Details

analyze4.1s (22.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
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)

sample329.0ms (1.8%)

Algorithm

1×

intervals

Results

252.0ms	177×	body	1024	valid
27.0ms	7×	body	2048	valid
22.0ms	34×	body	512	valid
5.0ms	27×	body	128	valid
5.0ms	11×	body	256	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 84 to 51 computations (39.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	3.0b	(cos.f64 (-.f64 lambda1 lambda2))
✓	3.2b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

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

series136.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

101.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
26.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
3.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify134.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-neg_binary64`
422×	`associate-r_binary64`
380×	`associate-l_binary64`
380×	`distribute-rgt-neg-in_binary64`
340×	`distribute-lft-neg-in_binary64`

Counts

162 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	368	3902
1	782	3174
2	2633	2887
3	4652	2788
4	5011	2788

prune190.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	149	13	162
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	13	163

Error

5.6b

Counts

163 → 13

Alt Table

Status	Error	Program
	21.2b	(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)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
	15.0b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	24.3b	(atan2.f64 (.f64 (log.f64 (exp.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)))))
	23.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (+.f64 (cos.f64 lambda2) (*.f64 lambda1 (sin.f64 lambda2))))))
	12.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	22.7b	(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)))))
	13.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
▶	5.9b	(atan2.f64 (.f64 (-.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)))))
	27.5b	(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)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	36.4b	(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)))))
	13.1b	(atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.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)))))
	12.8b	(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 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
	12.6b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 3925 to 1196 computations (69.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
✓	0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

3.0ms

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

series26.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

26.0ms

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

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

545×	`fma-neg_binary64`
500×	`distribute-rgt-neg-in_binary64`
440×	`distribute-lft-neg-in_binary64`
324×	`*-commutative_binary64`
267×	`associate-l_binary64`

Counts

44 → 44

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	568
1	191	518
2	565	496
3	1518	487
4	2933	485
5	4964	485
6	4967	485
7	4892	485

prune226.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	179	9	188

Error

0.1b

Counts

188 → 9

Alt Table

Status	Error	Program
	6.2b	(atan2.f64 (.f64 (-.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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
	15.0b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.9b	(atan2.f64 (.f64 (-.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 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	24.3b	(atan2.f64 (.f64 (log.f64 (exp.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)))))
▶	0.2b	(atan2.f64 (.f64 (-.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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	11.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.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)))))
	12.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 4618 to 1146 computations (75.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
	0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
✓	0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓	0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`

Counts

2 → 50

Calls

2 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series264.0ms (1.4%)

Counts

2 → 56

Calls

2 calls:

240.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
24.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

618×	`associate-r_binary64`
563×	`associate-l_binary64`
546×	`fma-neg_binary64`
385×	`distribute-rgt-neg-in_binary64`
300×	`*-commutative_binary64`

Counts

106 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	3509
1	965	3263
2	3764	3255
3	5052	3255

prune258.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	202	6	208
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	206	11	217

Error

0.1b

Counts

217 → 11

Alt Table

Status	Error	Program
	15.0b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.6b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	5.9b	(atan2.f64 (.f64 (-.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 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	24.3b	(atan2.f64 (.f64 (log.f64 (exp.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)))))
	12.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (cos.f64 lambda1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.2b	(atan2.f64 (.f64 (-.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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
	0.5b	(atan2.f64 (.f64 (-.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 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) 3)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	1.5b	(atan2.f64 (.f64 (-.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)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	0.2b	(atan2.f64 (.f64 (-.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)) (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))

Compiler

Compiled 6413 to 1483 computations (76.9% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
	0.6b	(cbrt.f64 (sin.f64 lambda1))
	0.6b	(cbrt.f64 (sin.f64 lambda1))
✓	0.6b	(cbrt.f64 (sin.f64 lambda1))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

9.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
1.0ms	(cbrt.f64 (sin.f64 lambda1))

series455.0ms (2.5%)

Counts

2 → 24

Calls

2 calls:

231.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1)))
222.0ms	(cbrt.f64 (sin.f64 lambda1))

simplify110.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

746×	`log-prod_binary64`
734×	`fma-neg_binary64`
495×	`unswap-sqr_binary64`
480×	`fma-def_binary64`
302×	`*-commutative_binary64`

Counts

79 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	96	878
1	219	796
2	564	756
3	1359	734
4	3162	612
5	4194	612
6	4702	612
7	4878	612

prune170.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	154	11	165

Error

0.1b

Counts

165 → 11

Alt Table

Status	Error	Program
	15.0b	(atan2.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.6b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	5.9b	(atan2.f64 (.f64 (-.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 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	24.3b	(atan2.f64 (.f64 (log.f64 (exp.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)))))
	12.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (cos.f64 lambda1))))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.2b	(atan2.f64 (.f64 (-.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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (sin.f64 lambda2) (cbrt.f64 (sin.f64 lambda1))))))))
	0.5b	(atan2.f64 (.f64 (-.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 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) 3)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	1.5b	(atan2.f64 (.f64 (-.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)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
	0.2b	(atan2.f64 (.f64 (-.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)) (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))))

Compiler

Compiled 3750 to 899 computations (76% saved)

regimes1.4s (7.8%)

Accuracy

Total 0.1b remaining (53.3%)

Threshold costs 0.1b (53.3%)

Compiler

Compiled 38056 to 23251 computations (38.9% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
17×	`+-commutative_binary64`
16×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	75
1	49	75
2	73	75
3	93	75
4	122	75
5	141	75
6	151	75
7	156	75
8	157	75
9	157	75

end1.0ms (0%)

Compiler: Compiled 49 to 28 computations (42.9% saved)

sample10.1s (54.8%)

Algorithm

1×

intervals

Results

7.4s	5275×	body	1024	valid
1000.0ms	1323×	body	512	valid
578.0ms	179×	body	2048	valid
188.0ms	431×	body	256	valid
167.0ms	792×	body	128	valid

Compiler

Compiled 555 to 318 computations (42.7% saved)

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

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

Details

analyze4.1s (22.4%)

sample329.0ms (1.8%)

simplify81.0ms (0.4%)

prune3.0ms (0%)

localize21.0ms (0.1%)

rewrite24.0ms (0.1%)

series136.0ms (0.7%)

simplify134.0ms (0.7%)

prune190.0ms (1%)

localize27.0ms (0.1%)

rewrite4.0ms (0%)

series26.0ms (0.1%)

simplify107.0ms (0.6%)

prune226.0ms (1.2%)

localize26.0ms (0.1%)

rewrite15.0ms (0.1%)

series264.0ms (1.4%)

simplify103.0ms (0.6%)

prune258.0ms (1.4%)

localize31.0ms (0.2%)

rewrite12.0ms (0.1%)

series455.0ms (2.5%)

simplify110.0ms (0.6%)

prune170.0ms (0.9%)

regimes1.4s (7.8%)

simplify7.0ms (0%)

end1.0ms (0%)

sample10.1s (54.8%)

Profiling

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