Details

analyze9.9s (20.8%)

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)

sample1.0s (2.2%)

Algorithm

1×

intervals

Results

829.0ms	166×	body	1024	valid
71.0ms	14×	body	2048	valid
67.0ms	42×	body	512	valid
18.0ms	15×	body	256	valid
8.0ms	19×	body	128	valid

Compiler

Compiled 146 to 98 computations (32.9% saved)

simplify179.0ms (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

prune9.0ms (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)

localize34.0ms (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))

rewrite452.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

21.7b

Rules

28×	`sin-diff_binary64`
28×	`div-sub_binary64`
20×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 140

Calls

4 calls:

15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
13.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 8060 to 4740 computations (41.2% saved)

series237.0ms (0.5%)

Error

21.4b

Counts

4 → 42

Calls

4 calls:

34.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
29.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
26.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
26.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 6985 to 4489 computations (35.7% saved)

simplify223.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
548×	`sub-neg_binary64`
441×	`fma-neg_binary64`
295×	`neg-mul-1_binary64`
271×	`fma-def_binary64`

Counts

182 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	3182
1	246	3038
2	680	2940
3	1860	2900
4	3957	2896
5	4625	2896
6	4895	2896
7	4982	2896
8	4861	2896

prune296.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	53	13	66
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	54	14	68

Error

21.6b

Counts

68 → 14

Alt Table

Status	Error	Program
	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)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (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 (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)))))))
	25.0b	(.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 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	23.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	23.3b	(.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)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (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 (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (.f64 1/2 lambda1))) (.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)))))))
	22.6b	(.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 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (*.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2)))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 1/2 lambda1 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (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 (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)))))))
	25.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	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 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (*.f64 1/2 lambda1))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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 (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (.f64 1/2 lambda1))) (.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)))))))
▶	22.3b	(.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)))))))))
	37.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 lambda1)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1)))) (.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 7267 to 4598 computations (36.7% saved)

localize36.0ms (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))

rewrite657.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

28×	`sin-diff_binary64`
28×	`div-sub_binary64`
20×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 140

Calls

4 calls:

15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
14.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 8270 to 4950 computations (40.1% saved)

series271.0ms (0.6%)

Error

21.3b

Counts

4 → 42

Calls

4 calls:

30.0ms	(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))
26.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7177 to 4681 computations (34.8% saved)

simplify217.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
548×	`sub-neg_binary64`
441×	`fma-neg_binary64`
295×	`neg-mul-1_binary64`
271×	`fma-def_binary64`

Counts

182 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	3182
1	246	3038
2	680	2940
3	1860	2900
4	3957	2896
5	4625	2896
6	4895	2896
7	4982	2896
8	4861	2896

prune399.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	67	13	80

Error

21.6b

Counts

80 → 13

Alt Table

Status	Error	Program
	25.0b	(.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 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	23.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	23.3b	(.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)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (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 (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (.f64 1/2 lambda1))) (.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)))))))
	22.6b	(.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 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (*.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2)))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 1/2 lambda1 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (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 (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)))))))
	25.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (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 (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)))))))))
	38.4b	(.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)) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (*.f64 1/2 lambda1)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 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 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (*.f64 1/2 lambda1))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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)))))))
	37.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 lambda1)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1)))) (.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 7259 to 4638 computations (36.1% saved)

localize43.0ms (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))

rewrite972.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

28×	`sin-diff_binary64`
28×	`div-sub_binary64`
20×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 140

Calls

4 calls:

361.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
19.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
14.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 8480 to 5160 computations (39.2% saved)

series333.0ms (0.7%)

Error

21.3b

Counts

4 → 42

Calls

4 calls:

35.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
34.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
33.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
31.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7369 to 4873 computations (33.9% saved)

simplify217.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
548×	`sub-neg_binary64`
441×	`fma-neg_binary64`
295×	`neg-mul-1_binary64`
271×	`fma-def_binary64`

Counts

182 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	3182
1	246	3038
2	680	2940
3	1860	2900
4	3957	2896
5	4625	2896
6	4895	2896
7	4982	2896
8	4861	2896

prune376.0ms (0.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	65	14	79

Error

21.6b

Counts

79 → 14

Alt Table

Status	Error	Program
	23.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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)))))))
	37.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (+.f64 (.f64 (cos.f64 (.f64 1/2 lambda1)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1)))) (.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)))))))
	23.3b	(.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)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (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 (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (.f64 1/2 lambda1))) (.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)))))))
	22.6b	(.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 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (*.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2)))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.0b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 1/2 lambda1 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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)))))))
	25.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (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 (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)))))))
	23.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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)))))))
	25.0b	(.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 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))))
	38.4b	(.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)) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (*.f64 1/2 lambda1)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 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 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (*.f64 1/2 lambda1))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 7559 to 4890 computations (35.3% saved)

localize46.0ms (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))

rewrite622.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

21.4b

Rules

28×	`sin-diff_binary64`
28×	`div-sub_binary64`
20×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 140

