Details

analyze3.6s (17.9%)

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)

sample336.0ms (1.7%)

Algorithm

1×

intervals

Results

264.0ms	180×	body	1024	valid
31.0ms	35×	body	512	valid
17.0ms	5×	body	2048	valid
5.0ms	12×	body	256	valid
5.0ms	24×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify28.0ms (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

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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite121.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

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 → 64

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
5.0ms	(.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))

Compiler

Compiled 1966 to 330 computations (83.2% saved)

series192.0ms (1%)

Error

10.4b

Counts

4 → 62

Calls

4 calls:

66.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
37.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
17.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4552 to 2188 computations (51.9% saved)

simplify111.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

789×	`cancel-sign-sub-inv_binary64`
483×	`sub-neg_binary64`
381×	`associate-r_binary64`
358×	`distribute-rgt-neg-in_binary64`
349×	`associate-l_binary64`

Counts

126 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	280	2571
1	713	2336
2	2195	2163
3	4137	2157
4	5065	2157

prune100.0ms (0.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	68	12	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	12	81

Error

5.9b

Counts

81 → 12

Alt Table

Status	Error	Program
	36.6b	(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)))))
	12.9b	(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))))))
	16.3b	(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)))))
	23.2b	(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 (cos.f64 lambda2) (*.f64 lambda1 (sin.f64 lambda2))))))
	13.0b	(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 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (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 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	13.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
	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)))))
	27.2b	(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)))))
▶	6.0b	(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)))))
	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)))))
	27.0b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 lambda2 (+.f64 (cos.f64 lambda1) (.f64 (.f64 1/2 (sin.f64 lambda1)) lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 2720 to 923 computations (66.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.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)))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite166.0ms (0.8%)

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 → 72

Calls

4 calls:

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

Compiler

Compiled 2703 to 370 computations (86.3% saved)

series251.0ms (1.2%)

Error

5.7b

Counts

4 → 57

Calls

4 calls:

68.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
66.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
25.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
19.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 5172 to 2634 computations (49.1% saved)

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

639×	`cancel-sign-sub-inv_binary64`
419×	`associate-r_binary64`
394×	`associate-l_binary64`
333×	`neg-sub0_binary64`
333×	`neg-mul-1_binary64`

Counts

129 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	2936
1	753	2634
2	2421	2507
3	4392	2507
4	4997	2507
5	4987	2507

prune264.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Error

0.1b

Counts

108 → 11

Alt Table

Status	Error	Program
	6.3b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 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)))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.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)))))
	9.4b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) 3)) (-.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 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
	15.6b	(atan2.f64 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	27.0b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 lambda2 (+.f64 (cos.f64 lambda1) (.f64 (.f64 1/2 (sin.f64 lambda1)) lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	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 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	36.6b	(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)))))
	33.9b	(atan2.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 3666 to 969 computations (73.6% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.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)))

rewrite249.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
22×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
11×	`cbrt-unprod_binary64`

Counts

4 → 78

Calls

4 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
8.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))
6.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3498 to 437 computations (87.5% saved)

series232.0ms (1.1%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

83.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
27.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))
27.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
25.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))

Compiler

Compiled 5689 to 2565 computations (54.9% saved)

simplify122.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

544×	`distribute-rgt-neg-in_binary64`
503×	`distribute-lft-neg-in_binary64`
413×	`associate-r_binary64`
361×	`associate-l_binary64`
339×	`cancel-sign-sub-inv_binary64`

Counts

125 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	2300
1	489	1993
2	1754	1854
3	3022	1814
4	5065	1814

prune184.0ms (0.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Error

0.1b

Counts

92 → 13

Alt Table

Status	Error	Program
	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 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	24.7b	(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)))) (exp.f64 (log.f64 (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))))
	36.6b	(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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))
	6.3b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 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)))))
	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 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
	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 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2))) (cbrt.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	15.6b	(atan2.f64 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	27.0b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 lambda2 (+.f64 (cos.f64 lambda1) (.f64 (.f64 1/2 (sin.f64 lambda1)) lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
▶	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 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (sin.f64 lambda2)))))
	33.9b	(atan2.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 3991 to 1106 computations (72.3% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite357.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
22×	`pow1_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`cbrt-unprod_binary64`

