Details

analyze4.2s (19.6%)

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)

sample368.0ms (1.7%)

Algorithm

1×

intervals

Results

241.0ms	170×	body	1024	valid
74.0ms	40×	body	512	valid
21.0ms	6×	body	2048	valid
8.0ms	18×	body	256	valid
5.0ms	22×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

83×	`cancel-sign-sub-inv_binary64`
59×	`distribute-rgt-neg-in_binary64`
56×	`sub-neg_binary64`
47×	`distribute-rgt-in_binary64`
42×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	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

12.0b

Counts

2 → 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 84 to 51 computations (39.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite113.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

5.7b

Rules

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

Counts

4 → 63

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

Compiler

Compiled 1912 to 347 computations (81.9% saved)

series196.0ms (0.9%)

Error

8.0b

Counts

4 → 56

Calls

4 calls:

75.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
26.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
19.0ms	(cos.f64 (-.f64 lambda1 lambda2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4179 to 2048 computations (51% saved)

simplify135.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

613×	`cancel-sign-sub-inv_binary64`
404×	`sub-neg_binary64`
377×	`neg-mul-1_binary64`
347×	`associate-r_binary64`
345×	`neg-sub0_binary64`

Counts

119 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	2299
1	694	2072
2	2084	1918
3	3764	1912
4	4759	1912
5	4986	1912

prune105.0ms (0.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	63	13	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	13	77

Error

5.8b

Counts

77 → 13

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)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
	24.4b	(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)))))
	27.3b	(atan2.f64 (.f64 (-.f64 (-.f64 (.f64 (cos.f64 lambda2) lambda1) (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)))))
	24.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (cos.f64 phi1)) (.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))))
	22.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) 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)))))
	11.9b	(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))))))
	15.4b	(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)))))
▶	5.9b	(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)))))
	39.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	11.9b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 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))))))
	13.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	12.1b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1))) (.f64 (sin.f64 phi2) (cbrt.f64 (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 2752 to 980 computations (64.4% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite127.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`

Counts

4 → 69

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
3.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 2441 to 380 computations (84.4% saved)

series242.0ms (1.1%)

Error

5.4b

Counts

4 → 57

Calls

4 calls:

85.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
28.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
26.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
21.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 5145 to 2558 computations (50.3% saved)

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

741×	`cancel-sign-sub-inv_binary64`
461×	`sub-neg_binary64`
430×	`associate-r_binary64`
404×	`associate-l_binary64`
354×	`distribute-rgt-neg-in_binary64`

Counts

126 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	2476
1	780	2234
2	2414	2041
3	4250	2038
4	5134	2038

prune143.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	85	10	95

Error

0.1b

Counts

95 → 10

Alt Table

Status	Error	Program
	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)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))))
	15.4b	(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)))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.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))))))
	24.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (cos.f64 phi1)) (.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (.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))))))
	8.2b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.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)))))
	36.2b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	6.9b	(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)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))

Compiler

Compiled 3162 to 956 computations (69.8% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite194.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
15×	`pow1_binary64`
12×	`associate-r_binary64`

Counts

4 → 82

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
7.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 3546 to 480 computations (86.5% saved)

series290.0ms (1.3%)

Error

0.1b

Counts

4 → 54

Calls

4 calls:

130.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
30.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
30.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
25.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 5990 to 2758 computations (54% saved)

simplify150.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

723×	`associate-r_binary64`
672×	`associate-l_binary64`
481×	`distribute-rgt-neg-in_binary64`
353×	`*-commutative_binary64`
169×	`sub-neg_binary64`

