Details

analyze3.9s (20.2%)

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)

sample285.0ms (1.5%)

Algorithm

1×

intervals

Results

207.0ms	161×	body	1024	valid
28.0ms	42×	body	512	valid
19.0ms	6×	body	2048	valid
10.0ms	22×	body	256	valid
5.0ms	25×	body	128	valid

Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify24.0ms (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

13.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.7b	(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:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.2b	(sin.f64 (-.f64 lambda1 lambda2))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite110.0ms (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:

6.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
5.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 1966 to 330 computations (83.2% saved)

series184.0ms (0.9%)

Error

9.7b

Counts

4 → 58

Calls

4 calls:

62.0ms	(.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	(cos.f64 (-.f64 lambda1 lambda2))
17.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4324 to 2121 computations (50.9% saved)

simplify164.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

571×	`distribute-rgt-neg-in_binary64`
533×	`cancel-sign-sub-inv_binary64`
495×	`distribute-lft-neg-in_binary64`
367×	`neg-mul-1_binary64`
364×	`sub-neg_binary64`

Counts

122 → 76

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	252	2324
1	637	2103
2	1874	1976
3	3347	1957
4	4650	1955
5	4993	1955
6	4999	1955
7	4956	1955

prune91.0ms (0.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	62	14	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	14	77

Error

5.9b

Counts

77 → 14

Alt Table

Status	Error	Program
	17.3b	(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)))))
	26.9b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (sin.f64 lambda1) (.f64 lambda2 (cos.f64 lambda1)))) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 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))))))
	19.8b	(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)))))
	14.7b	(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))))))
	28.3b	(atan2.f64 (.f64 (-.f64 (.f64 (cos.f64 lambda1) (-.f64 (.f64 1/6 (pow.f64 lambda2 3)) lambda2)) (.f64 (sin.f64 lambda1) (-.f64 (.f64 1/2 (.f64 lambda2 lambda2)) 1))) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶	6.2b	(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)) (cos.f64 (-.f64 lambda1 lambda2)))))
	25.5b	(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)))))
	24.7b	(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)))))
	13.8b	(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))))
	17.3b	(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)))))
	13.6b	(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))))))
	39.5b	(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)))))
	13.9b	(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)))))

Compiler

Compiled 2568 to 931 computations (63.7% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite132.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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 → 71

Calls

4 calls:

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

Compiler

Compiled 2666 to 378 computations (85.8% saved)

series250.0ms (1.3%)

Error

5.4b

Counts

4 → 54

Calls

4 calls:

67.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
66.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
25.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
20.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4963 to 2541 computations (48.8% saved)

simplify107.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

503×	`cancel-sign-sub-inv_binary64`
378×	`associate-l_binary64`
377×	`associate-r_binary64`
330×	`distribute-rgt-neg-in_binary64`
298×	`distribute-lft-neg-in_binary64`

Counts

125 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	2701
1	724	2457
2	2240	2355
3	4447	2353
4	5047	2353

prune136.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	7	85
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	87	12	99

Error

0.0b

Counts

99 → 12

Alt Table

Status	Error	Program
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 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))))))
	12.6b	(atan2.f64 (/.f64 (.f64 (cos.f64 phi2) (-.f64 (pow.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) 3) (pow.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) 3))) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (.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)))))
	9.7b	(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)))))
	13.8b	(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))))
	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))))))
	7.1b	(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)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
	24.7b	(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)))))
	9.3b	(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)))))
▶	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))))))
	35.5b	(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)))))
	39.5b	(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)))))
	13.9b	(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)))))

Compiler

Compiled 3277 to 947 computations (71.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite203.0ms (1%)

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 → 84

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))))
5.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
4.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

Compiler

Compiled 3785 to 478 computations (87.4% saved)

series292.0ms (1.5%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

102.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
64.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
29.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
24.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5909 to 2756 computations (53.4% saved)

simplify128.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

826×	`cancel-sign-sub-inv_binary64`
622×	`associate-r_binary64`
610×	`associate-l_binary64`
309×	`*-commutative_binary64`
162×	`exp-prod_binary64`

