Details

analyze2.8s (16.6%)

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)

sample8.0s (47.2%)

Results

5.7s	4583×	body	1024	valid
1.2s	1799×	body	512	valid
389.0ms	772×	body	256	valid
327.0ms	123×	body	2048	valid
235.0ms	979×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify29.0ms (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`

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

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(+.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))))
▶	0.5b	(+.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))))))

Status

Error

Program

0.5b

(+.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))))

▶

0.5b

(+.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 137 to 71 computations (48.2% 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))))
✓	1.8b	(cos.f64 (-.f64 lambda1 lambda2))
✓	1.9b	(sin.f64 (-.f64 lambda1 lambda2))

series44.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

26.0ms	(+.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))
3.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite63.0ms (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	4173	53
3	5090	53

Stop Event

1×	node limit

Counts

4 → 106

Calls

4 calls:

61.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
61.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
61.0ms	(cos.f64 (-.f64 lambda1 lambda2))
61.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

594×	`cancel-sign-sub-inv_binary64`
480×	`fma-def_binary64`
479×	`associate-r_binary64`
462×	`associate-l_binary64`
429×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	2746
1	393	2554
2	1248	2466
3	4322	2462
4	4968	2462

Stop Event

1×	node limit

Counts

218 → 168

prune240.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Error

0.3b

Counts

170 → 9

Alt Table

Status	Error	Program
	14.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) 1)))
	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 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
	6.4b	(+.f64 lambda1 (cbrt.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)))
	5.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.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)))))))
	32.4b	(+.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) (.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))))))
▶	0.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.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))))))))
	0.8b	(+.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)))
	5.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (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))))))

Compiler

Compiled 5442 to 1513 computations (72.2% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.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))))
✓	0.4b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
✓	0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.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))))))
	1.9b	(sin.f64 (-.f64 lambda1 lambda2))

series451.0ms (2.7%)

Counts

3 → 96

Calls

3 calls:

341.0ms

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

92.0ms

(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.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))))

18.0ms

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

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

388×	`prod-diff_binary64`
238×	`add-sqr-sqrt_binary64`
229×	`log1p-expm1-u_binary64`
229×	`expm1-log1p-u_binary64`
221×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	109
1	463	63
2	4980	63
3	5546	63

Stop Event

1×	node limit

Counts

3 → 62

Calls

3 calls:

67.0ms

(/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (*.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))))

67.0ms

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

67.0ms

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

simplify137.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

678×	`cancel-sign-sub-inv_binary64`
616×	`fma-def_binary64`
441×	`fma-neg_binary64`
244×	`distribute-rgt-neg-in_binary64`
244×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	5588
1	567	5502
2	2048	5400
3	4857	5400
4	5109	5400

Stop Event

1×	node limit

Counts

158 → 126

prune450.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	165	9	174

Error

0.1b

Counts

174 → 9

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) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.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))))))))
	32.4b	(+.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))
	14.5b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) 1)))
	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 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
	6.4b	(+.f64 lambda1 (cbrt.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)))
	5.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.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)))))))
	0.8b	(+.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))))))
	0.8b	(+.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)))
	5.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (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))))))

Compiler

Compiled 9456 to 2356 computations (75.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
	0.3b	(/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.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))))
	0.4b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
	0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.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))))))

series19.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

19.0ms

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

rewrite35.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

719×	`log1p-expm1-u_binary64`
719×	`expm1-log1p-u_binary64`
273×	`prod-diff_binary64`
136×	`log1p-udef_binary64`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	147	11
2	1826	11
3	5177	11

Stop Event

1×	node limit

Counts

1 → 17

Calls

1 calls:

35.0ms

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

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-neg_binary64`
572×	`unswap-sqr_binary64`
420×	`distribute-rgt-neg-in_binary64`
406×	`distribute-lft-neg-in_binary64`
344×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	512
1	139	504
2	460	456
3	1940	438
4	4722	438
5	5126	438

