Details

analyze2.7s (15.7%)

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 (46%)

Results

5.7s	4648×	body	1024	valid
1.2s	1785×	body	512	valid
364.0ms	124×	body	2048	valid
326.0ms	708×	body	256	valid
241.0ms	991×	body	128	valid

Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify32.0ms (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

0.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.7b	(+.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))))
▶	0.7b	(+.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

0.7b

(+.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))))

▶

0.7b

(+.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)))))
✓	0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
✓	3.3b	(sin.f64 (-.f64 lambda1 lambda2))
✓	3.3b	(cos.f64 (-.f64 lambda1 lambda2))

series50.0ms (0.3%)

Counts

4 → 112

Calls

4 calls:

31.0ms	(+.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)))))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (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:

8.0ms	(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)))))

simplify122.0ms (0.7%)

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

prune243.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	150	12	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	152	12	164

Error

0.5b

Counts

164 → 12

Alt Table

Status	Error	Program
	0.7b	(+.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))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) (*.f64 lambda1 lambda1)) -1/2))))))
	0.7b	(+.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)))))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.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))))))))
	1.0b	(+.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))))))
	1.0b	(+.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))))))
	1.2b	(+.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))))))
▶	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (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))))))
	4.7b	(+.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)))))))
	6.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.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 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))

Compiler

Compiled 6391 to 1705 computations (73.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))
✓	0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	3.3b	(sin.f64 (-.f64 lambda1 lambda2))
	3.3b	(cos.f64 (-.f64 lambda1 lambda2))

series495.0ms (2.9%)

Counts

2 → 72

Calls

2 calls:

465.0ms	(log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))
29.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2))))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

3.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
0.0ms	(log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

909×	`times-frac_binary64`
652×	`fma-def_binary64`
473×	`cancel-sign-sub-inv_binary64`
152×	`fma-neg_binary64`
148×	`sub-neg_binary64`

Counts

99 → 86

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2131
1	586	1967
2	2054	1875
3	5159	1875

prune416.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	168	12	180

Error

0.5b

Counts

180 → 12

Alt Table

Status	Error	Program
▶	0.7b	(+.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))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) (*.f64 lambda1 lambda1)) -1/2))))))
	0.7b	(+.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)))))))))
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.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))))))))
	1.0b	(+.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))))))
	1.0b	(+.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))))))
	1.2b	(+.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))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (expm1.f64 (-.f64 (log.f64 (+.f64 1 (cos.f64 (neg.f64 lambda2)))) (/.f64 (*.f64 (sin.f64 (neg.f64 lambda2)) lambda1) (+.f64 1 (cos.f64 (neg.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))))))
	4.7b	(+.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)))))))
	6.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.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 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))

Compiler

Compiled 7223 to 2227 computations (69.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))
✓	0.8b	(log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))
	3.3b	(sin.f64 (-.f64 lambda1 lambda2))
	3.3b	(cos.f64 (-.f64 lambda1 lambda2))

series58.0ms (0.3%)

Counts

2 → 96

Calls

2 calls:

29.0ms	(log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))
28.0ms	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`log-pow_binary64`

Counts

2 → 28

Calls

2 calls:

2.0ms	(log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))
0.0ms	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

884×	`fma-neg_binary64`
493×	`distribute-rgt-neg-in_binary64`
361×	`associate-r_binary64`
360×	`cancel-sign-sub-inv_binary64`
332×	`fma-def_binary64`

Counts

124 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	2545
1	299	2420
2	892	2312
3	3120	2288
4	5053	2288

prune498.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	157	13	170

Error

0.4b

Counts

170 → 13

Alt Table

Status	Error	Program
	14.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))) (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	14.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	1.0b	(+.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))))))
	1.0b	(+.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))))))
	1.2b	(+.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))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (expm1.f64 (-.f64 (log.f64 (+.f64 1 (cos.f64 (neg.f64 lambda2)))) (/.f64 (*.f64 (sin.f64 (neg.f64 lambda2)) lambda1) (+.f64 1 (cos.f64 (neg.f64 lambda2))))))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	1.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) (*.f64 lambda1 lambda1)) -1/2))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))))
	4.7b	(+.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) (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)))))))))
	6.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	14.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))

Compiler

Compiled 6430 to 1832 computations (71.5% saved)

localize24.0ms (0.1%)

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)
✓	1.4b	(-.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)))))
	3.3b	(sin.f64 (-.f64 lambda1 lambda2))
	3.3b	(cos.f64 (-.f64 lambda1 lambda2))

series205.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

142.0ms

(-.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)))))

63.0ms

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

rewrite20.0ms (0.1%)

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:

11.0ms

(-.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)))))

4.0ms

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

simplify129.0ms (0.7%)

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

prune1.2s (7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	350	4	354
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	352	15	367

Error

0.4b

Counts

367 → 15

Alt Table

Status	Error	Program
	0.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (log1p.f64 (expm1.f64 (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)))))))))
	14.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))) (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	14.9b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (log.f64 (exp.f64 (sqrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	1.0b	(+.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))))))
	1.0b	(+.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))))))
	1.2b	(+.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))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (expm1.f64 (-.f64 (log.f64 (+.f64 1 (cos.f64 (neg.f64 lambda2)))) (/.f64 (*.f64 (sin.f64 (neg.f64 lambda2)) lambda1) (+.f64 1 (cos.f64 (neg.f64 lambda2))))))))))
	1.0b	(+.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) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)))))))))
	0.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))
	0.7b	(+.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 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 4) (.f64 (pow.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 2) (.f64 (cos.f64 phi1) (cos.f64 phi1)))) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))))
	27.5b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (pow.f64 (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 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)))))))))
	1.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)))))))))
	4.7b	(+.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)))))))
	6.0b	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	14.8b	(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1))))))))

Compiler

Compiled 27132 to 6316 computations (76.7% saved)

regimes2.5s (14.6%)

Accuracy

Total 0.2b remaining (18.6%)

Threshold costs 0.2b (18.6%)

Counts

268 → 1

Compiler

Compiled 70525 to 37502 computations (46.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	36	48
2	49	48
3	57	48
4	62	48
5	63	48
6	63	48

end357.0ms (2.1%)

Compiler: Compiled 766 to 357 computations (53.4% 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

analyze2.7s (15.7%)

sample8.0s (46%)

simplify32.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series50.0ms (0.3%)

rewrite21.0ms (0.1%)

simplify122.0ms (0.7%)

prune243.0ms (1.4%)

localize18.0ms (0.1%)

series495.0ms (2.9%)

rewrite4.0ms (0%)

simplify59.0ms (0.3%)

prune416.0ms (2.4%)

localize17.0ms (0.1%)

series58.0ms (0.3%)

rewrite4.0ms (0%)

simplify83.0ms (0.5%)

prune498.0ms (2.9%)

localize24.0ms (0.1%)

series205.0ms (1.2%)

rewrite20.0ms (0.1%)

simplify129.0ms (0.7%)

prune1.2s (7%)

regimes2.5s (14.6%)

simplify3.0ms (0%)

end357.0ms (2.1%)

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