Details

analyze5.0s (21.6%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample315.0ms (1.4%)

Algorithm

1×

intervals

Results

238.0ms	142×	body	1024	valid
34.0ms	37×	body	512	valid
16.0ms	63×	body	128	valid
8.0ms	13×	body	256	valid
5.0ms	1×	body	2048	valid

Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

103×	`unsub-neg_binary64`
90×	`associate-l_binary64`
88×	`distribute-rgt-in_binary64`
82×	`cancel-sign-sub-inv_binary64`
80×	`associate-r_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

Status

Error

Program

▶

0.1b

(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

Compiler

Compiled 114 to 69 computations (39.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite121.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 58

Calls

4 calls:

4.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
4.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
3.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
3.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 2518 to 351 computations (86.1% saved)

series186.0ms (0.8%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

71.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
55.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
24.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
20.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 3616 to 1958 computations (45.9% saved)

simplify165.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

420×	`sub-neg_binary64`
412×	`distribute-rgt-neg-in_binary64`
350×	`distribute-lft-neg-in_binary64`
342×	`neg-mul-1_binary64`
302×	`cancel-sign-sub-inv_binary64`

Counts

100 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	3249
1	371	3060
2	967	3016
3	1788	3011
4	3312	3011
5	4403	3011
6	4926	3011

prune96.0ms (0.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	44	10	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	10	55

Error

0.0b

Counts

55 → 10

Alt Table

Status	Error	Program
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (sin.f64 delta) (cbrt.f64 (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	2.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	18.0b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	28.0b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (sqrt.f64 (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	29.2b	(+.f64 lambda1 (atan2.f64 (.f64 (exp.f64 (log.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (cbrt.f64 (sin.f64 phi1)))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))) (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))

Compiler

Compiled 3356 to 883 computations (73.7% saved)

localize162.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.4b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)

rewrite222.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 62

Calls

4 calls:

4.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)
2.0ms	(pow.f64 (cos.f64 delta) 3)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 5162 to 655 computations (87.3% saved)

series487.0ms (2.1%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

309.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
109.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)
28.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
15.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 6613 to 2318 computations (64.9% saved)

simplify142.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

563×	`sqr-pow_binary64`
410×	`log-prod_binary64`
346×	`*-commutative_binary64`
328×	`exp-prod_binary64`
281×	`unswap-sqr_binary64`

Counts

96 → 45

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	2597
1	242	2321
2	752	2297
3	1805	2297
4	3533	2291
5	4934	2291
6	4975	2291

prune91.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	45	10	55

Error

0.0b

Counts

55 → 10

Alt Table

Status	Error	Program
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (sin.f64 delta) (cbrt.f64 (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	2.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	18.0b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	28.0b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (sqrt.f64 (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	29.2b	(+.f64 lambda1 (atan2.f64 (.f64 (exp.f64 (log.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (cbrt.f64 (sin.f64 phi1)))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))) (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))

Compiler

Compiled 2937 to 741 computations (74.8% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.4b	(/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
0.4b	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
0.4b	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))

rewrite451.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
17×	`pow-prod-down_binary64`
16×	`sin-mult_binary64`

Counts

4 → 105

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
10.0ms	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))
7.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 10602 to 651 computations (93.9% saved)

series582.0ms (2.5%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

285.0ms	(/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
126.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
86.0ms	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))
25.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 8879 to 3307 computations (62.8% saved)

simplify312.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

380×	`cancel-sign-sub-inv_binary64`
217×	`distribute-rgt-neg-in_binary64`
211×	`associate-r_binary64`
202×	`unswap-sqr_binary64`
197×	`associate-l_binary64`

Counts

151 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	288	11866
1	767	11210
2	2900	11026
3	4583	10729
4	5071	10729

prune291.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	119	9	128

Error

0.0b

Counts

128 → 9

Alt Table

Status	Error	Program
	2.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (/.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) (cbrt.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))))
	28.0b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (sqrt.f64 (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 6))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	29.2b	(+.f64 lambda1 (atan2.f64 (.f64 (exp.f64 (log.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (cbrt.f64 (sin.f64 phi1)))))))

Compiler

Compiled 8155 to 1553 computations (81% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.4b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)
0.5b	(-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (/.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))

rewrite523.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

70×	`add-sqr-sqrt_binary64`
55×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`
24×	`cancel-sign-sub-inv_binary64`
20×	`difference-of-squares_binary64`

Counts

4 → 98

Calls

4 calls:

39.0ms	(-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (/.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
4.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 11926 to 1458 computations (87.8% saved)

series762.0ms (3.3%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

432.0ms	(-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (/.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
178.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
85.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)
27.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 9538 to 3186 computations (66.6% saved)

simplify507.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

253×	`cancel-sign-sub-inv_binary64`
219×	`unswap-sqr_binary64`
184×	`sub-neg_binary64`
183×	`associate-r_binary64`
180×	`distribute-neg-frac_binary64`

Counts

140 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	16094
1	851	15411
2	3161	14930
3	4657	14930
4	4985	14930
5	4948	14930

prune142.0ms (0.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	82	9	91

Error

0.0b

Counts

91 → 9

Alt Table

Status	Error	Program
	2.1b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (/.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) (cbrt.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))))
	28.0b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (sqrt.f64 (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 6))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	29.2b	(+.f64 lambda1 (atan2.f64 (.f64 (exp.f64 (log.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (cbrt.f64 (sin.f64 phi1)))))))

Compiler

Compiled 4809 to 921 computations (80.8% saved)

regimes1.5s (6.5%)

Accuracy

Total 0.1b remaining (46.4%)

Threshold costs 0.1b (46.4%)

Compiler

Compiled 51224 to 21742 computations (57.6% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
8×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	385
1	48	385
2	57	385
3	63	385
4	67	385
5	68	385
6	68	385

end2.0ms (0%)

Compiler: Compiled 234 to 46 computations (80.3% saved)

sample10.9s (47%)

Algorithm

1×

intervals

Results

7.4s	3904×	body	1024	valid
1.6s	1334×	body	512	valid
729.0ms	2229×	body	128	valid
322.0ms	524×	body	256	valid
46.0ms	9×	body	2048	valid

Compiler

Compiled 879 to 335 computations (61.9% saved)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Details

analyze5.0s (21.6%)

sample315.0ms (1.4%)

simplify48.0ms (0.2%)

prune3.0ms (0%)

localize27.0ms (0.1%)

rewrite121.0ms (0.5%)

series186.0ms (0.8%)

simplify165.0ms (0.7%)

prune96.0ms (0.4%)

localize162.0ms (0.7%)

rewrite222.0ms (1%)

series487.0ms (2.1%)

simplify142.0ms (0.6%)

prune91.0ms (0.4%)

localize39.0ms (0.2%)

rewrite451.0ms (2%)

series582.0ms (2.5%)

simplify312.0ms (1.4%)

prune291.0ms (1.3%)

localize44.0ms (0.2%)

rewrite523.0ms (2.3%)

series762.0ms (3.3%)

simplify507.0ms (2.2%)

prune142.0ms (0.6%)

regimes1.5s (6.5%)

simplify16.0ms (0.1%)

end2.0ms (0%)

sample10.9s (47%)

Profiling

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55