Stop Event

1×	node limit

Counts

41 → 35

prune495.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Error

0.1b

Counts

170 → 8

Alt Table

Status	Error	Program
	6.4b	(+.f64 lambda1 (cbrt.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)))
	5.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.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)))))))
	32.4b	(+.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) (.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))))))
	0.8b	(+.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)))
	5.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (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))))))
	0.5b	(+.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 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
▶	0.3b	(+.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 (fma.f64 (/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (pow.f64 (cos.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2)) (cos.f64 phi1)) (/.f64 (.f64 (pow.f64 (sin.f64 lambda1) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 lambda2) 2))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 10182 to 2597 computations (74.5% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 lambda1) 2)
✓	0.2b	(/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
✓	0.2b	(pow.f64 (cos.f64 lambda2) 2)
✓	0.6b	(fma.f64 (/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (pow.f64 (cos.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2)) (cos.f64 phi1))

series333.0ms (2%)

Counts

4 → 68

Calls

4 calls:

241.0ms	(fma.f64 (/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (pow.f64 (cos.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2)) (cos.f64 phi1))
86.0ms	(/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
3.0ms	(pow.f64 (sin.f64 lambda1) 2)
3.0ms	(pow.f64 (cos.f64 lambda2) 2)

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`prod-diff_binary64`
224×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
209×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	74
1	454	50
2	4780	50
3	5255	50

Stop Event

1×	node limit

Counts

4 → 74

Calls

4 calls:

61.0ms	(pow.f64 (sin.f64 lambda1) 2)
61.0ms	(/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
61.0ms	(pow.f64 (cos.f64 lambda2) 2)
61.0ms	(fma.f64 (/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (pow.f64 (cos.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2)) (cos.f64 phi1))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

951×	`times-frac_binary64`
794×	`fma-def_binary64`
416×	`cancel-sign-sub-inv_binary64`
162×	`unswap-sqr_binary64`
159×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	3301
1	606	3280
2	2170	3142
3	5294	3142

Stop Event

1×	node limit

Counts

142 → 144

prune318.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	144	8	152

Error

0.1b

Counts

152 → 8

Alt Table

Status	Error	Program
	6.4b	(+.f64 lambda1 (cbrt.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)))
	5.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (/.f64 (pow.f64 (cos.f64 phi1) 2) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (/.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)))))))
	32.4b	(+.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) (.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))))))
	0.8b	(+.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)))
	5.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (pow.f64 (cos.f64 phi1) 2) (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))))))
	0.5b	(+.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 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))
✓	0.3b	(+.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 (fma.f64 (/.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (pow.f64 (cos.f64 lambda2) 2) (pow.f64 (cos.f64 lambda1) 2)) (cos.f64 phi1)) (/.f64 (.f64 (pow.f64 (sin.f64 lambda1) 2) (.f64 (cos.f64 phi2) (pow.f64 (sin.f64 lambda2) 2))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 11336 to 3364 computations (70.3% saved)

regimes2.8s (16.4%)

Accuracy

Total 0.1b remaining (53%)

Threshold costs 0.1b (53%)

Counts

271 → 1

Compiler

Compiled 87780 to 47029 computations (46.4% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	93
1	53	93
2	71	93
3	82	93
4	87	93
5	87	93

Stop Event

1×

saturated

end218.0ms (1.3%)

Compiler: Compiled 444 to 221 computations (50.2% 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

analyze2.8s (16.6%)

sample8.0s (47.2%)

simplify29.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series44.0ms (0.3%)

rewrite63.0ms (0.4%)

simplify91.0ms (0.5%)

prune240.0ms (1.4%)

localize27.0ms (0.2%)

series451.0ms (2.7%)

rewrite69.0ms (0.4%)

simplify137.0ms (0.8%)

prune450.0ms (2.7%)

localize28.0ms (0.2%)

series19.0ms (0.1%)

rewrite35.0ms (0.2%)

simplify53.0ms (0.3%)

prune495.0ms (2.9%)

localize55.0ms (0.3%)

series333.0ms (2%)

rewrite62.0ms (0.4%)

simplify79.0ms (0.5%)

prune318.0ms (1.9%)

regimes2.8s (16.4%)

simplify6.0ms (0%)

end218.0ms (1.3%)

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