Details

analyze5.4s (26.1%)

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)

sample445.0ms (2.1%)

Algorithm

1×

intervals

Results

218.0ms	130×	body	1024	valid
41.0ms	45×	body	512	valid
17.0ms	66×	body	128	valid
10.0ms	15×	body	256	valid

Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify52.0ms (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 → 2

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

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.2b

Counts

3 → 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 146 to 78 computations (46.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))))))
✓	0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
✓	0.4b	(-.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)))))))

series150.0ms (0.7%)

Counts

4 → 144

Calls

4 calls:

69.0ms	(-.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)))))))
52.0ms	(.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))))))
20.0ms	(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))))))))
9.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

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:

5.0ms	(.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))))))))

simplify241.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

808×	`cancel-sign-sub-inv_binary64`
564×	`sub-neg_binary64`
377×	`fma-neg_binary64`
300×	`distribute-rgt-neg-in_binary64`
270×	`neg-mul-1_binary64`

Counts

204 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	7907
1	540	7331
2	1704	7144
3	4123	7144
4	4819	7144
5	4946	7144

prune368.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	144	11	155
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	11	156

Error

0.0b

Counts

156 → 11

Alt Table

Status	Error	Program
	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 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) 3))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))
	15.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (exp.f64 (log.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.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 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (/.f64 (exp.f64 (cos.f64 delta)) (exp.f64 (.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)))))))))))
	29.9b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 theta theta)) 1/2) (.f64 (.f64 (cos.f64 phi1) (pow.f64 theta 6)) 1/720))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)) 1/24)))))))
▶	0.1b	(+.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))))
	3.9b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
	8.3b	(+.f64 lambda1 (log.f64 (exp.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 (+.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) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)) (fma.f64 (cos.f64 delta) (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta))))))))

Compiler

Compiled 7885 to 1764 computations (77.6% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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 (+.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))))))
	0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
✓	0.4b	(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.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)))))))))

series95.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

74.0ms

(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (*.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)))))))))

21.0ms

(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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms

(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (*.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)))))))))

0.0ms

(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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))

simplify182.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-def_binary64`
437×	`cancel-sign-sub-inv_binary64`
399×	`sub-neg_binary64`
356×	`*-commutative_binary64`
297×	`distribute-rgt-neg-in_binary64`

Counts

112 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	5837
1	413	5181
2	1307	4665
3	3610	4665
4	4774	4665
5	4886	4665

prune491.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	168	11	179

Error

0.0b

Counts

179 → 11

Alt Table

Status	Error	Program
	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 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) 3))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))
	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 phi1) (cos.f64 delta) (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))))))))))
	15.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (exp.f64 (log.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
✓	0.1b	(+.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))))
	23.9b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (fma.f64 1/2 (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (.f64 theta theta)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta))) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 1/24 (.f64 (cos.f64 phi1) (pow.f64 theta 4))))))))
	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 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (/.f64 (exp.f64 (cos.f64 delta)) (exp.f64 (.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)))))))))))
	3.9b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) 3)))
	8.3b	(+.f64 lambda1 (log.f64 (exp.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 (+.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) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)) (fma.f64 (cos.f64 delta) (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta))))))))

Compiler

Compiled 9602 to 1988 computations (79.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))
✓	0.3b	(pow.f64 (sin.f64 phi1) 2)
✓	0.3b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
✓	0.4b	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))

series110.0ms (0.5%)

Counts

4 → 24

Calls

4 calls:

71.0ms	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))
20.0ms	(atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))
15.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
4.0ms	(pow.f64 (sin.f64 phi1) 2)

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

4 → 82

Calls

4 calls:

7.0ms	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))
5.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
2.0ms	(pow.f64 (sin.f64 phi1) 2)
0.0ms	(atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))

simplify123.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-neg_binary64`
691×	`cancel-sign-sub-inv_binary64`
282×	`associate-r_binary64`
250×	`associate-l_binary64`
240×	`distribute-rgt-neg-in_binary64`

