Details

analyze3.8s (17.6%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 29 to 18 computations (37.9% saved)

sample12.0s (56.4%)

Results

9.4s	5466×	body	1024	valid
1.2s	1340×	body	512	valid
709.0ms	179×	body	2048	valid
260.0ms	433×	body	256	valid
260.0ms	838×	body	128	valid

Compiler

Compiled 86 to 53 computations (38.4% saved)

simplify28.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary64`
194×	`fma-neg_binary64`
83×	`cancel-sign-sub-inv_binary64`
59×	`distribute-rgt-neg-in_binary64`
47×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

11.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 108 to 55 computations (49.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	4.2b	(cos.f64 (-.f64 lambda1 lambda2))
✓	4.4b	(sin.f64 (-.f64 lambda1 lambda2))

series68.0ms (0.3%)

Counts

4 → 100

Calls

4 calls:

43.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
16.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`cos-sum_binary64`

Counts

4 → 90

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
6.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify127.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

980×	`fma-neg_binary64`
457×	`associate-r_binary64`
441×	`distribute-rgt-neg-in_binary64`
422×	`associate-l_binary64`
395×	`distribute-lft-neg-in_binary64`

Counts

190 → 201

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	399	4414
1	862	3679
2	2913	3547
3	4681	3537
4	5070	3537

prune422.0ms (2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	185	16	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	16	202

Error

5.5b

Counts

202 → 16

Alt Table

Status	Error	Program
	15.4b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	23.5b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.7b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (fma.f64 1/2 (.f64 lambda1 (.f64 lambda1 (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (pow.f64 lambda1 3)) -1/6)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.4b	(atan2.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (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)))))))
	15.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (sin.f64 lambda1) (sin.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))))))
▶	5.7b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	16.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))))))))))
	11.4b	(atan2.f64 (.f64 (log1p.f64 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	24.5b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (+.f64 (.f64 1/2 (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi2) (pow.f64 lambda2 2)))) (.f64 (cos.f64 phi2) (.f64 lambda2 (cos.f64 lambda1))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	45.5b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2)))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	17.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))
	21.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))))))

Compiler

Compiled 9195 to 2291 computations (75.1% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
✓	0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	4.2b	(cos.f64 (-.f64 lambda1 lambda2))

series52.0ms (0.2%)

Counts

2 → 60

Calls

2 calls:

42.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

7.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
3.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

947×	`fma-neg_binary64`
803×	`fma-def_binary64`
529×	`cancel-sign-sub-inv_binary64`
242×	`distribute-rgt-neg-in_binary64`
240×	`associate-r_binary64`

Counts

102 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	2294
1	532	2178
2	1824	2115
3	4425	2109
4	5069	2109

prune576.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	206	10	216
Fresh	13	2	15
Picked	1	0	1
Done	0	0	0
Total	220	12	232

Error

0.0b

Counts

232 → 12

Alt Table

Status	Error	Program
	12.9b	(atan2.f64 (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (cos.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	9.8b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
	18.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sqrt.f64 (cos.f64 lambda1)) (.f64 (sqrt.f64 (cos.f64 lambda1)) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	21.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	17.4b	(atan2.f64 (log.f64 (exp.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.7b	(atan2.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 10463 to 2302 computations (78% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))
✓	0.2b	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

series138.0ms (0.6%)

Counts

4 → 140

Calls

4 calls:

51.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
51.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
26.0ms	(.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
32×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`

Counts

4 → 89

Calls

4 calls:

7.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
6.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
4.0ms	(.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))
3.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify125.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

747×	`cancel-sign-sub-inv_binary64`
721×	`associate-l_binary64`
470×	`fma-neg_binary64`
421×	`distribute-rgt-neg-in_binary64`
403×	`*-commutative_binary64`

Counts

229 → 217

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	5571
1	1167	4987
2	3095	4977
3	5019	4977

prune681.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	217	12	229

Error

0.0b

Counts

229 → 12

Alt Table

Status	Error	Program
	12.9b	(atan2.f64 (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (cos.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	9.8b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	1.7b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 lambda1)))))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	18.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sqrt.f64 (cos.f64 lambda1)) (.f64 (sqrt.f64 (cos.f64 lambda1)) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	21.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.7b	(atan2.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	1.7b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (log.f64 (exp.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	17.4b	(atan2.f64 (log.f64 (exp.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 13313 to 2771 computations (79.2% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))
	0.2b	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	4.3b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series12.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 16

Calls

1 calls:

2.0ms

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

simplify116.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-neg_binary64`
482×	`sub-neg_binary64`
444×	`distribute-rgt-neg-in_binary64`
390×	`distribute-lft-neg-in_binary64`
349×	`*-commutative_binary64`

Counts

40 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	545
1	156	509
2	434	485
3	1327	455
4	2552	455
5	4096	455
6	4513	455
7	4961	455
8	4999	455
9	4973	455

prune652.0ms (3.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	193	12	205

Error

0.0b

Counts

205 → 12

Alt Table

Status	Error	Program
	12.9b	(atan2.f64 (/.f64 (.f64 (-.f64 (pow.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (cos.f64 phi2)) (+.f64 (.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (cos.f64 lambda2))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	9.8b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	1.7b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 lambda1)))))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	18.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sqrt.f64 (cos.f64 lambda1)) (.f64 (sqrt.f64 (cos.f64 lambda1)) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	21.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.7b	(atan2.f64 (expm1.f64 (log1p.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	1.7b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (log.f64 (exp.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	17.4b	(atan2.f64 (log.f64 (exp.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
✓	0.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
	11.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 11406 to 2227 computations (80.5% saved)

regimes1.9s (9%)

Accuracy

Total 0.1b remaining (50.8%)

Threshold costs 0.1b (50.8%)

Counts

202 → 1

Compiler

Compiled 51892 to 29824 computations (42.5% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64`
15×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	77
1	45	77
2	62	77
3	88	77
4	115	77
5	130	77
6	138	77
7	140	77
8	140	77

end333.0ms (1.6%)

Compiler: Compiled 680 to 383 computations (43.7% saved)

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39

Details

analyze3.8s (17.6%)

sample12.0s (56.4%)

simplify28.0ms (0.1%)

prune3.0ms (0%)

localize20.0ms (0.1%)

series68.0ms (0.3%)

rewrite29.0ms (0.1%)

simplify127.0ms (0.6%)

prune422.0ms (2%)

localize26.0ms (0.1%)

series52.0ms (0.2%)

rewrite12.0ms (0.1%)

simplify87.0ms (0.4%)

prune576.0ms (2.7%)

localize28.0ms (0.1%)

series138.0ms (0.6%)

rewrite27.0ms (0.1%)

simplify125.0ms (0.6%)

prune681.0ms (3.2%)

localize37.0ms (0.2%)

series12.0ms (0.1%)

rewrite2.0ms (0%)

simplify116.0ms (0.5%)

prune652.0ms (3.1%)

regimes1.9s (9%)

simplify5.0ms (0%)

end333.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	18	39
1	32	39
2	61	39
3	115	39
4	155	39
5	246	39
6	348	39
7	437	39
8	572	39
9	622	39
10	694	39
11	720	39
12	669	39