Details

analyze5.1s (21.2%)

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
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)

sample340.0ms (1.4%)

Algorithm

1×

intervals

Results

244.0ms	125×	body	1024	valid
45.0ms	51×	body	512	valid
21.0ms	68×	body	128	valid
8.0ms	2×	body	2048	valid
6.0ms	10×	body	256	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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(+.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

▶

0.2b

(+.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))))))
0.3b	(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)))))))

rewrite109.0ms (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)))))))
1.0ms	(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)

series213.0ms (0.9%)

Error

0.1b

Counts

4 → 43

Calls

4 calls:

73.0ms	(-.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)))))))
59.0ms	(.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))))))
41.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
21.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 3739 to 2015 computations (46.1% saved)

simplify162.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

448×	`distribute-rgt-neg-in_binary64`
427×	`cancel-sign-sub-inv_binary64`
387×	`unsub-neg_binary64`
362×	`distribute-lft-neg-in_binary64`
360×	`neg-mul-1_binary64`

Counts

101 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	173	3269
1	390	3080
2	994	3021
3	1778	3006
4	3395	3006
5	4271	3006
6	4880	3006

prune98.0ms (0.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	46	9	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	9	56

Error

0.0b

Counts

56 → 9

Alt Table

Status	Error	Program
	0.2b	(+.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)))))))))))
▶	0.2b	(+.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))))))))))))))
	0.3b	(+.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))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.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)))))))) 3))))
	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 (.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))))))))))))
	35.9b	(+.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)))))))))
	0.3b	(+.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)))))))))
	29.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) (sqrt.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)))))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.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)))))))))

Compiler

Compiled 3298 to 849 computations (74.3% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(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 (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))))))))))))
0.4b	(pow.f64 (cos.f64 delta) 3)
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))))))) 3)

rewrite461.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

66×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
32×	`difference-of-squares_binary64`
26×	`sqr-pow_binary64`

Counts

4 → 128

Calls

4 calls:

16.0ms	(/.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))))))))))))
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)))))

Compiler

Compiled 13930 to 1595 computations (88.5% saved)

series983.0ms (4.1%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

780.0ms	(/.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))))))))))))
111.0ms	(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 12687 to 4078 computations (67.9% saved)

simplify485.0ms (2%)

Algorithm

1×	egg-herbie

Rules

289×	`associate-r_binary64`
276×	`associate-l_binary64`
226×	`associate-/l*_binary64`
211×	`log-prod_binary64`
176×	`exp-prod_binary64`

Counts

165 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	21175
1	925	20370
2	3948	20110
3	4655	20110
4	5004	20110

prune268.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.0b

Counts

135 → 9

Alt Table

Status	Error	Program
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.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 (-.f64 (pow.f64 (cos.f64 delta) 3) (cbrt.f64 (pow.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))))))) 3) 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 (.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)))))))))))
	0.3b	(+.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))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.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)))))))) 3))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 (.f64 (cbrt.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))) (cbrt.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 (cbrt.f64 (+.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 (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 (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 (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 (cbrt.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))) (cbrt.f64 (+.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 (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)))))))))))))))
	35.9b	(+.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)))))))))
	0.3b	(+.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)))))))))
	25.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 (+.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))))))) 3/2) (pow.f64 (cos.f64 delta) 3/2)) (.f64 (cbrt.f64 (+.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 (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 (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 (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) 3/2) (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))))))) 3/2)) (cbrt.f64 (+.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 (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)))))))))))))))

Compiler

Compiled 11247 to 1997 computations (82.2% saved)

localize49.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (cos.f64 delta) 3)
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))))))) 3)
0.4b	(pow.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))))))) 3) 3)
4.0b	(cbrt.f64 (pow.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))))))) 3) 3))

rewrite436.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`cube-prod_binary64`
24×	`unpow-prod-down_binary64`
22×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`

Counts

4 → 115

Calls

4 calls:

5.0ms	(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)
5.0ms	(pow.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))))))) 3) 3)
4.0ms	(cbrt.f64 (pow.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))))))) 3) 3))
2.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 8780 to 1314 computations (85% saved)

series453.0ms (1.9%)

Error

0.0b

Counts

4 → 35

Calls

4 calls:

167.0ms	(pow.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))))))) 3) 3)
110.0ms	(cbrt.f64 (pow.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))))))) 3) 3))
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)
16.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 7612 to 2730 computations (64.1% saved)

simplify322.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

748×	`log-prod_binary64`
435×	`exp-prod_binary64`
404×	`*-commutative_binary64`
385×	`sqr-pow_binary64`
349×	`cube-prod_binary64`