Counts

4 → 78

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (sin.f64 lambda2))
6.0ms	(.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (cos.f64 phi2)))
4.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
3.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))

Compiler

Compiled 3509 to 481 computations (86.3% saved)

series267.0ms (1.3%)

Error

0.1b

Counts

4 → 52

Calls

4 calls:

83.0ms	(.f64 (.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) (sin.f64 lambda2))
53.0ms	(.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (cos.f64 phi2)))
26.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
25.0ms	(*.f64 (cos.f64 phi2) (sin.f64 phi1))

Compiler

Compiled 6259 to 2867 computations (54.2% saved)

simplify131.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

609×	`distribute-rgt-neg-in_binary64`
563×	`distribute-lft-neg-in_binary64`
518×	`associate-r_binary64`
450×	`associate-l_binary64`
403×	`cancel-sign-sub-inv_binary64`

Counts

130 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	2580
1	562	2263
2	2045	2092
3	3381	2092
4	4867	2092
5	5019	2092

prune170.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	67	13	80

Error

0.1b

Counts

80 → 13

Alt Table

Status	Error	Program
	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 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))) (cbrt.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))))
	24.7b	(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)))) (exp.f64 (log.f64 (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))))
	36.6b	(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 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (sin.f64 phi1)))) (.f64 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (.f64 (sin.f64 lambda2) (cos.f64 phi2)))))))
	6.3b	(atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 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)))))
	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 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3))))
	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 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2))) (cbrt.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))) (cbrt.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)))))) (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
	15.6b	(atan2.f64 (log.f64 (exp.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	27.0b	(atan2.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 phi2)) (.f64 (cos.f64 phi2) (.f64 lambda2 (+.f64 (cos.f64 lambda1) (.f64 (.f64 1/2 (sin.f64 lambda1)) lambda2))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.0b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))))))
	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 (sin.f64 lambda1) (.f64 (sin.f64 phi1) (cos.f64 phi2))) (sin.f64 lambda2)))))
	33.9b	(atan2.f64 (exp.f64 (log.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 3210 to 807 computations (74.9% saved)

regimes2.5s (12.2%)

Accuracy

Total 0.1b remaining (49.1%)

Threshold costs 0.1b (49.1%)

Compiler

Compiled 60485 to 35157 computations (41.9% saved)

simplify8.0ms (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)

sample10.6s (52.2%)

Algorithm

1×

intervals

Results

7.8s	5362×	body	1024	valid
990.0ms	1317×	body	512	valid
632.0ms	176×	body	2048	valid
220.0ms	415×	body	256	valid
165.0ms	730×	body	128	valid

Compiler

Compiled 681 to 362 computations (46.8% 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

analyze3.6s (17.9%)

sample336.0ms (1.7%)

simplify28.0ms (0.1%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite121.0ms (0.6%)

series192.0ms (1%)

simplify111.0ms (0.5%)

prune100.0ms (0.5%)

localize28.0ms (0.1%)

rewrite166.0ms (0.8%)

series251.0ms (1.2%)

simplify149.0ms (0.7%)

prune264.0ms (1.3%)

localize33.0ms (0.2%)

rewrite249.0ms (1.2%)

series232.0ms (1.1%)

simplify122.0ms (0.6%)

prune184.0ms (0.9%)

localize35.0ms (0.2%)

rewrite357.0ms (1.8%)

series267.0ms (1.3%)

simplify131.0ms (0.6%)

prune170.0ms (0.8%)

regimes2.5s (12.2%)

simplify8.0ms (0%)

end1.0ms (0%)

sample10.6s (52.2%)

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