Calls

4 calls:

17.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
16.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
15.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
14.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 8900 to 5580 computations (37.3% saved)

series290.0ms (0.6%)

Error

21.3b

Counts

4 → 42

Calls

4 calls:

33.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
33.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
32.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
30.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7753 to 5257 computations (32.2% saved)

simplify218.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
548×	`sub-neg_binary64`
441×	`fma-neg_binary64`
295×	`neg-mul-1_binary64`
271×	`fma-def_binary64`

Counts

182 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	90	3182
1	246	3038
2	680	2940
3	1860	2900
4	3957	2896
5	4625	2896
6	4895	2896
7	4982	2896
8	4861	2896

prune341.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Error

21.6b

Counts

80 → 12

Alt Table

Status	Error	Program
	25.0b	(.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 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	23.3b	(.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)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2))) (sqrt.f64 (-.f64 1 (fma.f64 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	37.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (cos.f64 (.f64 -1/2 lambda2)) (fma.f64 1/2 lambda1 (.f64 (pow.f64 lambda1 3) -1/48)) (.f64 (+.f64 1 (.f64 (.f64 lambda1 lambda1) -1/8)) (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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))
	38.4b	(.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)) (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (*.f64 1/2 lambda1)))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))))
	25.6b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) 3) (pow.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2))) 3)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (sin.f64 (/.f64 lambda1 2)) (.f64 (cos.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda2 2)))) (.f64 (sin.f64 (/.f64 lambda2 2)) (.f64 (cos.f64 (/.f64 lambda1 2)) (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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)))))))
	35.8b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 1/2 (.f64 (cos.f64 (.f64 -1/2 lambda2)) lambda1) (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 (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)))))))
	23.1b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 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 (log.f64 (+.f64 (expm1.f64 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) 1)) (.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)))))))))
	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 (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1)))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (*.f64 1/2 lambda1))))) (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 (.f64 1/2 lambda1)) (fma.f64 1/48 (pow.f64 lambda2 3) (.f64 -1/2 lambda2))) (.f64 (+.f64 (.f64 (.f64 lambda2 lambda2) -1/8) 1) (sin.f64 (.f64 1/2 lambda1)))) (.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)))))))
	36.3b	(.f64 R (.f64 2 (atan2.f64 (sqrt.f64 (fma.f64 (fma.f64 -1/2 (.f64 lambda2 (cos.f64 (.f64 1/2 lambda1))) (sin.f64 (.f64 1/2 lambda1))) (.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)))))))
	22.6b	(.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 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2)) (neg.f64 (*.f64 (sin.f64 (/.f64 lambda2 2)) (cos.f64 (/.f64 lambda1 2)))))) (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2)))))))

Compiler

Compiled 6452 to 4199 computations (34.9% saved)

regimes8.9s (18.5%)

Accuracy

Total 0.7b remaining (2.8%)

Threshold costs 0.7b (2.8%)

Compiler

Compiled 266764 to 184948 computations (30.7% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	30	103
1	43	103
2	53	103
3	59	103
4	62	103
5	61	103

end32.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 350 to 230 computations (34.3% saved)

sample21.5s (44.9%)

Algorithm

1×

intervals

Results

15.2s	5273×	body	1024	valid
2.2s	415×	body	2048	valid
2.1s	1269×	body	512	valid
398.0ms	644×	body	128	valid
372.0ms	399×	body	256	valid
5.0ms	2×	body	1024	invalid

Compiler

Compiled 1221 to 853 computations (30.1% saved)

Details

analyze9.9s (20.8%)

sample1.0s (2.2%)

simplify179.0ms (0.4%)

prune9.0ms (0%)

localize34.0ms (0.1%)

rewrite452.0ms (0.9%)

series237.0ms (0.5%)

simplify223.0ms (0.5%)

prune296.0ms (0.6%)

localize36.0ms (0.1%)

rewrite657.0ms (1.4%)

series271.0ms (0.6%)

simplify217.0ms (0.5%)

prune399.0ms (0.8%)

localize43.0ms (0.1%)

rewrite972.0ms (2%)

series333.0ms (0.7%)

simplify217.0ms (0.5%)

prune376.0ms (0.8%)

localize46.0ms (0.1%)

rewrite622.0ms (1.3%)

series290.0ms (0.6%)

simplify218.0ms (0.5%)

prune341.0ms (0.7%)

regimes8.9s (18.5%)

simplify6.0ms (0%)

end32.0ms (0.1%)

sample21.5s (44.9%)

Profiling