Details

analyze2.7s (18.1%)

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)

sample7.5s (50.6%)

Results

5.4s	4573×	body	1024	valid
1.2s	1790×	body	512	valid
362.0ms	789×	body	256	valid
258.0ms	99×	body	2048	valid
241.0ms	1005×	body	128	valid

Compiler

Compiled 50 to 30 computations (40% saved)

preprocess89.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

732×	`fma-def_binary64`
699×	`fma-neg_binary64`
225×	`unsub-neg_binary64`
186×	`cancel-sign-sub-inv_binary64`
169×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	224
1	100	210
2	130	210
3	164	210
4	214	210
5	377	210
6	540	210
7	952	210
8	1385	210
9	1779	210
10	2307	210
11	2972	210
12	3608	210
13	3856	210
14	3960	210
15	4031	210
16	4058	210
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 24 to 14 computations (41.7% saved)

simplify29.0ms (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))) (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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Status

Error

Program

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))))

▶

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))))))

Compiler

Compiled 137 to 71 computations (48.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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))

series44.0ms (0.3%)

Counts

4 → 112

Calls

36 calls:

4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	phi1	-inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	lambda1	-inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	phi2	-inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	phi2	inf
2.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))	lambda2	inf

rewrite65.0ms (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

simplify60.0ms (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

prune313.0ms (2.1%)

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
	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)))
	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))))))
	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))))
	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)))))))
▶	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)))))))
	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))))))
	1.0b	(+.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))))))
	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))))))
	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))))))
	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))))))
	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))))))
	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)))

Compiler

Compiled 5625 to 1676 computations (70.2% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.7b	(+.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))

series80.0ms (0.5%)

Counts

3 → 104

Calls

30 calls:

8.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	lambda1	-inf
7.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi2	inf
6.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi1	inf
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi1	-inf
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))	phi2	-inf

rewrite37.0ms (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

simplify73.0ms (0.5%)

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

prune369.0ms (2.5%)

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
	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)))
	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))))))
	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))))
	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)))))))
▶	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)))))))
	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))))))
	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))))))
	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))))))
	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)))
	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)))))))))

Compiler

Compiled 6017 to 1735 computations (71.2% saved)

localize23.0ms (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)))))

series24.0ms (0.2%)

Counts

2 → 72

Calls

18 calls:

2.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))	lambda2	inf
2.0ms	(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))))))	phi2	inf
1.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))	lambda2	-inf
1.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))	lambda1	-inf
1.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))	lambda1	inf

rewrite30.0ms (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

simplify82.0ms (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

prune325.0ms (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
	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)))
	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))))))
	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)))))))
✓	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) (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))))
	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))))))
	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))))))
	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)))
▶	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)))))))))

Compiler

Compiled 7008 to 1893 computations (73% saved)

localize23.0ms (0.2%)

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))

series644.0ms (4.3%)

Counts

2 → 72

Calls

18 calls:

87.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))	lambda1	-inf
87.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))	phi2	inf
84.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))	lambda1	inf
79.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))	lambda2	inf
77.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (log.f64 (+.f64 1 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))	lambda2	-inf

rewrite58.0ms (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

simplify42.0ms (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

prune400.0ms (2.7%)

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
	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)))
	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))))))
	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)))))))
✓	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) (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))))
	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))))))
	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))))))
	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)))
✓	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)))))))))

Compiler

Compiled 6904 to 2359 computations (65.8% saved)

regimes1.6s (10.6%)

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

end224.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 435 to 246 computations (43.4% saved)

Details

analyze2.7s (18.1%)

sample7.5s (50.6%)

preprocess89.0ms (0.6%)

simplify29.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series44.0ms (0.3%)

rewrite65.0ms (0.4%)

simplify60.0ms (0.4%)

prune313.0ms (2.1%)

localize21.0ms (0.1%)

series80.0ms (0.5%)

rewrite37.0ms (0.2%)

simplify73.0ms (0.5%)

prune369.0ms (2.5%)

localize23.0ms (0.2%)

series24.0ms (0.2%)

rewrite30.0ms (0.2%)

simplify82.0ms (0.5%)

prune325.0ms (2.2%)

localize23.0ms (0.2%)

series644.0ms (4.3%)

rewrite58.0ms (0.4%)

simplify42.0ms (0.3%)

prune400.0ms (2.7%)

regimes1.6s (10.6%)

simplify3.0ms (0%)

end224.0ms (1.5%)

Profiling