Details

analyze3.0s (11.4%)

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)

sample9.7s (36.8%)

Results

6.9s	4660×	body	1024	valid
1.5s	1776×	body	512	valid
415.0ms	739×	body	256	valid
408.0ms	132×	body	2048	valid
283.0ms	949×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify43.0ms (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

prune7.0ms (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

0.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(+.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))))
	0.7b	(+.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

▶

0.6b

(+.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))))

0.7b

(+.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)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
✓	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓	2.9b	(cos.f64 (-.f64 lambda1 lambda2))
✓	3.1b	(sin.f64 (-.f64 lambda1 lambda2))

series102.0ms (0.4%)

Counts

4 → 76

Calls

4 calls:

57.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
30.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
7.0ms	(cos.f64 (-.f64 lambda1 lambda2))
7.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite112.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

671×	`prod-diff_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`

Counts

4 → 115

Calls

4 calls:

105.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
104.0ms	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
104.0ms	(cos.f64 (-.f64 lambda1 lambda2))
104.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	255	37
2	3243	37
3	5281	37
0	0	0
1	0	0

simplify119.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

191 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1717
1	512	1597
2	1659	1465
3	4225	1461
4	5096	1461

prune554.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	186	11	197
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	188	11	199

Error

0.5b

Counts

199 → 11

Alt Table

Status	Error	Program
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3) (pow.f64 (cos.f64 phi1) 3)) (+.f64 (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (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 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
	0.8b	(+.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))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (cos.f64 phi1))))
	5.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (/.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))))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
▶	0.6b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.2b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	6.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.7b	(+.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))))
	17.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))

Compiler

Compiled 6885 to 1815 computations (73.6% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
	2.9b	(cos.f64 (-.f64 lambda1 lambda2))
	3.1b	(sin.f64 (-.f64 lambda1 lambda2))

series1.6s (6%)

Counts

1 → 36

Calls

1 calls:

1.6s	(log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))

rewrite78.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

958×	`prod-diff_binary64`
198×	`expm1-udef_binary64`
198×	`log1p-udef_binary64`
108×	`add-sqr-sqrt_binary64`
104×	`expm1-log1p-u_binary64`

Counts

1 → 16

Calls

1 calls:

77.0ms

(log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	199	13
2	2630	13
3	5061	13
0	0	0
1	0	0

simplify86.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

737×	`associate-/r*_binary64`
288×	`fma-def_binary64`
265×	`associate-/r/_binary64`
223×	`unswap-sqr_binary64`
161×	`associate-r_binary64`

Counts

52 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1391
1	492	1365
2	1946	1344
3	5214	1344

prune838.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	201	11	212

Error

0.4b

Counts

212 → 11

Alt Table

Status	Error	Program
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3) (pow.f64 (cos.f64 phi1) 3)) (+.f64 (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.2b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	22.2b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (-.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) 1)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.7b	(+.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))))
	0.9b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (fma.f64 (/.f64 (cos.f64 phi2) (fma.f64 (cos.f64 phi2) (sin.f64 (neg.f64 lambda2)) 1)) (.f64 (cos.f64 lambda2) lambda1) (log1p.f64 (.f64 (cos.f64 phi2) (sin.f64 (neg.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (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 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
▶	0.6b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	6.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	17.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))

Compiler

Compiled 8252 to 2458 computations (70.2% saved)

localize54.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))))
✓	0.3b	(log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))
	0.6b	(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
	2.9b	(cos.f64 (-.f64 lambda1 lambda2))

series3.0s (11.4%)

Counts

2 → 72

Calls

2 calls:

2.9s

(log1p.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))

75.0ms

(expm1.f64 (log1p.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))))

rewrite76.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

680×	`prod-diff_binary64`
242×	`expm1-udef_binary64`
242×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
132×	`expm1-log1p-u_binary64`

Counts

2 → 50

Calls

2 calls:

73.0ms

(expm1.f64 (log1p.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))))

73.0ms

(log1p.f64 (*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	279	44
2	3087	44
3	5011	44
0	0	0
1	0	0

simplify175.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

416×	`unswap-sqr_binary64`
403×	`associate-r_binary64`
268×	`associate-l_binary64`
240×	`times-frac_binary64`
221×	`fma-def_binary64`

Counts

122 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	288	4143
1	979	3844
2	4197	3844
3	5623	3844

prune809.0ms (3.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	200	10	210

Error

0.0b

Counts

210 → 10

Alt Table

Status	Error	Program
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3) (pow.f64 (cos.f64 phi1) 3)) (+.f64 (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.2b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	22.2b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (-.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) 1)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (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 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	0.6b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))) (fma.f64 (cos.f64 phi2) (-.f64 (cos.f64 lambda2) (.f64 lambda1 (-.f64 (.f64 (*.f64 (cos.f64 lambda2) 1/2) lambda1) (sin.f64 lambda2)))) (cos.f64 phi1))))
	6.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	0.7b	(+.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))))
	17.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))

Compiler

Compiled 10131 to 3008 computations (70.3% saved)

localize51.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
	0.3b	(log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))
✓	0.6b	(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

series141.0ms (0.5%)

Counts

2 → 56

Calls

2 calls:

121.0ms	(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
19.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite73.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`prod-diff_binary64`
266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
135×	`log1p-expm1-u_binary64`

Counts

2 → 43

Calls

2 calls:

71.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
71.0ms	(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	279	22
2	3338	22
3	5235	22
0	0	0
1	0	0

simplify116.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-def_binary64`
731×	`cancel-sign-sub-inv_binary64`
728×	`fma-neg_binary64`
637×	`associate-r_binary64`
614×	`associate-l_binary64`

Counts

99 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	1917
1	470	1823
2	1559	1624
3	4861	1620
4	5390	1620

prune722.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	195	10	205

Error

0.0b

Counts

205 → 10

Alt Table

Status	Error	Program
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3) (pow.f64 (cos.f64 phi1) 3)) (+.f64 (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (-.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	5.2b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) (pow.f64 (cos.f64 phi2) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	22.2b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (-.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) 1)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
	0.7b	(+.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))))
	0.3b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda2) lambda1)) (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 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
	6.7b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
	17.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))

Compiler

Compiled 10682 to 2970 computations (72.2% saved)

regimes4.4s (16.7%)

Accuracy

Total 0.1b remaining (50.1%)

Threshold costs 0.1b (50.1%)

Counts

221 → 1

Compiler

Compiled 47733 to 28920 computations (39.4% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	30	52
2	40	52
3	46	52
4	50	52
5	51	52
6	51	52

end438.0ms (1.7%)

Compiler: Compiled 404 to 222 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

analyze3.0s (11.4%)

sample9.7s (36.8%)

simplify43.0ms (0.2%)

prune7.0ms (0%)

localize28.0ms (0.1%)

series102.0ms (0.4%)

rewrite112.0ms (0.4%)

simplify119.0ms (0.5%)

prune554.0ms (2.1%)

localize34.0ms (0.1%)

series1.6s (6%)

rewrite78.0ms (0.3%)

simplify86.0ms (0.3%)

prune838.0ms (3.2%)

localize54.0ms (0.2%)

series3.0s (11.4%)

rewrite76.0ms (0.3%)

simplify175.0ms (0.7%)

prune809.0ms (3.1%)

localize51.0ms (0.2%)

series141.0ms (0.5%)

rewrite73.0ms (0.3%)

simplify116.0ms (0.4%)

prune722.0ms (2.7%)

regimes4.4s (16.7%)

simplify11.0ms (0%)

end438.0ms (1.7%)

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