Details

analyze2.9s (19.1%)

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)

sample7.8s (50.9%)

Results

5.6s	4610×	body	1024	valid
1.2s	1730×	body	512	valid
382.0ms	797×	body	256	valid
272.0ms	106×	body	2048	valid
261.0ms	1013×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify36.0ms (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`

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

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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.8b	(+.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))))
▶	0.8b	(+.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

0.8b

(+.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))))

▶

0.8b

(+.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)

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)))))
✓	0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	1.1b	(sin.f64 (-.f64 lambda1 lambda2))
✓	1.2b	(cos.f64 (-.f64 lambda1 lambda2))

series70.0ms (0.5%)

Counts

4 → 112

Calls

4 calls:

52.0ms	(+.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)))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms (0.1%)

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

simplify126.0ms (0.8%)

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

prune236.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	149	13	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	151	13	164

Error

0.5b

Counts

164 → 13

Alt Table

Status	Error	Program
	1.3b	(+.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))))))
	5.5b	(+.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))))))
	4.8b	(+.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)))))))
▶	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	17.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.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))) (cbrt.f64 (.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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	5.7b	(+.f64 lambda1 (cbrt.f64 (.f64 (.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	1.4b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2))))))
	0.9b	(+.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))))))
	8.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (+.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))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (*.f64 (cos.f64 phi1) (cos.f64 phi1))))))
	31.8b	(+.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))))))

Compiler

Compiled 6519 to 1729 computations (73.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 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))))
	1.2b	(cos.f64 (-.f64 lambda1 lambda2))

series30.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

16.0ms

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

14.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

5.0ms

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

0.0ms

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

simplify125.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-neg_binary64`
484×	`unsub-neg_binary64`
449×	`sub-neg_binary64`
316×	`fma-def_binary64`
315×	`*-commutative_binary64`

Counts

116 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	3508
1	313	3242
2	941	3201
3	2006	3170
4	4154	3170
5	5037	3170

prune428.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	173	12	185

Error

0.1b

Counts

185 → 12

Alt Table

Status	Error	Program
	1.3b	(+.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))))))
	5.5b	(+.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))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	17.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.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))) (cbrt.f64 (.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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	5.7b	(+.f64 lambda1 (cbrt.f64 (.f64 (.f64 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.9b	(+.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))))))
	8.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	4.8b	(+.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 (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)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (*.f64 (cos.f64 phi1) (cos.f64 phi1))))))
	31.8b	(+.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))))))

Compiler

Compiled 7664 to 1703 computations (77.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
✓	0.5b	(fma.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1))

series92.0ms (0.6%)

Counts

4 → 140

Calls

4 calls:

41.0ms	(fma.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1))
25.0ms	(.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
15.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
11.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

4 → 61

Calls

4 calls:

5.0ms	(.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
3.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.0ms	(fma.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

360×	`associate-r_binary64`
358×	`distribute-rgt-neg-in_binary64`
356×	`fma-neg_binary64`
331×	`distribute-lft-neg-in_binary64`
277×	`associate-l_binary64`

Counts

201 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	6319
1	720	5888
2	2434	5666
3	4979	5666

prune411.0ms (2.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	162	12	174

Error

0.1b

Counts

174 → 12

Alt Table

Status	Error	Program
	1.3b	(+.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))))))
	5.5b	(+.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))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (fma.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (cos.f64 phi2)) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	5.1b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (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) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) 3)))
	8.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	31.8b	(+.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))))))
▶	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	17.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.9b	(+.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))))))
	4.8b	(+.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 (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)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (*.f64 (cos.f64 phi1) (cos.f64 phi1))))))

Compiler

Compiled 8378 to 1829 computations (78.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
✓	0.5b	(fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1))
✓	0.5b	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3))
✓	0.6b	(pow.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)

series234.0ms (1.5%)

Counts

4 → 192

Calls

4 calls:

138.0ms	(pow.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)
40.0ms	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3))
39.0ms	(fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1))
16.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

4 → 67

Calls

4 calls:

3.0ms	(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3))
2.0ms	(pow.f64 (fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)
0.0ms	(fma.f64 (cos.f64 phi2) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify197.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

791×	`associate-r_binary64`
578×	`associate-l_binary64`
535×	`fma-def_binary64`
412×	`fma-neg_binary64`
177×	`*-commutative_binary64`

Counts

259 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	417	10209
1	1339	9590
2	4792	9586
3	5170	9586

prune437.0ms (2.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	1	9	10
Picked	0	1	1
Done	1	0	1
Total	164	12	176

Error

0.1b

Counts

176 → 12

Alt Table

Status	Error	Program
	1.3b	(+.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))))))
	5.5b	(+.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))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))
	6.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (expm1.f64 (log1p.f64 (fma.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2) (cos.f64 phi1)))) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	31.8b	(+.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))))))
✓	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) 3)) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	17.6b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))) (sqrt.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))))
	0.9b	(+.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))))))
	17.3b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi1)) (sqrt.f64 3)) (sqrt.f64 3))) (.f64 (cos.f64 phi2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	5.1b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (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) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) 3)))
	4.8b	(+.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 (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)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1))) (*.f64 (cos.f64 phi1) (cos.f64 phi1))))))

Compiler

Compiled 11072 to 3451 computations (68.8% saved)

regimes1.5s (9.9%)

Accuracy

Total 0.1b remaining (59.9%)

Threshold costs 0.1b (59.9%)

Counts

166 → 1

Compiler

Compiled 42686 to 23628 computations (44.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
7×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	36	56
2	46	56
3	52	56
4	56	56
5	57	56
6	57	56

end410.0ms (2.7%)

Compiler: Compiled 581 to 277 computations (52.3% 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

analyze2.9s (19.1%)

sample7.8s (50.9%)

simplify36.0ms (0.2%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series70.0ms (0.5%)

rewrite19.0ms (0.1%)

simplify126.0ms (0.8%)

prune236.0ms (1.5%)

localize23.0ms (0.1%)

series30.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify125.0ms (0.8%)

prune428.0ms (2.8%)

localize25.0ms (0.2%)

series92.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify119.0ms (0.8%)

prune411.0ms (2.7%)

localize29.0ms (0.2%)

series234.0ms (1.5%)

rewrite8.0ms (0.1%)

simplify197.0ms (1.3%)

prune437.0ms (2.8%)

regimes1.5s (9.9%)

simplify4.0ms (0%)

end410.0ms (2.7%)

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