Details

analyze3.9s (19.5%)

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)

sample11.6s (57.9%)

Results

9.1s	5478×	body	1024	valid
1.2s	1337×	body	512	valid
726.0ms	193×	body	2048	valid
249.0ms	437×	body	256	valid
243.0ms	811×	body	128	valid

Compiler

Compiled 86 to 53 computations (38.4% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	32	39
2	67	39
3	132	39
4	209	39
5	322	39
6	501	39
7	666	39
8	903	39
9	1361	39
10	1522	39
11	1548	39

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

10.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

Compiler

Compiled 108 to 55 computations (49.1% saved)

localize19.0ms (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	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))
✓	2.4b	(cos.f64 (-.f64 lambda1 lambda2))
✓	2.5b	(sin.f64 (-.f64 lambda1 lambda2))

series78.0ms (0.4%)

Counts

4 → 100

Calls

4 calls:

55.0ms	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))
16.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
3.0ms	(cos.f64 (-.f64 lambda1 lambda2))

rewrite70.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

337×	`log1p-udef_binary64`
196×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
181×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	365	47
2	4961	47

Stop Event

1×	node limit

Counts

4 → 92

Calls

4 calls:

68.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
68.0ms	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))
68.0ms	(cos.f64 (-.f64 lambda1 lambda2))
68.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

845×	`cancel-sign-sub-inv_binary64`
348×	`fma-neg_binary64`
312×	`distribute-rgt-neg-in_binary64`
280×	`distribute-lft-neg-in_binary64`
252×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2419
1	638	2392
2	2123	2242

Stop Event

1×	node limit

Counts

192 → 178

prune313.0ms (1.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	158	20	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	20	179

Error

5.3b

Counts

179 → 20

Alt Table

Status	Error	Program
▶	5.6b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	31.7b	(atan2.f64 (.f64 (sin.f64 (neg.f64 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	22.6b	(atan2.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) 1) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	38.5b	(atan2.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) 1/3) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	25.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (-.f64 (cos.f64 lambda2) (.f64 lambda1 (+.f64 (.f64 (.f64 (cos.f64 lambda2) 1/2) lambda1) (sin.f64 (neg.f64 lambda2))))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.4b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	31.9b	(atan2.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	23.6b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (fma.f64 -1 (sin.f64 lambda2) (.f64 (.f64 lambda1 lambda1) (-.f64 (.f64 1/2 (sin.f64 lambda2)) (.f64 (.f64 (cos.f64 lambda2) 1/6) lambda1))))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	40.0b	(atan2.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3) 1/3) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	14.8b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	25.0b	(atan2.f64 (+.f64 (.f64 (cos.f64 phi2) (sin.f64 (neg.f64 lambda2))) (.f64 (cos.f64 phi2) (.f64 (cos.f64 (neg.f64 lambda2)) lambda1))) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	14.8b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.9b	(atan2.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) 1) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	35.4b	(atan2.f64 (.f64 (sqrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 2)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	7.9b	(atan2.f64 (.f64 (/.f64 (-.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

Compiler

Compiled 7240 to 1984 computations (72.6% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
✓	0.1b	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))
	0.2b	(fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))
	2.4b	(cos.f64 (-.f64 lambda1 lambda2))

series49.0ms (0.2%)

Counts

2 → 84

Calls

2 calls:

36.0ms

(*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))

13.0ms

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

rewrite37.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

257×	`add-sqr-sqrt_binary64`
236×	`log1p-expm1-u_binary64`
236×	`expm1-log1p-u_binary64`
235×	`add-cbrt-cube_binary64`
233×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	74
1	493	74

Stop Event

1×	node limit

Counts

2 → 29

Calls

2 calls:

36.0ms

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

36.0ms

(*.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

548×	`fma-def_binary64`
481×	`associate-l_binary64`
478×	`associate-r_binary64`
329×	`cancel-sign-sub-inv_binary64`
231×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	3513
1	324	3509
2	1065	3468
3	4874	3468

Stop Event

1×	node limit

Counts

113 → 58

prune349.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	148	7	155
Fresh	13	6	19
Picked	1	0	1
Done	0	0	0
Total	162	13	175

Error

0.0b

Counts

175 → 13

Alt Table

Status	Error	Program
	5.6b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) 1) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	17.5b	(atan2.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)))) 1) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.4b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	5.8b	(atan2.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2))) 3) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	9.5b	(cbrt.f64 (pow.f64 (atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))) 3))
	14.8b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.9b	(atan2.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	38.5b	(atan2.f64 (.f64 (pow.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3) 1/3) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	34.6b	(pow.f64 (sqrt.f64 (atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))) 2)
	0.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
▶	0.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

Compiler

Compiled 7134 to 1648 computations (76.9% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series96.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

79.0ms

(fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2)))