Counts

150 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	5664
1	321	5490
2	1138	5414
3	2443	5414
4	4662	5414
5	5061	5414

prune178.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	115	9	124

Error

0.0b

Counts

124 → 9

Alt Table

Status	Error	Program
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.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 (-.f64 (pow.f64 (cos.f64 delta) 3) (cbrt.f64 (pow.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))))))) 3) 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 (.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)))))))))))
	0.3b	(+.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))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.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)))))))) 3))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 (.f64 (cbrt.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))) (cbrt.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 (cbrt.f64 (+.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 (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 (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 (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 (cbrt.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))) (cbrt.f64 (+.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 (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)))))))))))))))
	35.9b	(+.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)))))))))
	0.3b	(+.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)))))))))
	25.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 (+.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))))))) 3/2) (pow.f64 (cos.f64 delta) 3/2)) (.f64 (cbrt.f64 (+.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 (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 (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 (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) 3/2) (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))))))) 3/2)) (cbrt.f64 (+.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 (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)))))))))))))))

Compiler

Compiled 5221 to 1046 computations (80% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite337.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 72

Calls

4 calls:

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)))))
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 6171 to 472 computations (92.4% saved)

series280.0ms (1.2%)

Error

0.0b

Counts

4 → 40

Calls

4 calls:

109.0ms	(-.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)))))))))
91.0ms	(.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))))))))
24.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
24.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 6460 to 2409 computations (62.7% saved)

simplify270.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

497×	`distribute-rgt-neg-in_binary64`
478×	`distribute-lft-neg-in_binary64`
442×	`cancel-sign-sub-inv_binary64`
326×	`*-commutative_binary64`
171×	`exp-prod_binary64`

Counts

112 → 71

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	137	4839
1	331	4504
2	1043	4463
3	2553	4463
4	4605	4343
5	4949	4343
6	4920	4343

prune125.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	72	8	80

Error

0.0b

Counts

80 → 8

Alt Table

Status	Error	Program
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.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 (-.f64 (pow.f64 (cos.f64 delta) 3) (cbrt.f64 (pow.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))))))) 3) 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))))))))))))))
	0.3b	(+.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))))))))))))
	0.4b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 (.f64 (cbrt.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))) (cbrt.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 (cbrt.f64 (+.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 (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 (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 (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 (cbrt.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))) (cbrt.f64 (+.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 (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 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (pow.f64 (sin.f64 phi1) 2)) (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)))))))))))
	35.9b	(+.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)))))))))
	0.3b	(+.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)))))))))
	25.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (/.f64 (+.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))))))) 3/2) (pow.f64 (cos.f64 delta) 3/2)) (.f64 (cbrt.f64 (+.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 (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 (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 (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) 3/2) (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))))))) 3/2)) (cbrt.f64 (+.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 (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)))))))))))))))

Compiler

Compiled 3438 to 640 computations (81.4% saved)

regimes3.5s (14.3%)

Accuracy

Total 0.1b remaining (49.3%)

Threshold costs 0.1b (49.3%)

Compiler

Compiled 109212 to 43526 computations (60.1% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-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	26	133
1	41	133
2	51	133
3	57	133
4	61	133
5	62	133
6	62	133

end1.0ms (0%)

Compiler: Compiled 84 to 26 computations (69% saved)

sample9.8s (40.7%)

Algorithm

1×

intervals

Results

6.8s	3941×	body	1024	valid
1.2s	1294×	body	512	valid
631.0ms	2191×	body	128	valid
332.0ms	566×	body	256	valid
34.0ms	8×	body	2048	valid

Compiler

Compiled 997 to 333 computations (66.6% 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

analyze5.1s (21.2%)

sample340.0ms (1.4%)

simplify48.0ms (0.2%)

prune3.0ms (0%)

localize27.0ms (0.1%)

rewrite109.0ms (0.5%)

series213.0ms (0.9%)

simplify162.0ms (0.7%)

prune98.0ms (0.4%)

localize44.0ms (0.2%)

rewrite461.0ms (1.9%)

series983.0ms (4.1%)

simplify485.0ms (2%)

prune268.0ms (1.1%)

localize49.0ms (0.2%)

rewrite436.0ms (1.8%)

series453.0ms (1.9%)

simplify322.0ms (1.3%)

prune178.0ms (0.7%)

localize41.0ms (0.2%)

rewrite337.0ms (1.4%)

series280.0ms (1.2%)

simplify270.0ms (1.1%)

prune125.0ms (0.5%)

regimes3.5s (14.3%)

simplify8.0ms (0%)

end1.0ms (0%)

sample9.8s (40.7%)

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