Details

analyze3.9s (18.2%)

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)

sample319.0ms (1.5%)

Algorithm

1×

intervals

Results

244.0ms	174×	body	1024	valid
33.0ms	40×	body	512	valid
14.0ms	5×	body	2048	valid
8.0ms	17×	body	256	valid
4.0ms	20×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify33.0ms (0.2%)

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

13.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.0b	(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 84 to 51 computations (39.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.6b	(sin.f64 (-.f64 lambda1 lambda2))
4.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite187.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

6.8b

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

Compiler

Compiled 3500 to 635 computations (81.9% saved)

series217.0ms (1%)

Error

9.8b

Counts

4 → 66

Calls

4 calls:

62.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
42.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
18.0ms	(sin.f64 (-.f64 lambda1 lambda2))
18.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4850 to 2306 computations (52.5% saved)

simplify179.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-neg_binary64`
494×	`associate-r_binary64`
450×	`associate-l_binary64`
314×	`*-commutative_binary64`
260×	`sub-neg_binary64`

Counts

156 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	491	5705
1	1086	4959
2	3641	4839
3	4819	4835
4	4975	4835

prune134.0ms (0.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	101	20	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	20	122

Error

6.8b

Counts

122 → 20

Alt Table

Status	Error	Program
	36.5b	(atan2.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	21.1b	(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)) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1)))))
	13.2b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	27.7b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (fma.f64 (cos.f64 phi2) (.f64 (sin.f64 phi1) (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (.f64 lambda2 lambda2)))) -1/2))))
	18.4b	(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)) (cos.f64 lambda1))))
	15.9b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	31.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 1/6 (.f64 (sin.f64 (neg.f64 lambda2)) (pow.f64 lambda1 3)))) (-.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (+.f64 (cos.f64 lambda2) (.f64 lambda1 (sin.f64 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 1/2 (.f64 (cos.f64 lambda2) (.f64 lambda1 lambda1))))))))
	13.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (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)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 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 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))) 3))))
	27.4b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (fma.f64 1/6 (.f64 (cos.f64 lambda1) (pow.f64 lambda2 3)) (sin.f64 lambda1)) (fma.f64 lambda2 (cos.f64 lambda1) (.f64 1/2 (.f64 lambda2 (.f64 lambda2 (sin.f64 lambda1))))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	7.1b	(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)))))
	27.6b	(atan2.f64 (.f64 (cos.f64 phi2) (fma.f64 lambda1 (cos.f64 lambda2) (sin.f64 (neg.f64 lambda2)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (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 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	31.0b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (neg.f64 lambda2))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))))
	22.0b	(atan2.f64 (log.f64 (pow.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)))))
	32.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (fma.f64 (cos.f64 phi2) (.f64 phi1 (cos.f64 (-.f64 lambda1 lambda2))) (.f64 (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (.f64 (cos.f64 phi2) (pow.f64 phi1 3))) -1/6))))
	27.0b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (sin.f64 lambda1) (fma.f64 lambda2 (cos.f64 lambda1) (.f64 1/2 (.f64 lambda2 (.f64 lambda2 (sin.f64 lambda1))))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))))
	29.5b	(atan2.f64 (.f64 (cos.f64 phi2) (+.f64 (fma.f64 lambda1 (cos.f64 lambda2) (fma.f64 -1 (sin.f64 lambda2) (.f64 1/2 (.f64 (.f64 lambda1 lambda1) (sin.f64 lambda2))))) (.f64 -1/6 (.f64 (cos.f64 lambda2) (pow.f64 lambda1 3))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.9b	(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)))))

Compiler

Compiled 3619 to 1335 computations (63.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite181.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 86

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
3.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 3431 to 588 computations (82.9% saved)

series222.0ms (1%)

Error

6.1b

Counts

4 → 55

Calls

4 calls:

65.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
24.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
22.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
19.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4982 to 2499 computations (49.8% saved)

simplify232.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

843×	`fma-neg_binary64`
484×	`associate-r_binary64`
443×	`associate-l_binary64`
291×	`*-commutative_binary64`
239×	`sub-neg_binary64`

Counts

141 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	474	5129
1	1095	4629
2	3548	4567
3	4743	4499
4	4961	4499
5	4995	4499
6	4919	4499

prune140.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	13	6	19
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Error

0.1b

Counts

120 → 10

Alt Table

Status	Error	Program
	36.5b	(atan2.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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))))))
	13.2b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	15.9b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.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 (log.f64 (pow.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)))))
	7.1b	(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)) (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 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (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))))))
	7.2b	(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 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))) 3))))
	15.9b	(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)))))

