Details

analyze2.8s (17.8%)

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)

sample7.9s (51.3%)

Alt Table

Status	Error	Program
▶	0.8b	(+.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))))))

Results

5.6s	4648×	body	1024	valid
1.2s	1742×	body	512	valid
375.0ms	139×	body	2048	valid
351.0ms	742×	body	256	valid
244.0ms	985×	body	128	valid

Compiler

Compiled 122 to 72 computations (41% saved)

localize17.0ms (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) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	4.1b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.4b	(sin.f64 (-.f64 lambda1 lambda2))

series48.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

30.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
9.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite73.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

307×	`expm1-udef_binary64`
307×	`log1p-udef_binary64`
168×	`add-sqr-sqrt_binary64`
159×	`log1p-expm1-u_binary64`
159×	`expm1-log1p-u_binary64`

Counts

4 → 106

Calls

4 calls:

70.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
70.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
70.0ms	(cos.f64 (-.f64 lambda1 lambda2))
70.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	310	53
2	4173	53
3	5090	53
0	0	0
1	0	0

prune292.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	204	14	218
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	14	219

Error

0.6b

Counts

219 → 14

Alt Table

Status	Error	Program
	32.0b	(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3) 1/3))
▶	0.7b	(+.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) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	5.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2))))
	29.6b	(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	2.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 1 (/.f64 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2))))))
	17.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2)))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3)))
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (.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))))))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 2) (cbrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 phi1)) 2) (cbrt.f64 (cos.f64 phi1)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))

Compiler

Compiled 6444 to 1449 computations (77.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
✓	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	4.1b	(cos.f64 (-.f64 lambda1 lambda2))

series54.0ms (0.3%)

Counts

4 → 128

Calls

4 calls:

28.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
13.0ms	(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) (cos.f64 (-.f64 lambda1 lambda2)))))
9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite73.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`prod-diff_binary64`
227×	`add-sqr-sqrt_binary64`
212×	`log1p-expm1-u_binary64`
212×	`expm1-log1p-u_binary64`
207×	`add-cbrt-cube_binary64`

Counts

4 → 90

Calls

4 calls:

70.0ms	(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) (cos.f64 (-.f64 lambda1 lambda2)))))
70.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
70.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
70.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	71
1	428	65
2	4700	65
3	5246	65
0	0	0
1	0	0

prune582.0ms (3.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	0	13	13
Picked	1	0	1
Done	0	0	0
Total	217	15	232

Error

0.1b

Counts

232 → 15

Alt Table

Status	Error	Program
	29.6b	(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
▶	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)))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	5.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3)))
	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))))) (-.f64 (+.f64 (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (*.f64 (sin.f64 (neg.f64 lambda2)) lambda1)))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2))))
	32.0b	(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3) 1/3))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	2.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 1 (/.f64 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2))))))
	17.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2)))
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (.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))))))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 2) (cbrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 phi1)) 2) (cbrt.f64 (cos.f64 phi1)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))

Compiler

Compiled 7873 to 1529 computations (80.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series92.0ms (0.6%)

Counts

4 → 128

Calls

4 calls:

59.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.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))))))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite88.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

830×	`prod-diff_binary64`
218×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`

Counts

4 → 94

Calls

4 calls:

85.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
85.0ms	(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))))))
85.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
85.0ms	(+.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	20	93
1	416	67
2	4766	67
3	6416	67
0	0	0
1	0	0

prune624.0ms (4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	218	4	222
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	221	16	237

Error

0.1b

Counts

237 → 16

Alt Table

Status	Error	Program
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	5.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	17.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2)))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (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)))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2))))
▶	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (expm1.f64 (log1p.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)))))))
	29.6b	(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
	32.0b	(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3) 1/3))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	2.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 1 (/.f64 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3)))
	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))))) (+.f64 (.f64 (cos.f64 phi2) (cos.f64 lambda2)) (+.f64 (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) lambda1)) (cos.f64 phi1)))))
	7.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 1)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 2) (cbrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 phi1)) 2) (cbrt.f64 (cos.f64 phi1)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))

Compiler

Compiled 9186 to 1702 computations (81.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (expm1.f64 (log1p.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))
✓	0.3b	(log1p.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
✓	0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series484.0ms (3.1%)

Counts

4 → 128

Calls

4 calls:

401.0ms	(log1p.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
59.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
14.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (expm1.f64 (log1p.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))))))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite77.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

522×	`prod-diff_binary64`
224×	`add-sqr-sqrt_binary64`
209×	`expm1-log1p-u_binary64`
208×	`log1p-expm1-u_binary64`
203×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

74.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (expm1.f64 (log1p.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))))))
74.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
74.0ms	(log1p.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))
74.0ms	(+.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	22	95
1	431	69
2	4681	69
3	5670	69
0	0	0
1	0	0

prune572.0ms (3.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	214	15	229

Error

0.1b

Counts

229 → 15

Alt Table

Status	Error	Program
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
	5.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	17.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2)))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (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)))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 2))))
	29.6b	(+.f64 lambda1 (pow.f64 (sqrt.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 2))
	32.0b	(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3) 1/3))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	2.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 1 (/.f64 (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) 3)))
	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))))) (+.f64 (.f64 (cos.f64 phi2) (cos.f64 lambda2)) (+.f64 (.f64 (cos.f64 phi2) (*.f64 (sin.f64 lambda2) lambda1)) (cos.f64 phi1)))))
	7.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 1)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 2) (cbrt.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 phi1)) 2) (cbrt.f64 (cos.f64 phi1)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))

Compiler

Compiled 8770 to 1600 computations (81.8% saved)

regimes1.3s (8.7%)

Accuracy

Total 0.5b remaining (82.2%)

Threshold costs 0.5b (82.2%)

Counts

140 → 1

Compiler

Compiled 33124 to 19267 computations (41.8% 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	21	52
1	35	52
2	43	52
3	48	52
4	50	52
5	50	52

end293.0ms (1.9%)

Compiler: Compiled 544 to 313 computations (42.5% saved)

Details

analyze2.8s (17.8%)

sample7.9s (51.3%)

localize17.0ms (0.1%)

series48.0ms (0.3%)

rewrite73.0ms (0.5%)

prune292.0ms (1.9%)

localize23.0ms (0.1%)

series54.0ms (0.3%)

rewrite73.0ms (0.5%)

prune582.0ms (3.8%)

localize24.0ms (0.2%)

series92.0ms (0.6%)

rewrite88.0ms (0.6%)

prune624.0ms (4%)

localize26.0ms (0.2%)

series484.0ms (3.1%)

rewrite77.0ms (0.5%)

prune572.0ms (3.7%)

regimes1.3s (8.7%)

simplify3.0ms (0%)

end293.0ms (1.9%)

Profiling