Details

analyze9.9s (23.4%)

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
0.6%	99.2%	0.2%	13
1.8%	98%	0.2%	14

Compiler

Compiled 71 to 47 computations (33.8% saved)

sample673.0ms (1.6%)

Algorithm

1×

intervals

Results

477.0ms	166×	body	1024	valid
71.0ms	42×	body	512	valid
68.0ms	14×	body	2048	valid
16.0ms	15×	body	256	valid
8.0ms	19×	body	128	valid

Compiler

Compiled 146 to 98 computations (32.9% saved)

simplify181.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
571×	`fma-neg_binary64`
563×	`sub-neg_binary64`
520×	`distribute-rgt-neg-in_binary64`
460×	`sqr-pow_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	103
1	59	99
2	123	99
3	247	99
4	552	99
5	1018	99
6	1698	99
7	2589	99
8	3560	99
9	3893	99
10	4414	99
11	4607	99
12	4426	99
13	4413	99
14	4778	99
15	4761	99

prune7.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

22.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	22.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
▶	22.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Status

Error

Program

22.3b

(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (*.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))

▶

22.3b

(*.f64 R (*.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 344 to 224 computations (34.9% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite147.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

22.0b

Rules

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

Counts

4 → 40

Calls

4 calls:

6.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 2789 to 1570 computations (43.7% saved)

series194.0ms (0.5%)

Error

21.4b

Counts

4 → 42

Calls

4 calls:

29.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
28.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
26.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
25.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 6985 to 4489 computations (35.7% saved)

simplify141.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-r_binary64`
485×	`fma-neg_binary64`
457×	`distribute-rgt-neg-in_binary64`
448×	`distribute-lft-neg-in_binary64`
420×	`associate-l_binary64`

Counts

82 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	5190
1	570	5098
2	1057	5064
3	3114	5048
4	5062	5048

prune83.0ms (0.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	35	9	44
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	36	10	46

Error

21.6b

Counts

46 → 10

Alt Table

Status	Error	Program
	38.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (*.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
▶	22.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	33.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (.f64 lambda1 1/2)) (fma.f64 (cos.f64 (.f64 lambda1 1/2)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2)) (.f64 (.f64 (sin.f64 (.f64 lambda1 1/2)) (.f64 lambda2 lambda2)) -1/8))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	36.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (.f64 lambda1 1/2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (.f64 -1/2 lambda2)) (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 lambda1 1/2 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 lambda1 lambda1) -1/8)))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (-.f64 (sin.f64 (.f64 lambda1 1/2)) (fma.f64 1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (.f64 1/8 (.f64 (sin.f64 (.f64 lambda1 1/2)) (*.f64 lambda2 lambda2))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 2842 to 1791 computations (37% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite156.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

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

Counts

4 → 40

Calls

4 calls:

4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 2869 to 1650 computations (42.5% saved)

series208.0ms (0.5%)

Error

21.4b

Counts

4 → 42

Calls

4 calls:

28.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
27.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
25.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
25.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7177 to 4681 computations (34.8% saved)

simplify157.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
709×	`associate-r_binary64`
655×	`associate-l_binary64`
438×	`fma-neg_binary64`
350×	`cancel-sign-sub-inv_binary64`

Counts

82 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	5358
1	652	5098
2	1405	5064
3	4632	5056
4	5001	5056

prune97.0ms (0.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	43	13	56

Error

21.4b

Counts

56 → 13

Alt Table

Status	Error	Program
	38.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (*.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
✓	22.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	38.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (*.f64 lambda1 1/2)))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (.f64 lambda1 1/2)) (fma.f64 (cos.f64 (.f64 lambda1 1/2)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2)) (.f64 (.f64 (sin.f64 (.f64 lambda1 1/2)) (.f64 lambda2 lambda2)) -1/8))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	36.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (.f64 lambda1 1/2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	32.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (*.f64 -1/2 lambda2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (.f64 -1/2 lambda2)) (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 lambda1 1/2 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 lambda1 lambda1) -1/8)))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
▶	22.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 -1/2 lambda2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 3170 to 2013 computations (36.5% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
7.4b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))

rewrite215.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

21.3b

Rules

12×	`cbrt-prod_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 3683 to 2142 computations (41.8% saved)

series286.0ms (0.7%)

Error

21.4b

Counts

4 → 45

Calls

4 calls:

95.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))
32.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
31.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
30.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7569 to 4948 computations (34.6% saved)

simplify190.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

567×	`*-commutative_binary64`
520×	`distribute-rgt-in_binary64`
513×	`fma-neg_binary64`
498×	`distribute-lft-in_binary64`
433×	`fma-def_binary64`

Counts

98 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	324	5770
1	604	5516
2	1451	5379
3	3993	5361
4	4954	5361
5	5006	5361

prune504.0ms (1.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	61	9	70
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	65	18	83

