Details

analyze5.3s (22.7%)

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)

sample339.0ms (1.4%)

Algorithm

1×

intervals

Results

236.0ms	125×	body	1024	valid
59.0ms	53×	body	512	valid
16.0ms	59×	body	128	valid
12.0ms	19×	body	256	valid

Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify63.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-def_binary64`
244×	`fma-neg_binary64`
103×	`unsub-neg_binary64`
90×	`associate-l_binary64`
88×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53

prune4.0ms (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 113 to 68 computations (39.8% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(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))))))))
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))))
0.6b	(-.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)))))))

rewrite139.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

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

Counts

4 → 60

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))))))
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))))
0.0ms	(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 2886 to 338 computations (88.3% saved)

series178.0ms (0.8%)

Error

0.2b

Counts

4 → 44

Calls

4 calls:

64.0ms	(-.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)))))))
56.0ms	(.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	(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))))))))
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 3722 to 1999 computations (46.3% saved)

simplify191.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-neg_binary64`
367×	`fma-def_binary64`
333×	`distribute-rgt-neg-in_binary64`
299×	`distribute-lft-neg-in_binary64`
289×	`associate-l_binary64`

Counts

104 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	5419
1	371	4955
2	863	4805
3	2497	4805
4	4574	4805
5	4925	4805

prune126.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	11	95

Error

0.1b

Counts

95 → 11

Alt Table

Status	Error	Program
	4.1b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))) 3)))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))))
✓	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)))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	28.0b	(+.f64 lambda1 (exp.f64 (log.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	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 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3)) (fma.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (cos.f64 delta))) (*.f64 (cos.f64 delta) (cos.f64 delta))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))) 3))))

Compiler

Compiled 3442 to 863 computations (74.9% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))
0.4b	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))
0.6b	(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))

rewrite257.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 71

Calls

4 calls:

4.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))
4.0ms	(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))
1.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))
0.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))))))

Compiler

Compiled 4304 to 473 computations (89% saved)

series245.0ms (1%)

Error

0.1b

Counts

4 → 44

Calls

4 calls:

119.0ms	(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))
49.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))
27.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))))))
23.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))

Compiler

Compiled 3926 to 2169 computations (44.8% saved)

simplify255.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-neg_binary64`
589×	`fma-def_binary64`
392×	`distribute-rgt-in_binary64`
326×	`distribute-rgt-neg-in_binary64`
322×	`sub-neg_binary64`

Counts

115 → 86

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	217	6497
1	402	5688
2	1074	5205
3	2738	5205
4	4653	5174
5	4983	5174
6	4822	5174

prune97.0ms (0.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	86	11	97

Error

0.1b

Counts

97 → 11

Alt Table

Status	Error	Program
	4.1b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))) 3)))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))))
✓	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)))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	28.0b	(+.f64 lambda1 (exp.f64 (log.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
▶	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 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3)) (fma.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (cos.f64 delta))) (*.f64 (cos.f64 delta) (cos.f64 delta))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))) 3))))

Compiler

Compiled 2775 to 750 computations (73% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))))
0.4b	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))
0.6b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))

rewrite218.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

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

Counts

4 → 62

Calls

4 calls:

4.0ms	(.f64 (sin.f64 phi1) (sin.f64 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))))
3.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))
1.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))
1.0ms	(expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))

Compiler

Compiled 2921 to 403 computations (86.2% saved)

series285.0ms (1.2%)

Error

0.1b

Counts

4 → 44

Calls

4 calls:

100.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))
93.0ms	(.f64 (sin.f64 phi1) (sin.f64 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))))
31.0ms	(expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))
21.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))

Compiler

Compiled 3897 to 2124 computations (45.5% saved)

simplify188.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

737×	`fma-neg_binary64`
354×	`fma-def_binary64`
335×	`distribute-rgt-neg-in_binary64`
331×	`distribute-rgt-in_binary64`
299×	`distribute-lft-neg-in_binary64`

Counts

106 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	5148
1	364	4726
2	875	4572
3	2573	4572
4	4807	4572
5	4999	4572

prune105.0ms (0.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	82	11	93

Error

0.1b

Counts

93 → 11

Alt Table

Status	Error	Program
	4.1b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))) 3)))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))))
✓	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)))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	28.0b	(+.f64 lambda1 (exp.f64 (log.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
✓	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 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
▶	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3)) (fma.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (cos.f64 delta))) (*.f64 (cos.f64 delta) (cos.f64 delta))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))) 3))))

