Details

analyze3.8s (16.2%)

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)

sample330.0ms (1.4%)

Algorithm

1×

intervals

Results

256.0ms	181×	body	1024	valid
35.0ms	39×	body	512	valid
15.0ms	5×	body	2048	valid
5.0ms	25×	body	128	valid
4.0ms	6×	body	256	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify33.0ms (0.1%)

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 → 2

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

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

12.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	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)) (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
✓	0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
✓	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
✓	2.4b	(cos.f64 (-.f64 lambda1 lambda2))
✓	2.5b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite25.0ms (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:

6.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series161.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

123.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
29.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify136.0ms (0.6%)

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 → 276

Iterations

Useful iterations: 3 (0.0ms)

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

prune402.0ms (1.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	260	16	276
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	16	277

Error

6.1b

Counts

277 → 16

Alt Table

Status	Error	Program
	24.5b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (.f64 (cbrt.f64 lambda2) (.f64 (cbrt.f64 lambda2) (cbrt.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)))))
▶	6.4b	(atan2.f64 (.f64 (-.f64 (.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)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.0b	(atan2.f64 (.f64 (log1p.f64 (expm1.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)))))
	16.4b	(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 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1))))))))
	25.5b	(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)))))
	24.1b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (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)))))
	39.3b	(atan2.f64 (.f64 (exp.f64 (log.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)))))
	22.4b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (cos.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 lambda2 1)))) (.f64 (cos.f64 (fma.f64 (.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (.f64 lambda2 1)))) (sin.f64 (fma.f64 (neg.f64 lambda2) 1 (.f64 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)))))
	14.3b	(atan2.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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)))))
	11.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))))))
	17.1b	(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 lambda1) (cos.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (.f64 (sin.f64 lambda1) (sin.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))))))
	12.4b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 (-.f64 lambda1 lambda2)))))))
	43.1b	(atan2.f64 (.f64 (+.f64 (.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (.f64 (sqrt.f64 lambda2) (sqrt.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 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.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 (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 8614 to 2364 computations (72.6% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.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)))
	2.4b	(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))

series31.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

31.0ms

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

simplify108.0ms (0.5%)

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 → 64

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

prune492.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	282	7	289
Fresh	12	3	15
Picked	1	0	1
Done	0	0	0
Total	295	10	305

Error

0.1b

Counts

305 → 10

Alt Table

Status	Error	Program
	37.7b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sqrt.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (sqrt.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)))))
	12.0b	(atan2.f64 (.f64 (log1p.f64 (expm1.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)))))
	6.4b	(atan2.f64 (.f64 (-.f64 (.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 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.6b	(atan2.f64 (.f64 (-.f64 (.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 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	39.3b	(atan2.f64 (.f64 (exp.f64 (log.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)))))
	6.4b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda1))) (.f64 (cbrt.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 (-.f64 (.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 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.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 (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))))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	6.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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)))))

Compiler

Compiled 8931 to 2045 computations (77.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cbrt-cube_binary64`
26×	`add-exp-log_binary64`
26×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

3 → 69

Calls

3 calls:

10.0ms

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

6.0ms

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

4.0ms

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

series379.0ms (1.6%)

Counts

3 → 104

Calls

3 calls:

180.0ms

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

171.0ms

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

28.0ms

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

simplify126.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

845×	`associate-r_binary64`
662×	`associate-l_binary64`
600×	`fma-neg_binary64`
545×	`distribute-rgt-neg-in_binary64`
342×	`*-commutative_binary64`

Counts

173 → 321

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	4454
1	1008	3995
2	3754	3987
3	5368	3987

prune524.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	378	7	385
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	382	13	395

Error

0.1b

Counts

395 → 13

Alt Table

Status	Error	Program
	12.0b	(atan2.f64 (.f64 (log1p.f64 (expm1.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)))))
	6.4b	(atan2.f64 (.f64 (-.f64 (.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 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.6b	(atan2.f64 (.f64 (-.f64 (.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 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	39.3b	(atan2.f64 (.f64 (exp.f64 (log.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)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cbrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	35.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sqrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (sqrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))))))
	6.9b	(atan2.f64 (.f64 (-.f64 (.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 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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 (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))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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 (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))))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
▶	0.2b	(atan2.f64 (.f64 (-.f64 (.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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

Compiler

Compiled 12831 to 2615 computations (79.6% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
	0.2b	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
	0.2b	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
✓	28.0b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite57.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`associate-*r/_binary64`
12×	`sin-mult_binary64`
7×	`cbrt-div_binary64`
5×	`associate-*l/_binary64`
5×	`frac-times_binary64`

Counts

1 → 19

Calls

1 calls:

54.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series177.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

176.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify110.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
458×	`cancel-sign-sub-inv_binary64`
358×	`associate-r_binary64`
295×	`associate-l_binary64`
250×	`sub-neg_binary64`

Counts

67 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2605
1	475	2133
2	1704	1950
3	4337	1950
4	5032	1950

prune996.0ms (4.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	1123	0	1123
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	1123	13	1136

Error

0.1b

Counts

1136 → 13

Alt Table

Status	Error	Program
	12.0b	(atan2.f64 (.f64 (log1p.f64 (expm1.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)))))
	6.4b	(atan2.f64 (.f64 (-.f64 (.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 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	7.6b	(atan2.f64 (.f64 (-.f64 (.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 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	39.3b	(atan2.f64 (.f64 (exp.f64 (log.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)))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cbrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	35.5b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sqrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (sqrt.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (.f64 (cbrt.f64 (sin.f64 lambda1)) (sin.f64 lambda2)))))))
	6.9b	(atan2.f64 (.f64 (-.f64 (.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 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)))) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))) (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))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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 (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))))))
	0.2b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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 (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))))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (exp.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
✓	0.2b	(atan2.f64 (.f64 (-.f64 (.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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

Compiler

Compiled 21057 to 3296 computations (84.3% saved)

regimes1.8s (7.7%)

Accuracy

Total 0.1b remaining (43.6%)

Threshold costs 0.1b (43.6%)

Compiler

Compiled 48916 to 27842 computations (43.1% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
16×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	73
1	44	73
2	61	73
3	87	73
4	120	73
5	138	73
6	148	73
7	151	73
8	150	73

end1.0ms (0%)

Compiler: Compiled 48 to 25 computations (47.9% saved)

sample13.8s (58.3%)

Algorithm

1×

intervals

Results

10.1s	5313×	body	1024	valid
1.3s	1289×	body	512	valid
821.0ms	185×	body	2048	valid
250.0ms	834×	body	128	valid
240.0ms	379×	body	256	valid

Compiler

Compiled 706 to 376 computations (46.7% 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

analyze3.8s (16.2%)

sample330.0ms (1.4%)

simplify33.0ms (0.1%)

prune3.0ms (0%)

localize20.0ms (0.1%)

rewrite25.0ms (0.1%)

series161.0ms (0.7%)

simplify136.0ms (0.6%)

prune402.0ms (1.7%)

localize31.0ms (0.1%)

rewrite4.0ms (0%)

series31.0ms (0.1%)

simplify108.0ms (0.5%)

prune492.0ms (2.1%)

localize29.0ms (0.1%)

rewrite24.0ms (0.1%)

series379.0ms (1.6%)

simplify126.0ms (0.5%)

prune524.0ms (2.2%)

localize35.0ms (0.1%)

rewrite57.0ms (0.2%)

series177.0ms (0.7%)

simplify110.0ms (0.5%)

prune996.0ms (4.2%)

regimes1.8s (7.7%)

simplify7.0ms (0%)

end1.0ms (0%)

sample13.8s (58.3%)

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