Error

21.4b

Counts

83 → 18

Alt Table

Status	Error	Program
▶	22.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	32.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (*.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
✓	22.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	34.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (.f64 lambda1 1/2)) (fma.f64 (cos.f64 (.f64 lambda1 1/2)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2)) (.f64 (.f64 (sin.f64 (.f64 lambda1 1/2)) (.f64 lambda2 lambda2)) -1/8))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (.f64 lambda1 1/2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 -1/2 lambda2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (*.f64 lambda1 1/2)))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	36.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (.f64 lambda1 1/2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (+.f64 (sin.f64 (.f64 -1/2 lambda2)) (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 lambda1 1/2 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 lambda1 lambda1) -1/8)))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 4733 to 3013 computations (36.3% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.8b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite221.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

21.3b

Rules

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

Counts

4 → 40

Calls

4 calls:

4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 3269 to 1930 computations (41% saved)

series263.0ms (0.6%)

Error

21.3b

Counts

4 → 41

Calls

4 calls:

34.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
33.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
30.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
28.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7935 to 5216 computations (34.3% saved)

simplify194.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-def_binary64`
475×	`fma-neg_binary64`
298×	`cancel-sign-sub-inv_binary64`
265×	`distribute-rgt-in_binary64`
243×	`distribute-lft-in_binary64`

Counts

81 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	5885
1	658	5665
2	1648	5567
3	3686	5555
4	4985	5555
5	5077	5555

prune228.0ms (0.5%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	35	10	45
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	39	24	63

Error

21.3b

Counts

63 → 24

Alt Table

Status	Error	Program
	37.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6)) (cbrt.f64 (+.f64 (sin.f64 (.f64 -1/2 lambda2)) (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (-.f64 (.f64 lambda1 1/2) (.f64 1/48 (pow.f64 lambda1 3))) (.f64 (.f64 lambda1 lambda1) (.f64 (sin.f64 (.f64 -1/2 lambda2)) -1/8)))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (*.f64 lambda1 1/2)))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (.f64 -1/2 lambda2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (*.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	32.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (*.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
✓	22.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	33.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 lambda1 1/2))) 6))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 lambda1 1/2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (.f64 lambda1 1/2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6))) (.f64 (sin.f64 (.f64 -1/2 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) 3))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.9b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (.f64 -1/2 lambda2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	36.5b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 lambda1 1/2))) (sin.f64 (.f64 lambda1 1/2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	22.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.4b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (sin.f64 (.f64 lambda1 1/2))) (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.2b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (.f64 -1/2 lambda2)))) 6))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	33.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 -1/2 lambda2))) 6)) (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))) (.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	34.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (.f64 lambda1 1/2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (pow.f64 (cbrt.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 6) (.f64 (cos.f64 phi1) (cos.f64 phi2)) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (fma.f64 1/2 (.f64 lambda1 (cos.f64 (.f64 -1/2 lambda2))) (sin.f64 (.f64 -1/2 lambda2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 4669 to 2997 computations (35.8% saved)

regimes6.3s (14.8%)

Accuracy

Total 0.9b remaining (3.8%)

Threshold costs 0.9b (3.8%)

Compiler

Compiled 169540 to 114988 computations (32.2% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	103
1	41	103
2	51	103
3	57	103
4	60	103
5	59	103

end30.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 350 to 230 computations (34.3% saved)

sample21.7s (51.5%)

Algorithm

1×

intervals

Results

14.9s	5273×	body	1024	valid
2.3s	415×	body	2048	valid
2.3s	1269×	body	512	valid
382.0ms	399×	body	256	valid
277.0ms	644×	body	128	valid
5.0ms	2×	body	1024	invalid

Compiler

Compiled 1926 to 1326 computations (31.2% saved)

Details

analyze9.9s (23.4%)

sample673.0ms (1.6%)

simplify181.0ms (0.4%)

prune7.0ms (0%)

localize32.0ms (0.1%)

rewrite147.0ms (0.3%)

series194.0ms (0.5%)

simplify141.0ms (0.3%)

prune83.0ms (0.2%)

localize41.0ms (0.1%)

rewrite156.0ms (0.4%)

series208.0ms (0.5%)

simplify157.0ms (0.4%)

prune97.0ms (0.2%)

localize37.0ms (0.1%)

rewrite215.0ms (0.5%)

series286.0ms (0.7%)

simplify190.0ms (0.4%)

prune504.0ms (1.2%)

localize48.0ms (0.1%)

rewrite221.0ms (0.5%)

series263.0ms (0.6%)

simplify194.0ms (0.5%)

prune228.0ms (0.5%)

regimes6.3s (14.8%)

simplify6.0ms (0%)

end30.0ms (0.1%)

sample21.7s (51.5%)

Profiling