Details

analyze3.2s (2.1%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 25 to 15 computations (40% saved)

sample7.9s (5.3%)

Results

5.5s	4553×	body	1024	valid
1.3s	1794×	body	512	valid
340.0ms	735×	body	256	valid
315.0ms	119×	body	2048	valid
261.0ms	1055×	body	128	valid

Compiler

Compiled 49 to 29 computations (40.8% saved)

simplify34.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(+.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))))
▶	0.3b	(+.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

0.3b

(+.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))))

▶

0.3b

(+.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%)

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))))
✓	3.1b	(sin.f64 (-.f64 lambda1 lambda2))
✓	3.2b	(cos.f64 (-.f64 lambda1 lambda2))

series52.0ms (0%)

Counts

4 → 112

Calls

4 calls:

32.0ms	(+.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)))))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`sin-sum_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

simplify130.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

994×	`fma-neg_binary64`
723×	`fma-def_binary64`
670×	`cancel-sign-sub-inv_binary64`
245×	`distribute-rgt-neg-in_binary64`
219×	`distribute-lft-neg-in_binary64`

Counts

185 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	300	4873
1	598	4011
2	1754	3815
3	4238	3804
4	4942	3804

prune209.0ms (0.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	10	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	154	10	164

Error

0.1b

Counts

164 → 10

Alt Table

Status	Error	Program
	12.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	6.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1))) (cbrt.f64 (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	33.3b	(+.f64 lambda1 (.f64 (sqrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (sqrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	4.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
	0.8b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
▶	0.4b	(+.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 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	32.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 6267 to 1627 computations (74% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)
✓	1.7b	(-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
	3.1b	(sin.f64 (-.f64 lambda1 lambda2))
	3.2b	(cos.f64 (-.f64 lambda1 lambda2))

series179.0ms (0.1%)

Counts

2 → 84

Calls

2 calls:

109.0ms

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

70.0ms

(pow.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cos-mult_binary64`
8×	`distribute-lft-in_binary64`
8×	`distribute-rgt-in_binary64`
8×	`cos-diff_binary64`
7×	`associate-*r/_binary64`

Counts

2 → 55

Calls

2 calls:

9.0ms

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

5.0ms

(pow.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)

simplify124.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-r_binary64`
579×	`associate-l_binary64`
439×	`fma-def_binary64`
175×	`*-commutative_binary64`
130×	`cancel-sign-sub-inv_binary64`

Counts

139 → 146

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	392	5017
1	1221	4794
2	4827	4794
3	5034	4794

prune1.0s (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	352	2	354
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	354	10	364

Error

0.1b

Counts

364 → 10

Alt Table

Status	Error	Program
	12.6b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	6.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1))) (cbrt.f64 (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))))
	33.3b	(+.f64 lambda1 (.f64 (sqrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (sqrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	4.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
▶	0.3b	(+.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 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))))
	0.8b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	32.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 27412 to 6373 computations (76.8% saved)

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	1.8b	(-.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	3.1b	(sin.f64 (-.f64 lambda1 lambda2))
	3.2b	(cos.f64 (-.f64 lambda1 lambda2))

series375.0ms (0.2%)

Counts

2 → 96

Calls

2 calls:

259.0ms

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

114.0ms

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

rewrite108.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

203×	`cos-mult_binary64`
149×	`associate-*r/_binary64`
79×	`frac-times_binary64`
66×	`associate-*l/_binary64`
45×	`frac-sub_binary64`

Counts

2 → 118

Calls

2 calls:

43.0ms

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

16.0ms

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

simplify282.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-def_binary64`
546×	`fma-neg_binary64`
301×	`*-commutative_binary64`
280×	`cancel-sign-sub-inv_binary64`
212×	`associate-r_binary64`

Counts

214 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	638	15954
1	1816	13083
2	4795	13082
3	5111	13082

prune2.5s (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	697	5	702
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	702	10	712

Error

0.1b

Counts

712 → 10

Alt Table

Status	Error	Program
	0.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1))) (cbrt.f64 (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	1.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	33.3b	(+.f64 lambda1 (.f64 (sqrt.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (sqrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	4.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (-.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
	0.4b	(+.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 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (.f64 (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))))))))
▶	0.3b	(+.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 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (/.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) (+.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))) (+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))))
	4.1b	(+.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 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 4) (pow.f64 (cos.f64 phi2) 4)) (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 2) (.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (cos.f64 phi2) 2)))) (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))))))
	0.4b	(+.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 phi2) (cos.f64 (-.f64 lambda1 lambda2))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (/.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 4) (pow.f64 (cos.f64 phi2) 4)) (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 2) (.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (cos.f64 phi2) 2))))) (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 4) (pow.f64 (cos.f64 phi2) 4)) (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 2) (.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (cos.f64 phi2) 2)))))) (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 4) (pow.f64 (cos.f64 phi2) 4)) (.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 2) (.f64 (pow.f64 (cos.f64 phi1) 2) (pow.f64 (cos.f64 phi2) 2)))))) (+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))))
	32.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 93209 to 14318 computations (84.6% saved)

localize39.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(+.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	1.6b	(-.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (.f64 (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
	3.1b	(sin.f64 (-.f64 lambda1 lambda2))
	3.2b	(cos.f64 (-.f64 lambda1 lambda2))

series379.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

379.0ms

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

rewrite14.9s (9.9%)

Algorithm

1×	rewrite-expression-head

Rules

25232×	`cos-mult_binary64`
18143×	`associate-*r/_binary64`
16882×	`frac-times_binary64`
9127×	`associate-*l/_binary64`
3825×	`frac-sub_binary64`

Counts

1 → 4224

Calls

1 calls:

5.3s

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

simplify58.6s (39.1%)

Algorithm

1×	egg-herbie

Counts

4272 → 8066

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6032	993851

prune59.9s (39.9%)

Compiler: Compiled 2427183 to 235739 computations (90.3% saved)

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

Iter	Nodes	Cost
0	15	32
1	21	30
2	28	30
3	35	30
4	42	30
5	68	30
6	98	30
7	132	30
8	176	30
9	220	30
10	288	30
11	310	30
12	346	30
13	393	30
14	403	30
15	421	30
16	442	30
17	449	30
18	470	30
19	478	30
20	480	30
21	453	30

Details

analyze3.2s (2.1%)

sample7.9s (5.3%)

simplify34.0ms (0%)

prune5.0ms (0%)

localize18.0ms (0%)

series52.0ms (0%)

rewrite19.0ms (0%)

simplify130.0ms (0.1%)

prune209.0ms (0.1%)

localize27.0ms (0%)

series179.0ms (0.1%)

rewrite19.0ms (0%)

simplify124.0ms (0.1%)

prune1.0s (0.7%)

localize33.0ms (0%)

series375.0ms (0.2%)

rewrite108.0ms (0.1%)

simplify282.0ms (0.2%)

prune2.5s (1.7%)

localize39.0ms (0%)

series379.0ms (0.3%)

rewrite14.9s (9.9%)

simplify58.6s (39.1%)

prune59.9s (39.9%)

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