1b (49.3%)

Counts

299 → 1

Compiler

Compiled 67452 to 39826 computations (41% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	54
1	38	54
2	46	54
3	51	54
4	53	54
5	52	54

end216.0ms (1.2%)

Compiler: Compiled 389 to 214 computations (45% saved)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

Details

analyze2.8s (15.3%)

sample8.4s (46.3%)

simplify37.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series55.0ms (0.3%)

rewrite218.0ms (1.2%)

simplify85.0ms (0.5%)

prune363.0ms (2%)

localize26.0ms (0.1%)

series78.0ms (0.4%)

rewrite225.0ms (1.2%)

simplify139.0ms (0.8%)

prune379.0ms (2.1%)

localize24.0ms (0.1%)

series51.0ms (0.3%)

rewrite170.0ms (0.9%)

simplify109.0ms (0.6%)

prune424.0ms (2.3%)

localize23.0ms (0.1%)

series108.0ms (0.6%)

rewrite189.0ms (1%)

simplify76.0ms (0.4%)

prune482.0ms (2.7%)

regimes3.5s (19.1%)

simplify3.0ms (0%)

end216.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30