Compiler

Compiled 2979 to 874 computations (70.7% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
0.2b	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite206.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
7.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3985 to 482 computations (87.9% saved)

series268.0ms (1.2%)

Error

0.1b

Counts

4 → 61

Calls

4 calls:

79.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
69.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
23.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
22.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 7308 to 3186 computations (56.4% saved)

simplify294.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

815×	`associate-r_binary64`
644×	`associate-l_binary64`
478×	`fma-neg_binary64`
343×	`fma-def_binary64`
279×	`cancel-sign-sub-inv_binary64`

Counts

150 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	447	6936
1	1331	6078
2	4582	6074
3	5005	6074

prune146.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Error

0.1b

Counts

107 → 11

Alt Table

Status	Error	Program
	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)))) (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) 3)))))
	13.2b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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)))) (log.f64 (pow.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))))))
	15.9b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	36.5b	(atan2.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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 (log.f64 (pow.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)))))
	7.1b	(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)) (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 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	15.9b	(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 (.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1))) (cbrt.f64 (cos.f64 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.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)) (+.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) 3)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 3886 to 1067 computations (72.5% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.3b	(log.f64 (pow.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (sin.f64 phi1))))

rewrite239.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
17×	`pow1_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`

Counts

4 → 84

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
7.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
4.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
3.0ms	(log.f64 (pow.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (sin.f64 phi1))))

Compiler

Compiled 4095 to 530 computations (87.1% saved)

series424.0ms (2%)

Error

0.1b

Counts

4 → 61

Calls

4 calls:

193.0ms	(log.f64 (pow.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (cos.f64 phi2) (sin.f64 phi1))))
93.0ms	(.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
27.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
24.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 7588 to 3395 computations (55.3% saved)

simplify165.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-r_binary64`
534×	`associate-l_binary64`
307×	`fma-def_binary64`
234×	`cancel-sign-sub-inv_binary64`
206×	`fma-neg_binary64`

Counts

145 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	473	6836
1	1350	6131
2	4626	6131
3	4974	6131

prune148.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Error

0.1b

Counts

107 → 11

Alt Table

Status	Error	Program
	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)))) (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) 3)))))
	13.2b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (.f64 (cos.f64 phi2) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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)))) (log.f64 (pow.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))))))
	15.9b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) 3)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	36.5b	(atan2.f64 (.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (.f64 (cos.f64 phi2) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (-.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 (log.f64 (pow.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)))))
	7.1b	(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)) (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 (.f64 (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (cos.f64 (-.f64 lambda1 lambda2)))))))
	15.9b	(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 (.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1))) (cbrt.f64 (cos.f64 lambda2)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.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)) (+.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) 3)) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 3710 to 847 computations (77.2% saved)

regimes3.3s (15.1%)

Accuracy

Total 0.1b remaining (51.8%)

Threshold costs 0.1b (51.8%)

Compiler

Compiled 81576 to 46212 computations (43.4% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	81
1	46	81
2	63	81
3	77	81
4	86	81
5	89	81
6	89	81

end1.0ms (0%)

Compiler: Compiled 52 to 29 computations (44.2% saved)

sample10.6s (48.9%)

Algorithm

1×

intervals

Results

7.7s	5320×	body	1024	valid
1.0s	1303×	body	512	valid
689.0ms	211×	body	2048	valid
211.0ms	390×	body	256	valid
186.0ms	776×	body	128	valid

Compiler

Compiled 559 to 306 computations (45.3% 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

analyze3.9s (18.2%)

sample319.0ms (1.5%)

simplify33.0ms (0.2%)

prune3.0ms (0%)

localize20.0ms (0.1%)

rewrite187.0ms (0.9%)

series217.0ms (1%)

simplify179.0ms (0.8%)

prune134.0ms (0.6%)

localize28.0ms (0.1%)

rewrite181.0ms (0.8%)

series222.0ms (1%)

simplify232.0ms (1.1%)

prune140.0ms (0.6%)

localize36.0ms (0.2%)

rewrite206.0ms (1%)

series268.0ms (1.2%)

simplify294.0ms (1.4%)

prune146.0ms (0.7%)

localize35.0ms (0.2%)

rewrite239.0ms (1.1%)

series424.0ms (2%)

simplify165.0ms (0.8%)

prune148.0ms (0.7%)

regimes3.3s (15.1%)

simplify7.0ms (0%)

end1.0ms (0%)

sample10.6s (48.9%)

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