Compiler

Compiled 2786 to 747 computations (73.2% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite881.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

96×	`prod-diff_binary64`
55×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
43×	`cube-prod_binary64`

Counts

4 → 184

Calls

4 calls:

12.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3))
4.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3)
1.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))
1.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))

Compiler

Compiled 20249 to 2667 computations (86.8% saved)

series290.0ms (1.2%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

112.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3))
88.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))) 3)
31.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))
26.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))

Compiler

Compiled 7722 to 2703 computations (65% saved)

simplify618.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-neg_binary64`
515×	`cancel-sign-sub-inv_binary64`
429×	`exp-prod_binary64`
346×	`unswap-sqr_binary64`
194×	`log-prod_binary64`

Counts

226 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	20269
1	474	16671
2	1707	13255
3	4003	13255
4	4950	13255
5	4968	13255
6	4775	13255

prune258.0ms (1.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	0	7	7
Picked	1	0	1
Done	0	3	3
Total	214	13	227

Error

0.1b

Counts

227 → 13

Alt Table

Status	Error	Program
	4.1b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))) 3)))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (log.f64 (exp.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) 3)))) (fma.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (cos.f64 delta))) (*.f64 (cos.f64 delta) (cos.f64 delta))))))
	28.0b	(+.f64 lambda1 (exp.f64 (log.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 6) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) 6)) (+.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) 3))) (fma.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (cos.f64 delta))) (.f64 (cos.f64 delta) (cos.f64 delta))))))
✓	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)))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	0.5b	(+.f64 lambda1 (.f64 (.f64 (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta)))))))))) (cbrt.f64 (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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	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 (-.f64 (/.f64 PI.f64 2) (acos.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))) 3)) (fma.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (sin.f64 phi1) (cos.f64 delta))))) (cos.f64 delta))) (*.f64 (cos.f64 delta) (cos.f64 delta))))))
✓	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 (log1p.f64 (expm1.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta)))))))))))
	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 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (sin.f64 phi1) (cos.f64 delta))))))) 3))))

Compiler

Compiled 6497 to 1122 computations (82.7% saved)

regimes2.6s (11.3%)

Accuracy

Total 0.1b remaining (54.1%)

Threshold costs 0.1b (54.1%)

Compiler

Compiled 73681 to 30665 computations (58.4% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	59
1	35	59
2	40	59
3	42	59
4	43	59
5	43	59

end1.0ms (0%)

Compiler: Compiled 40 to 25 computations (37.5% saved)

sample10.6s (45.2%)

Algorithm

1×

intervals

Results

7.2s	3928×	body	1024	valid
1.5s	1371×	body	512	valid
648.0ms	2202×	body	128	valid
338.0ms	484×	body	256	valid
64.0ms	15×	body	2048	valid

Compiler

Compiled 880 to 415 computations (52.8% saved)

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53

Details

analyze5.3s (22.7%)

sample339.0ms (1.4%)

simplify63.0ms (0.3%)

prune4.0ms (0%)

localize29.0ms (0.1%)

rewrite139.0ms (0.6%)

series178.0ms (0.8%)

simplify191.0ms (0.8%)

prune126.0ms (0.5%)

localize31.0ms (0.1%)

rewrite257.0ms (1.1%)

series245.0ms (1%)

simplify255.0ms (1.1%)

prune97.0ms (0.4%)

localize34.0ms (0.1%)

rewrite218.0ms (0.9%)

series285.0ms (1.2%)

simplify188.0ms (0.8%)

prune105.0ms (0.4%)

localize43.0ms (0.2%)

rewrite881.0ms (3.7%)

series290.0ms (1.2%)

simplify618.0ms (2.6%)

prune258.0ms (1.1%)

regimes2.6s (11.3%)

simplify5.0ms (0%)

end1.0ms (0%)

sample10.6s (45.2%)

Profiling

Iter	Nodes	Cost
0	23	53
1	40	53
2	66	53
3	85	53
4	99	53
5	133	53
6	173	53
7	217	53
8	281	53
9	305	53
10	362	53
11	407	53
12	468	53
13	604	53
14	728	53
15	836	53
16	943	53
17	891	53
18	893	53
19	899	53
20	904	53
21	841	53