Counts

136 → 88

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	365	3527
1	1072	3206
2	3950	3206
3	4927	3206
4	4967	3206

prune165.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	86	12	98

Error

0.0b

Counts

98 → 12

Alt Table

Status	Error	Program
	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)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))))
	41.0b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 lambda1)) (sqrt.f64 (cos.f64 lambda2))) (.f64 (sqrt.f64 (sin.f64 lambda1)) (sqrt.f64 (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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	15.4b	(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)))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	2.4b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.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))))))
▶	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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))
	16.9b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (cos.f64 phi1)) (.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1))) (.f64 (sin.f64 phi2) (cbrt.f64 (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	33.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.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)) (/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	1.2b	(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)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 4420 to 1212 computations (72.6% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))
0.3b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
26.2b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

rewrite266.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 86

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))
4.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
4.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

Compiler

Compiled 3967 to 933 computations (76.5% saved)

series337.0ms (1.6%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

128.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))
48.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
37.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))
31.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 6214 to 3003 computations (51.7% saved)

simplify154.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

673×	`associate-r_binary64`
594×	`associate-l_binary64`
325×	`*-commutative_binary64`
167×	`unswap-sqr_binary64`
165×	`sub-neg_binary64`

Counts

140 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	3732
1	1055	3385
2	3964	3369
3	4887	3369
4	4985	3369

prune259.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	111	13	124

Error

0.0b

Counts

124 → 13

Alt Table

Status	Error	Program
	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)) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)))))
	41.0b	(atan2.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 lambda1)) (sqrt.f64 (cos.f64 lambda2))) (.f64 (sqrt.f64 (sin.f64 lambda1)) (sqrt.f64 (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)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	15.4b	(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)))))
	6.1b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.3b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (log.f64 (exp.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	2.4b	(atan2.f64 (.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3)) (.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))))))
	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)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))
	16.9b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (cos.f64 phi1)) (.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	0.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1))) (.f64 (sin.f64 phi2) (cbrt.f64 (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	33.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1))) (sqrt.f64 (.f64 (sin.f64 phi2) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.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)) (/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (+.f64 (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3))) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))))
	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 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	1.2b	(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)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

Compiler

Compiled 4777 to 1252 computations (73.8% saved)

regimes2.9s (13.4%)

Accuracy

Total 0.1b remaining (54.2%)

Threshold costs 0.1b (54.2%)

Compiler

Compiled 66558 to 39216 computations (41.1% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
14×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	68
1	47	68
2	71	68
3	91	68
4	114	68
5	124	68
6	128	68
7	129	68
8	129	68

end1.0ms (0%)

Compiler: Compiled 45 to 27 computations (40% saved)

sample11.0s (50.8%)

Algorithm

1×

intervals

Results

7.9s	5392×	body	1024	valid
1.1s	1305×	body	512	valid
709.0ms	179×	body	2048	valid
204.0ms	410×	body	256	valid
162.0ms	714×	body	128	valid

Compiler

Compiled 718 to 398 computations (44.6% saved)

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39

Details

analyze4.2s (19.6%)

sample368.0ms (1.7%)

simplify27.0ms (0.1%)

prune3.0ms (0%)

localize21.0ms (0.1%)

rewrite113.0ms (0.5%)

series196.0ms (0.9%)

simplify135.0ms (0.6%)

prune105.0ms (0.5%)

localize30.0ms (0.1%)

rewrite127.0ms (0.6%)

series242.0ms (1.1%)

simplify112.0ms (0.5%)

prune143.0ms (0.7%)

localize30.0ms (0.1%)

rewrite194.0ms (0.9%)

series290.0ms (1.3%)

simplify150.0ms (0.7%)

prune165.0ms (0.8%)

localize37.0ms (0.2%)

rewrite266.0ms (1.2%)

series337.0ms (1.6%)

simplify154.0ms (0.7%)

prune259.0ms (1.2%)

regimes2.9s (13.4%)

simplify7.0ms (0%)

end1.0ms (0%)

sample11.0s (50.8%)

Profiling

Iter	Nodes	Cost
0	18	39
1	31	39
2	59	39
3	105	39
4	129	39
5	196	39
6	248	39
7	309	39
8	420	39
9	430	39
10	436	39
11	385	39