9.0ms

(*.f64 (cos.f64 phi1) (sin.f64 phi2))

8.0ms

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

rewrite62.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`prod-diff_binary64`
200×	`add-sqr-sqrt_binary64`
183×	`log1p-expm1-u_binary64`
183×	`expm1-log1p-u_binary64`
181×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	52
1	382	40
2	4846	40

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

61.0ms

(*.f64 (cos.f64 phi1) (sin.f64 phi2))

61.0ms

(fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2)))

60.0ms

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

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

866×	`cancel-sign-sub-inv_binary64`
375×	`fma-neg_binary64`
273×	`associate-r_binary64`
273×	`distribute-rgt-neg-in_binary64`
237×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2817
1	611	2764
2	2241	2373

Stop Event

1×	node limit

Counts

139 → 120

prune346.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	162	12	174

Error

0.0b

Counts

174 → 12

Alt Table

Status	Error	Program
▶	0.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (log1p.f64 (expm1.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	0.4b	(atan2.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2))) 3) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	5.6b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) 1) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	17.5b	(atan2.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)))) 1) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.4b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	34.2b	(atan2.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) 3) 1/3) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	4.3b	(atan2.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 phi2) 3) (pow.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) 3))) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	9.5b	(cbrt.f64 (pow.f64 (atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2)))) 3))
	10.9b	(atan2.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	34.6b	(pow.f64 (sqrt.f64 (atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))) 2)
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

Compiler

Compiled 8133 to 1933 computations (76.2% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
	0.1b	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))
✓	0.2b	(fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (log1p.f64 (expm1.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2)))
	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series82.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

82.0ms

(fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2)))

rewrite25.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
193×	`expm1-log1p-u_binary64`
192×	`log1p-expm1-u_binary64`
188×	`add-cbrt-cube_binary64`
188×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	36
1	404	24

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

25.0ms

(fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (log1p.f64 (expm1.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2)))

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
616×	`cancel-sign-sub-inv_binary64`
469×	`*-commutative_binary64`
243×	`fma-neg_binary64`
217×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	2289
1	425	2272
2	1592	1904

Stop Event

1×	node limit

Counts

71 → 56

prune321.0ms (1.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	163	12	175

Error

0.0b

Counts

175 → 12

Alt Table

Status	Error	Program
✓	0.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (log1p.f64 (expm1.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	0.4b	(atan2.f64 (pow.f64 (cbrt.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2))) 3) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	5.6b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (-.f64 (exp.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) 1) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	17.5b	(atan2.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)))) 1) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.4b	(atan2.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))
	34.2b	(atan2.f64 (pow.f64 (pow.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) 3) 1/3) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	4.3b	(atan2.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 phi2) 3) (pow.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) 3))) (fma.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	10.9b	(atan2.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) 3) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))
	13.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (fma.f64 (sin.f64 phi2) (cos.f64 phi1) (.f64 (sin.f64 phi1) (.f64 (cos.f64 lambda1) (neg.f64 (cos.f64 phi2))))))
	34.6b	(pow.f64 (sqrt.f64 (atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (neg.f64 (cos.f64 lambda1)) (sin.f64 lambda2))) (cos.f64 phi2)) (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (sin.f64 phi2))))) 2)
	10.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) 3) (.f64 (cos.f64 phi2) (neg.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (sin.f64 phi2))))

Compiler

Compiled 7893 to 1695 computations (78.5% saved)

regimes2.0s (9.9%)

Accuracy

Total 0.1b remaining (55.5%)

Threshold costs 0.1b (55.5%)

Counts

210 → 1

Compiler

Compiled 48482 to 29783 computations (38.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	65
1	43	65
2	60	65
3	71	65
4	76	65
5	77	65

Stop Event

1×

saturated

end328.0ms (1.6%)

Compiler: Compiled 580 to 349 computations (39.8% saved)

Details

analyze3.9s (19.5%)

sample11.6s (57.9%)

simplify23.0ms (0.1%)

prune4.0ms (0%)

localize19.0ms (0.1%)

series78.0ms (0.4%)

rewrite70.0ms (0.4%)

simplify56.0ms (0.3%)

prune313.0ms (1.6%)

localize27.0ms (0.1%)

series49.0ms (0.2%)

rewrite37.0ms (0.2%)

simplify88.0ms (0.4%)

prune349.0ms (1.7%)

localize28.0ms (0.1%)

series96.0ms (0.5%)

rewrite62.0ms (0.3%)

simplify56.0ms (0.3%)

prune346.0ms (1.7%)

localize30.0ms (0.1%)

series82.0ms (0.4%)

rewrite25.0ms (0.1%)

simplify45.0ms (0.2%)

prune321.0ms (1.6%)

regimes2.0s (9.9%)

simplify5.0ms (0%)

end328.0ms (1.6%)

Profiling