Details

analyze3.4s (17.8%)

Algorithm

1×

Search

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

sample456.0ms (2.4%)

Algorithm

1×

intervals

Results

213.0ms	164×	body	1024	valid
30.0ms	43×	body	512	valid
20.0ms	5×	body	2048	valid
8.0ms	19×	body	256	valid
5.0ms	25×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify29.0ms (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

12.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.5b	(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)

localize19.0ms (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)))
✓	3.1b	(sin.f64 (-.f64 lambda1 lambda2))
✓	3.4b	(cos.f64 (-.f64 lambda1 lambda2))

series57.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

38.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
10.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (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×	`sin-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	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
3.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify120.0ms (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 → 194

Iterations

Useful iterations: 3 (0.0ms)

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

prune388.0ms (2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	177	17	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	17	195

Error

5.7b

Counts

195 → 17

Alt Table

Status	Error	Program
	13.2b	(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)))))))
	17.6b	(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 lambda2) (cos.f64 phi2)))))
	12.5b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
▶	5.9b	(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 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.5b	(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)))))
	20.3b	(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)))))
	16.3b	(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)))))
	39.8b	(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)) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (.f64 (sin.f64 lambda1) (sin.f64 (.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2))))))))
	16.2b	(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)) (-.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))))))))
	24.9b	(atan2.f64 (.f64 (fma.f64 (cos.f64 lambda2) lambda1 (.f64 (+.f64 (.f64 -1/2 (.f64 lambda1 lambda1)) 1) (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)))))
	32.7b	(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)))))
	12.7b	(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)) (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	25.2b	(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)))))
	12.7b	(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)))))
	12.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)) (cos.f64 (-.f64 lambda1 lambda2)))))
	26.6b	(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)))))
	12.5b	(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 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 8543 to 2322 computations (72.8% 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))
	0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
	0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
	3.4b	(cos.f64 (-.f64 lambda1 lambda2))

series10.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

10.0ms

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

rewrite5.0ms (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:

4.0ms

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

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-neg_binary64`
480×	`distribute-rgt-neg-in_binary64`
423×	`distribute-lft-neg-in_binary64`
325×	`*-commutative_binary64`
265×	`associate-l_binary64`

Counts

44 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	572
1	191	512
2	572	487
3	1551	483
4	3033	483
5	4866	483
6	4975	483
7	4902	483

prune433.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	191	8	199
Fresh	13	3	16
Picked	1	0	1
Done	0	0	0
Total	205	11	216

Error

0.1b

Counts

216 → 11

Alt Table

Status	Error	Program
	12.5b	(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)))))
▶	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))))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 (cbrt.f64 (sin.f64 phi2)) (cbrt.f64 (sin.f64 phi2)))) (cbrt.f64 (sin.f64 phi2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.7b	(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)))))
	5.9b	(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 (sin.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	40.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (exp.f64 (+.f64 (log.f64 (cos.f64 phi1)) (log.f64 (sin.f64 phi2)))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log1p.f64 (expm1.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 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	35.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (sqrt.f64 (sin.f64 phi2))) (sqrt.f64 (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (sin.f64 phi2) (sin.f64 phi2)) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 9126 to 2054 computations (77.5% saved)

localize29.0ms (0.2%)

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 phi2) (sin.f64 phi1))
✓	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)))

series126.0ms (0.7%)

Counts

4 → 128

Calls

4 calls:

55.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
52.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
29×	`pow1_binary64`
16×	`cbrt-unprod_binary64`
16×	`prod-exp_binary64`

Counts

4 → 89

Calls

4 calls:

7.0ms	(.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))
3.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))

simplify147.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-l_binary64`
674×	`cancel-sign-sub-inv_binary64`
640×	`fma-neg_binary64`
385×	`distribute-rgt-neg-in_binary64`
371×	`*-commutative_binary64`

Counts

217 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	374	5026
1	1085	4513
2	3017	4500
3	4823	4490
4	4980	4490

prune638.0ms (3.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	251	5	256
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	252	15	267