Counts

106 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	4090
1	685	3269
2	2297	2913
3	4287	2913
4	4919	2913

prune420.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	8	1	9
Picked	1	0	1
Done	1	0	1
Total	155	8	163

Error

0.0b

Counts

163 → 8

Alt Table

Status	Error	Program
	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 phi1) (cos.f64 delta) (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (+.f64 (.f64 (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) 3))))
	15.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (exp.f64 (log.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
	3.9b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)))
	8.3b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))

Compiler

Compiled 8204 to 2410 computations (70.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
✓	0.2b	(atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))
	0.3b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
✓	0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

series58.0ms (0.3%)

Counts

3 → 60

Calls

3 calls:

39.0ms

(*.f64 (sin.f64 delta) (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))

15.0ms

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

4.0ms

(*.f64 (cos.f64 phi1) (cos.f64 phi1))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

6.0ms

(*.f64 (sin.f64 delta) (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))

3.0ms

(*.f64 (cos.f64 phi1) (cos.f64 phi1))

0.0ms

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

simplify114.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

507×	`fma-def_binary64`
410×	`associate-r_binary64`
395×	`cancel-sign-sub-inv_binary64`
317×	`associate-l_binary64`
257×	`unswap-sqr_binary64`

Counts

122 → 111

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	3767
1	558	3442
2	1921	3216
3	3890	3205
4	4961	3205

prune354.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	146	8	154

Error

0.0b

Counts

154 → 8

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (+.f64 (.f64 (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 delta) (sin.f64 phi1)) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) 3))))
	3.9b	(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (.f64 (cos.f64 phi1) (-.f64 (.f64 (cos.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (sin.f64 delta) (sin.f64 phi1)) (cos.f64 theta))))) 3)))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (.f64 (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi1))) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))
	15.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (exp.f64 (log.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (sin.f64 theta) (cos.f64 phi1))) (-.f64 (.f64 (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 phi1) 2))) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))
	8.3b	(+.f64 lambda1 (log.f64 (exp.f64 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))

Compiler

Compiled 6259 to 1449 computations (76.8% saved)

regimes1.5s (7.3%)

Accuracy

Total 0.0b remaining (57.4%)

Threshold costs 0.0b (57.4%)

Counts

127 → 1

Compiler

Compiled 35473 to 20415 computations (42.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	51
1	33	51
2	49	51
3	65	51
4	77	51
5	84	51
6	86	51
7	86	51

end1.0ms (0%)

Compiler: Compiled 36 to 21 computations (41.7% saved)

sample10.4s (50.4%)

Algorithm

1×

intervals

Results

7.4s	3988×	body	1024	valid
1.3s	1335×	body	512	valid
594.0ms	2165×	body	128	valid
314.0ms	502×	body	256	valid
51.0ms	10×	body	2048	valid

Compiler

Compiled 454 to 259 computations (43% 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

analyze5.4s (26.1%)

sample445.0ms (2.1%)

simplify52.0ms (0.3%)

prune4.0ms (0%)

localize26.0ms (0.1%)

series150.0ms (0.7%)

rewrite13.0ms (0.1%)

simplify241.0ms (1.2%)

prune368.0ms (1.8%)

localize28.0ms (0.1%)

series95.0ms (0.5%)

rewrite8.0ms (0%)

simplify182.0ms (0.9%)

prune491.0ms (2.4%)

localize22.0ms (0.1%)

series110.0ms (0.5%)

rewrite20.0ms (0.1%)

simplify123.0ms (0.6%)

prune420.0ms (2%)

localize22.0ms (0.1%)

series58.0ms (0.3%)

rewrite13.0ms (0.1%)

simplify114.0ms (0.5%)

prune354.0ms (1.7%)

regimes1.5s (7.3%)

simplify4.0ms (0%)

end1.0ms (0%)

sample10.4s (50.4%)

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