Details

analyze2.7s (16.8%)

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)

sample7.7s (47.9%)

Results

5.5s	4587×	body	1024	valid
1.2s	1791×	body	512	valid
342.0ms	755×	body	256	valid
330.0ms	125×	body	2048	valid
253.0ms	998×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify40.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1003×	`fma-def_binary64`
487×	`rules-43_binary64`
481×	`rules-42_binary64`
476×	`rules-41_binary64`
471×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	84	30
2	237	30
3	751	23
4	1652	23
5	8	23

prune2.0ms (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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	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 87 to 52 computations (40.2% saved)

localize15.0ms (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))))
✓	4.2b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.2b	(sin.f64 (-.f64 lambda1 lambda2))

series46.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

27.0ms	(+.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)))))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite94.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

302×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
152×	`add-cbrt-cube_binary64`

Counts

4 → 149

Calls

4 calls:

90.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
90.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
90.0ms	(cos.f64 (-.f64 lambda1 lambda2))
90.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	348	53
2	4909	53
3	5374	53
0	0	0
1	0	0

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

424×	`rules-21_binary64`
408×	`fma-neg_binary64`
339×	`rules-14-rev_binary64`
323×	`rules-7-rev_binary64`
254×	`rules-20_binary64`

Counts

261 → 211

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	2746
1	919	2521
2	4419	2521
3	5214	2521

prune339.0ms (2.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	197	14	211
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	198	14	212

Error

0.3b

Counts

212 → 14

Alt Table

Status	Error	Program
	12.3b	(+.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)))
	4.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 1)))
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.0b	(+.f64 lambda1 (log.f64 (exp.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))))))
	0.6b	(+.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))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 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))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (/.f64 (cos.f64 phi1) (cos.f64 phi2))))))
	10.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2)))))) (+.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)))))))
	1.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2))) (.f64 1/2 (.f64 (sin.f64 (neg.f64 lambda2)) (.f64 lambda1 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))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
	0.9b	(+.f64 lambda1 (pow.f64 (cbrt.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))
	4.9b	(+.f64 lambda1 (/.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) (+.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))) 2) (+.f64 0 (.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))) 0)))))

Compiler

Compiled 6914 to 1963 computations (71.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))
✓	0.2b	(/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2))
	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
	4.2b	(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))
21.0ms	(/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2))

rewrite76.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

624×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
204×	`log-div_binary64`
194×	`log-pow_binary64`

Counts

2 → 92

Calls

2 calls:

74.0ms	(.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))
74.0ms	(/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	262	31
2	3575	14
3	5868	14
0	0	0
1	0	0

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

729×	`rules-21_binary64`
651×	`rules-40_binary64`
651×	`rules-41_binary64`
651×	`rules-42_binary64`
651×	`rules-43_binary64`

Counts

140 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	896
1	554	882
2	2519	882
3	4794	882
4	5183	882

prune542.0ms (3.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	253	3	256
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	258	12	270

Error

0.0b

Counts

270 → 12

Alt Table

Status	Error	Program
	12.3b	(+.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)))
	4.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 1)))
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.0b	(+.f64 lambda1 (log.f64 (exp.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))))))
	0.6b	(+.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))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (/.f64 (cos.f64 phi1) (cos.f64 phi2))) (cos.f64 phi2))))
	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 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
	0.9b	(+.f64 lambda1 (pow.f64 (cbrt.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))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	4.9b	(+.f64 lambda1 (/.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) (+.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))) 2) (+.f64 0 (.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))) 0)))))
	10.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2)))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 9909 to 2442 computations (75.4% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (+.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 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))
	0.2b	(/.f64 (*.f64 (cos.f64 lambda2) (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)))))

series139.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

123.0ms

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

rewrite90.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

234×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
213×	`add-cbrt-cube_binary64`
213×	`add-exp-log_binary64`

Counts

2 → 52

Calls

2 calls:

89.0ms

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

88.0ms

(+.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	21	77
1	509	53
2	4884	53
3	5270	53
0	0	0
1	0	0

simplify145.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

582×	`rules-21_binary64`
362×	`fma-def_binary64`
341×	`fma-neg_binary64`
335×	`rules-7-rev_binary64`
268×	`rules-13_binary64`

