Details

analyze3.9s (19.1%)

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)

sample11.4s (56.3%)

Results

8.9s	5521×	body	1024	valid
1.3s	1392×	body	512	valid
730.0ms	176×	body	2048	valid
252.0ms	385×	body	256	valid
247.0ms	782×	body	128	valid

Compiler

Compiled 58 to 36 computations (37.9% saved)

preprocess56.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

848×	`fma-neg_binary64`
807×	`fma-def_binary64`
360×	`cancel-sign-sub-inv_binary64`
209×	`sub-neg_binary64`
190×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	273
1	163	273
2	376	273
3	798	273
4	1264	273
5	1906	273
6	2810	273
7	3765	273
8	4582	273
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 28 to 17 computations (39.3% 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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

12.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.2b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 108 to 55 computations (49.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	4.1b	(sin.f64 (-.f64 lambda1 lambda2))
✓	4.1b	(cos.f64 (-.f64 lambda1 lambda2))

series53.0ms (0.3%)

Counts

4 → 88

Calls

30 calls:

4.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))	lambda1	-inf
4.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))	phi1	-inf
3.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))	phi2	-inf
3.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))	lambda2	-inf
3.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))	lambda2	inf

rewrite61.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

315×	`expm1-udef_binary64`
315×	`log1p-udef_binary64`
173×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	321	36
2	4350	36

Stop Event

1×	node limit

Counts

4 → 86

simplify47.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

873×	`cancel-sign-sub-inv_binary64`
358×	`distribute-rgt-neg-in_binary64`
356×	`fma-neg_binary64`
340×	`distribute-lft-neg-in_binary64`
268×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	1845
1	603	1774
2	2087	1605

Stop Event

1×	node limit

Counts

174 → 165

prune406.0ms (2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	147	18	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	18	166

Error

5.8b

Counts

166 → 18

Alt Table

Status	Error	Program
	24.2b	(atan2.f64 (.f64 (-.f64 (sin.f64 lambda1) (.f64 lambda2 (cos.f64 lambda1))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	20.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (sqrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 2))))
	31.2b	(atan2.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.f64 (+.f64 (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)))))))))
	21.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (sin.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)))))
	25.7b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (.f64 (+.f64 (.f64 -1/2 (.f64 lambda1 lambda1)) 1) (neg.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	6.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.7b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	10.7b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	33.9b	(atan2.f64 (.f64 (sin.f64 (neg.f64 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.9b	(atan2.f64 (.f64 (-.f64 (sin.f64 lambda1) (.f64 lambda2 (+.f64 (cos.f64 lambda1) (.f64 (.f64 1/2 (sin.f64 lambda1)) lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	19.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (neg.f64 lambda2))))))
	13.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) 1) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	20.9b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	22.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
	32.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 phi1 (cos.f64 phi2)))))
	12.2b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 6739 to 2010 computations (70.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))
	0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	4.1b	(cos.f64 (-.f64 lambda1 lambda2))

series37.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

5.0ms	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))	lambda2	-inf
5.0ms	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))	lambda1	inf
5.0ms	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))	phi2	-inf
5.0ms	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))	phi2	inf
5.0ms	(.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2))	lambda1	-inf

rewrite42.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`prod-diff_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
149×	`fma-def_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	260	21
2	3254	21

Stop Event

1×	node limit

Counts

1 → 19

simplify45.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
469×	`associate-l_binary64`
464×	`associate-r_binary64`
409×	`sub-neg_binary64`
329×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	1065
1	298	1061
2	1023	1020
3	4768	1020

Stop Event

1×	node limit

Counts

55 → 46

prune336.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	14	3	17
Picked	1	0	1
Done	0	0	0
Total	180	9	189

Error

0.1b

Counts

189 → 9

Alt Table

Status	Error	Program
	6.1b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	10.7b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	20.9b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	6.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.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)))))))))
	38.9b	(atan2.f64 (log.f64 (pow.f64 (exp.f64 (cos.f64 phi2)) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.7b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.9b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) 1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 7641 to 1842 computations (75.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series79.0ms (0.4%)

Counts

2 → 56

Calls

18 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))	phi1	inf
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))	phi2	inf
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))	lambda2	inf
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))	phi2	-inf
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))	phi1	-inf

rewrite51.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

698×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`
148×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	306	24
2	3992	24