Error

0.1b

Counts

267 → 15

Alt Table

Status	Error	Program
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.9b	(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 (log.f64 (exp.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))))))
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.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 (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 (.f64 (cos.f64 phi2) (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1)))) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	12.5b	(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)))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 (cbrt.f64 (sin.f64 phi2)) (cbrt.f64 (sin.f64 phi2)))) (cbrt.f64 (sin.f64 phi2))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.7b	(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)))))
	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 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	5.9b	(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 (sin.f64 phi1) (.f64 (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 (pow.f64 (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))) 3)))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (sin.f64 phi2) (sin.f64 phi2)) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)) (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)))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
	40.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (exp.f64 (+.f64 (log.f64 (cos.f64 phi1)) (log.f64 (sin.f64 phi2)))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	35.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (sqrt.f64 (sin.f64 phi2))) (sqrt.f64 (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 15264 to 3106 computations (79.7% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (cos.f64 phi2) (sin.f64 phi1))
✓	0.2b	(.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2))))
✓	0.2b	(.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))
✓	26.0b	(cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))) 3))

series127.0ms (0.7%)

Counts

3 → 132

Calls

3 calls:

52.0ms

(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))) 3))

50.0ms

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

26.0ms

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

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
17×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 65

Calls

3 calls:

7.0ms

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

5.0ms

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

3.0ms

(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda2) (cos.f64 phi2)))) 3))

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1000×	`fma-neg_binary64`
784×	`cancel-sign-sub-inv_binary64`
485×	`associate-r_binary64`
348×	`associate-l_binary64`
348×	`distribute-rgt-neg-in_binary64`

Counts

197 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	4842
1	687	4766
2	2424	4476
3	4301	4470
4	5107	4470

prune599.0ms (3.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	185	14	199

Error

0.1b

Counts

199 → 14

Alt Table

Status	Error	Program
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (log1p.f64 (expm1.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	0.9b	(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 (log.f64 (exp.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))))))
	5.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (expm1.f64 (log1p.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 (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 (.f64 (cos.f64 phi2) (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1)))) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	12.5b	(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)))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 (cbrt.f64 (sin.f64 phi2)) (cbrt.f64 (sin.f64 phi2)))) (cbrt.f64 (sin.f64 phi2))) (.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 (pow.f64 (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))))) 3)))))
	12.7b	(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)))))
	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 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	5.9b	(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 (sin.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
	40.9b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (exp.f64 (+.f64 (log.f64 (cos.f64 phi1)) (log.f64 (sin.f64 phi2)))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	35.1b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 phi1) (sqrt.f64 (sin.f64 phi2))) (sqrt.f64 (sin.f64 phi2))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.0b	(atan2.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1)) (.f64 (.f64 (sin.f64 phi2) (sin.f64 phi2)) (sin.f64 phi2)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 11118 to 2531 computations (77.2% saved)

regimes1.8s (9.5%)

Accuracy

Total 0.1b remaining (57.2%)

Threshold costs 0.1b (57.2%)

Counts

203 → 1

Compiler

Compiled 55153 to 30889 computations (44% saved)

simplify6.0ms (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	27	73
1	43	73
2	60	73
3	85	73
4	110	73
5	129	73
6	140	73
7	146	73
8	148	73
9	148	73

end1.0ms (0%)

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

sample10.5s (54.4%)

Algorithm

1×

intervals

Results

7.7s	5367×	body	1024	valid
979.0ms	1312×	body	512	valid
669.0ms	183×	body	2048	valid
180.0ms	764×	body	128	valid
179.0ms	374×	body	256	valid

Compiler

Compiled 672 to 398 computations (40.8% 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

analyze3.4s (17.8%)

sample456.0ms (2.4%)

simplify29.0ms (0.1%)

prune3.0ms (0%)

localize19.0ms (0.1%)

series57.0ms (0.3%)

rewrite23.0ms (0.1%)

simplify120.0ms (0.6%)

prune388.0ms (2%)

localize28.0ms (0.1%)

series10.0ms (0.1%)

rewrite5.0ms (0%)

simplify91.0ms (0.5%)

prune433.0ms (2.2%)

localize29.0ms (0.2%)

series126.0ms (0.7%)

rewrite26.0ms (0.1%)

simplify147.0ms (0.8%)

prune638.0ms (3.3%)

localize34.0ms (0.2%)

series127.0ms (0.7%)

rewrite18.0ms (0.1%)

simplify139.0ms (0.7%)

prune599.0ms (3.1%)

regimes1.8s (9.5%)

simplify6.0ms (0%)

end1.0ms (0%)

sample10.5s (54.4%)

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