Counts

148 → 88

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	121	4065
1	930	3763
2	4758	3763
3	4994	3763
4	4976	3763

prune478.0ms (3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	211	12	223

Error

0.0b

Counts

223 → 12

Alt Table

Status	Error	Program
	12.3b	(+.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)))
	4.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 1)))
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.0b	(+.f64 lambda1 (log.f64 (exp.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))))))
	0.6b	(+.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))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (/.f64 (cos.f64 phi1) (cos.f64 phi2))) (cos.f64 phi2))))
	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 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
	0.9b	(+.f64 lambda1 (pow.f64 (cbrt.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))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	4.9b	(+.f64 lambda1 (/.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) (+.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))) 2) (+.f64 0 (.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))) 0)))))
	10.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2)))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 8946 to 2053 computations (77.1% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2))
✓	0.5b	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))
✓	0.7b	(log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))
	4.2b	(cos.f64 (-.f64 lambda1 lambda2))

series57.0ms (0.4%)

Counts

2 → 96

Calls

2 calls:

28.0ms	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))
28.0ms	(log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))

rewrite66.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

572×	`prod-diff_binary64`
219×	`expm1-udef_binary64`
219×	`log1p-udef_binary64`
121×	`add-sqr-sqrt_binary64`
114×	`log1p-expm1-u_binary64`

Counts

2 → 72

Calls

2 calls:

64.0ms	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))
64.0ms	(log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	258	28
2	3410	28
3	5181	28
0	0	0
1	0	0

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

745×	`rules-40_binary64`
745×	`rules-41_binary64`
745×	`rules-42_binary64`
745×	`rules-43_binary64`
257×	`fma-neg_binary64`

Counts

168 → 72

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	86	2084
1	623	1872
2	2929	1872
3	5165	1872

prune396.0ms (2.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	172	12	184

Error

0.0b

Counts

184 → 12

Alt Table

Status	Error	Program
	12.3b	(+.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)))
	4.1b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) 1)))
	0.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.0b	(+.f64 lambda1 (log.f64 (exp.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))))))
	0.6b	(+.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))))
	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (/.f64 (cos.f64 phi1) (cos.f64 phi2))) (cos.f64 phi2))))
	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 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (+.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))))))
	0.9b	(+.f64 lambda1 (pow.f64 (cbrt.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))
✓	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	4.9b	(+.f64 lambda1 (/.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) (+.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))) 2) (+.f64 0 (.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))) 0)))))
	10.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2)))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda2) (-.f64 (/.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (sin.f64 lambda2)) (cos.f64 lambda1)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 6950 to 1687 computations (75.7% saved)

regimes2.5s (15.8%)

Accuracy

Total 0.1b remaining (56.3%)

Threshold costs 0.1b (56.3%)

Counts

283 → 1

Compiler

Compiled 64771 to 39455 computations (39.1% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	57
1	21	57

end248.0ms (1.5%)

Compiler: Compiled 511 to 271 computations (47% saved)

Details

analyze2.7s (16.8%)

sample7.7s (47.9%)

simplify40.0ms (0.2%)

prune2.0ms (0%)

localize15.0ms (0.1%)

series46.0ms (0.3%)

rewrite94.0ms (0.6%)

simplify92.0ms (0.6%)

prune339.0ms (2.1%)

localize22.0ms (0.1%)

series51.0ms (0.3%)

rewrite76.0ms (0.5%)

simplify72.0ms (0.4%)

prune542.0ms (3.4%)

localize24.0ms (0.1%)

series139.0ms (0.9%)

rewrite90.0ms (0.6%)

simplify145.0ms (0.9%)

prune478.0ms (3%)

localize27.0ms (0.2%)

series57.0ms (0.4%)

rewrite66.0ms (0.4%)

simplify70.0ms (0.4%)

prune396.0ms (2.5%)

regimes2.5s (15.8%)

simplify1.0ms (0%)

end248.0ms (1.5%)

Profiling