Stop Event

1×	node limit

Counts

2 → 39

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

413×	`fma-neg_binary64`
374×	`associate-r_binary64`
321×	`associate--l+_binary64`
315×	`distribute-rgt-neg-in_binary64`
297×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	194	2127
1	658	2042
2	2579	1864

Stop Event

1×	node limit

Counts

95 → 90

prune323.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	168	9	177

Error

0.0b

Counts

177 → 9

Alt Table

Status	Error	Program
	34.6b	(atan2.f64 (log1p.f64 (expm1.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
▶	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)) (-.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	20.9b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	1.0b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 phi2)) (cos.f64 phi1))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.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)))))))))
	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	10.7b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.9b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) 1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 8645 to 2097 computations (75.7% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
✓	0.3b	(pow.f64 (cos.f64 phi1) 3)
✓	0.4b	(pow.f64 (sin.f64 phi2) 3)
✓	21.4b	(cbrt.f64 (*.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3)))

series20.0ms (0.1%)

Counts

3 → 32

Calls

12 calls:

3.0ms	(pow.f64 (cos.f64 phi1) 3)	phi1	inf
2.0ms	(pow.f64 (cos.f64 phi1) 3)	phi1	-inf
2.0ms	(pow.f64 (sin.f64 phi2) 3)	phi2	inf
2.0ms	(pow.f64 (sin.f64 phi2) 3)	phi2	-inf
2.0ms	(cbrt.f64 (*.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3)))	phi2	0

rewrite44.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

813×	`log1p-expm1-u_binary64`
813×	`expm1-log1p-u_binary64`
95×	`add-sqr-sqrt_binary64`
89×	`add-cbrt-cube_binary64`
87×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	203	20
2	2313	20

Stop Event

1×	node limit

Counts

3 → 70

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-neg_binary64`
360×	`*-commutative_binary64`
258×	`distribute-lft-neg-in_binary64`
258×	`distribute-rgt-neg-in_binary64`
238×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	444
1	204	414
2	636	381
3	2268	377
4	4968	377

Stop Event

1×	node limit

Counts

102 → 98

prune367.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	152	9	161

Error

0.0b

Counts

161 → 9

Alt Table

Status	Error	Program
	34.6b	(atan2.f64 (log1p.f64 (expm1.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
✓	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)) (-.f64 (cbrt.f64 (.f64 (pow.f64 (sin.f64 phi2) 3) (pow.f64 (cos.f64 phi1) 3))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	20.9b	(atan2.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (sin.f64 (-.f64 lambda1 lambda2)))) 1) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2))) 3) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	1.0b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 phi2)) (cos.f64 phi1))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.2b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (/.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)))))))))
	0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (fma.f64 (cos.f64 lambda1) (cos.f64 lambda2) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	10.7b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.9b	(atan2.f64 (.f64 (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) 1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 7920 to 2175 computations (72.5% saved)

regimes2.5s (12.2%)

Accuracy

Total 0.3b remaining (79.1%)

Threshold costs 0.3b (79.1%)

Counts

261 → 1

Compiler

Compiled 63780 to 40211 computations (37% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	81
1	49	81
2	65	81
3	89	81
4	118	81
5	134	81
6	145	81
7	149	81

Stop Event

1×

saturated

end277.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 544 to 301 computations (44.7% saved)

Details

analyze3.9s (19.1%)

sample11.4s (56.3%)

preprocess56.0ms (0.3%)

simplify23.0ms (0.1%)

prune3.0ms (0%)

localize20.0ms (0.1%)

series53.0ms (0.3%)

rewrite61.0ms (0.3%)

simplify47.0ms (0.2%)

prune406.0ms (2%)

localize26.0ms (0.1%)

series37.0ms (0.2%)

rewrite42.0ms (0.2%)

simplify45.0ms (0.2%)

prune336.0ms (1.7%)

localize29.0ms (0.1%)

series79.0ms (0.4%)

rewrite51.0ms (0.3%)

simplify52.0ms (0.3%)

prune323.0ms (1.6%)

localize32.0ms (0.2%)

series20.0ms (0.1%)

rewrite44.0ms (0.2%)

simplify59.0ms (0.3%)

prune367.0ms (1.8%)

regimes2.5s (12.2%)

simplify5.0ms (0%)

end277.0ms (1.4%)

Profiling