Counts

139 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	344	3692
1	993	3378
2	3581	3378
3	4947	3378
4	4995	3378

prune212.0ms (1.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Error

0.0b

Counts

119 → 10

Alt Table

Status	Error	Program
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 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))))))
▶	0.4b	(atan2.f64 (.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (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))))))
	13.8b	(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))))
	39.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (cos.f64 phi2))) (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (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))))))
	24.7b	(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)))))
	9.3b	(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)))))
	3.7b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.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))))))
	1.1b	(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)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
✓	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))))))
	35.5b	(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 4834 to 1059 computations (78.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))
0.3b	(cbrt.f64 (cos.f64 phi2))
0.3b	(cbrt.f64 (cos.f64 phi2))
0.3b	(cbrt.f64 (cos.f64 phi2))

rewrite167.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))
2.0ms	(cbrt.f64 (cos.f64 phi2))
1.0ms	(cbrt.f64 (cos.f64 phi2))
1.0ms	(cbrt.f64 (cos.f64 phi2))

Compiler

Compiled 3588 to 365 computations (89.8% saved)

series96.0ms (0.5%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

17.0ms	(cbrt.f64 (cos.f64 phi2))
17.0ms	(cbrt.f64 (cos.f64 phi2))
17.0ms	(cbrt.f64 (cos.f64 phi2))
17.0ms	(*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))

Compiler

Compiled 2414 to 1135 computations (53% saved)

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

796×	`log-prod_binary64`
575×	`distribute-rgt-in_binary64`
534×	`distribute-lft-in_binary64`
467×	`unswap-sqr_binary64`
462×	`sqr-pow_binary64`

Counts

92 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	917
1	113	847
2	329	825
3	785	807
4	1811	647
5	4194	647
6	4475	647
7	4307	647
8	5156	647

prune85.0ms (0.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	69	10	79

Error

0.0b

Counts

79 → 10

Alt Table

Status	Error	Program
	13.8b	(atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (.f64 (cos.f64 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))))))
	0.4b	(atan2.f64 (.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (cbrt.f64 (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))))))
	13.8b	(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))))
	39.7b	(atan2.f64 (.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (cos.f64 phi2))) (.f64 (sqrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (sqrt.f64 (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))))))
	0.4b	(atan2.f64 (.f64 (.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 phi2))) 4))) (cbrt.f64 (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))))))
	9.3b	(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)))))
	3.7b	(atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) 3)) (-.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))))))
	1.1b	(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)) (log.f64 (pow.f64 (exp.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1))) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
	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))))))
	35.5b	(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 2156 to 519 computations (75.9% saved)

regimes2.4s (12.4%)

Accuracy

Total 0.1b remaining (53.6%)

Threshold costs 0.1b (53.6%)

Compiler

Compiled 60885 to 35162 computations (42.2% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
15×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	63
1	44	63
2	68	63
3	88	63
4	116	63
5	128	63
6	134	63
7	136	63
8	136	63

end1.0ms (0%)

Compiler: Compiled 42 to 24 computations (42.9% saved)

sample10.2s (52.4%)

Algorithm

1×

intervals

Results

7.5s	5363×	body	1024	valid
921.0ms	1275×	body	512	valid
695.0ms	189×	body	2048	valid
187.0ms	408×	body	256	valid
169.0ms	765×	body	128	valid

Compiler

Compiled 524 to 300 computations (42.7% 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

analyze3.9s (20.2%)

sample285.0ms (1.5%)

simplify24.0ms (0.1%)

prune3.0ms (0%)

localize20.0ms (0.1%)

rewrite110.0ms (0.6%)

series184.0ms (0.9%)

simplify164.0ms (0.8%)

prune91.0ms (0.5%)

localize29.0ms (0.1%)

rewrite132.0ms (0.7%)

series250.0ms (1.3%)

simplify107.0ms (0.5%)

prune136.0ms (0.7%)

localize29.0ms (0.1%)

rewrite203.0ms (1%)

series292.0ms (1.5%)

simplify128.0ms (0.7%)

prune212.0ms (1.1%)

localize34.0ms (0.2%)

rewrite167.0ms (0.9%)

series96.0ms (0.5%)

simplify111.0ms (0.6%)

prune85.0ms (0.4%)

regimes2.4s (12.4%)

simplify6.0ms (0%)

end1.0ms (0%)

sample10.2s (52.4%)

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