Details

analyze2.7s (17.9%)

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)

sample7.6s (51.1%)

Results

5.5s	4573×	body	1024	valid
1.2s	1790×	body	512	valid
371.0ms	789×	body	256	valid
253.0ms	99×	body	2048	valid
243.0ms	1005×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	45	30
5	71	30
6	115	30
7	168	30
8	240	30
9	327	30
10	454	30
11	600	30
12	646	30
13	748	30
14	852	30
15	874	30
16	907	30
17	951	30
18	994	30
19	1015	30
20	1017	30

Stop Event

1×

saturated

Counts

1 → 2

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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.0b	(+.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))))))
	1.0b	(+.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))))

Status

Error

Program

▶

1.0b

(+.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))))))

1.0b

(+.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))))

Compiler

Compiled 137 to 71 computations (48.2% saved)

localize19.0ms (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)))))
✓	0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	4.3b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.5b	(sin.f64 (-.f64 lambda1 lambda2))

series47.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

29.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
10.0ms	(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	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite64.0ms (0.4%)

Algorithm

1×	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`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	310	53
2	4398	53

Stop Event

1×	node limit

Counts

4 → 106

Calls

4 calls:

62.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
62.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
62.0ms	(cos.f64 (-.f64 lambda1 lambda2))
62.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

609×	`cancel-sign-sub-inv_binary64`
479×	`fma-def_binary64`
477×	`associate-r_binary64`
458×	`associate-l_binary64`
200×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	2746
1	395	2554
2	1346	2466

Stop Event

1×	node limit

Counts

218 → 169

prune298.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	13	169
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	158	13	171

Error

0.7b

Counts

171 → 13

Alt Table

Status	Error	Program
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (.f64 (.f64 lambda1 lambda1) (-.f64 (.f64 1/2 (sin.f64 lambda2)) (.f64 (cos.f64 lambda2) (.f64 1/6 lambda1))))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	10.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) lambda1) (sin.f64 lambda2))) (+.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))) (log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))
	12.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.4b	(+.f64 lambda1 (.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)))) (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)))) 2)))
▶	0.9b	(+.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)))))))
	4.8b	(+.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))))))
	0.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.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))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
	29.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	16.5b	(+.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)))

Compiler

Compiled 5625 to 1676 computations (70.2% saved)

localize23.0ms (0.2%)

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))
✓	0.7b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
	4.5b	(sin.f64 (-.f64 lambda1 lambda2))

series82.0ms (0.6%)

Counts

3 → 104

Calls

3 calls:

61.0ms

(+.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))))))

10.0ms

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

rewrite36.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

210×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
195×	`add-cbrt-cube_binary64`
192×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	73
1	399	49

Stop Event

1×	node limit

Counts

3 → 73

Calls

3 calls:

35.0ms

(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))))))

35.0ms

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

35.0ms

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

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

733×	`cancel-sign-sub-inv_binary64`
633×	`associate-r_binary64`
611×	`associate-l_binary64`
207×	`distribute-rgt-neg-in_binary64`
194×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	3693
1	488	3419
2	1698	3344

Stop Event

1×	node limit

Counts

177 → 125

prune362.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	168	10	178

Error

0.1b

Counts

178 → 10

Alt Table

Status	Error	Program
▶	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)))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))
	12.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.4b	(+.f64 lambda1 (.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)))) (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)))) 2)))
	4.8b	(+.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))))))
	10.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
	1.0b	(+.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))))
	29.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	16.5b	(+.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)))

Compiler

Compiled 6017 to 1735 computations (71.2% saved)

localize25.0ms (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))
	0.7b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series26.0ms (0.2%)

Counts

2 → 72

Calls

2 calls:

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

12.0ms

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

rewrite32.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

218×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
200×	`add-cbrt-cube_binary64`
198×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	59
1	416	45

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

31.0ms

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

31.0ms

(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))))))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

645×	`cancel-sign-sub-inv_binary64`
467×	`fma-neg_binary64`
305×	`*-commutative_binary64`
259×	`sub-neg_binary64`
206×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	2672
1	166	2656
2	463	2634
3	1661	2627
4	4272	2627

Stop Event

1×	node limit

Counts

110 → 55

prune336.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	160	11	171

Error

0.1b

Counts

171 → 11

Alt Table

Status	Error	Program
✓	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)))))))
▶	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))))
	31.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (exp.f64 (log.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)))))))
	10.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))
	12.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	16.5b	(+.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) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.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))))
	1.4b	(+.f64 lambda1 (.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)))) (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)))) 2)))
	4.8b	(+.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))))))
	29.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 7008 to 1893 computations (73% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))
✓	0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
	4.3b	(cos.f64 (-.f64 lambda1 lambda2))
	4.5b	(sin.f64 (-.f64 lambda1 lambda2))

series657.0ms (4.4%)

Counts

2 → 72

Calls

2 calls:

646.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))
11.0ms	(+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

282×	`expm1-udef_binary64`
281×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	308	22
2	4117	22

Stop Event

1×	node limit

Counts

2 → 74

Calls

2 calls:

59.0ms	(+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))
59.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

707×	`cancel-sign-sub-inv_binary64`
301×	`associate--l+_binary64`
262×	`associate-+l+_binary64`
213×	`associate-r_binary64`
209×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1610
1	492	1497
2	1836	1382

Stop Event

1×	node limit

Counts

146 → 121

prune388.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	201	11	212

Error

0.1b

Counts

212 → 11

Alt Table

Status	Error	Program
✓	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)))))))
✓	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))))
	31.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (exp.f64 (log.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)))))))
	10.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (+.f64 1 (expm1.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))
	12.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (log.f64 (exp.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	16.5b	(+.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) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.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))))
	1.4b	(+.f64 lambda1 (.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)))) (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)))) 2)))
	4.8b	(+.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))))))
	29.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (pow.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 2)) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 6904 to 2359 computations (65.8% saved)

regimes1.6s (11%)

Accuracy

Total 0.1b remaining (46.2%)

Threshold costs 0.1b (46.2%)

Counts

189 → 1

Compiler

Compiled 38752 to 23572 computations (39.2% 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	54
1	35	54
2	44	54
3	49	54
4	51	54

Stop Event

1×

saturated

end239.0ms (1.6%)

Compiler: Compiled 435 to 246 computations (43.4% saved)

Details

analyze2.7s (17.9%)

sample7.6s (51.1%)

simplify27.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series47.0ms (0.3%)

rewrite64.0ms (0.4%)

simplify53.0ms (0.4%)

prune298.0ms (2%)

localize23.0ms (0.2%)

series82.0ms (0.6%)

rewrite36.0ms (0.2%)

simplify62.0ms (0.4%)

prune362.0ms (2.4%)

localize25.0ms (0.2%)

series26.0ms (0.2%)

rewrite32.0ms (0.2%)

simplify76.0ms (0.5%)

prune336.0ms (2.2%)

localize22.0ms (0.1%)

series657.0ms (4.4%)

rewrite61.0ms (0.4%)

simplify45.0ms (0.3%)

prune388.0ms (2.6%)

regimes1.6s (11%)

simplify3.0ms (0%)

end239.0ms (1.6%)

Profiling