Details

analyze4.9s (25.1%)

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
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
9.9%	89.8%	0.2%	13
9.9%	89.8%	0.2%	14

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample10.6s (54.5%)

Results

7.7s	4056×	body	1024	valid
1.5s	1382×	body	512	valid
813.0ms	2277×	body	128	valid
399.0ms	527×	body	256	valid
72.0ms	14×	body	2048	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	41	53
2	70	53
3	94	53
4	114	53
5	152	53
6	223	53
7	294	53
8	423	53
9	559	53
10	633	53
11	762	53
12	897	53
13	1091	53
14	1332	53
15	1650	53
16	1817	53
17	1991	53
18	1993	53
19	1999	53
20	2004	53

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

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

Status

Error

Program

▶

0.1b

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

0.1b

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

Compiler

Compiled 220 to 124 computations (43.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))
✓	0.2b	(.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))
✓	0.3b	(asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
✓	0.5b	(fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))

series114.0ms (0.6%)

Counts

4 → 144

Calls

4 calls:

55.0ms	(fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
29.0ms	(fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))
24.0ms	(.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))
5.0ms	(asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))

rewrite83.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`prod-diff_binary64`
193×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
175×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	88
1	374	86
2	4743	86

Stop Event

1×	node limit

Counts

4 → 101

Calls

4 calls:

80.0ms	(fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))
80.0ms	(.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))
80.0ms	(asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
80.0ms	(fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

383×	`fma-neg_binary64`
327×	`distribute-rgt-neg-in_binary64`
299×	`distribute-lft-neg-in_binary64`
290×	`associate-r_binary64`
220×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3774
1	643	3732
2	2210	3535

Stop Event

1×	node limit

Counts

245 → 177

prune380.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	169	8	177
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Error

0.0b

Counts

179 → 8

Alt Table

Status	Error	Program
	8.0b	(+.f64 lambda1 (atan2.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (sin.f64 theta)) (sin.f64 delta))) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.2b	(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta)))) 3) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 1) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	22.6b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (+.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (+.f64 (.f64 (.f64 (sin.f64 delta) 1/2) (.f64 theta theta)) (.f64 1/720 (.f64 (sin.f64 delta) (pow.f64 theta 6)))))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (+.f64 (.f64 (*.f64 (sin.f64 delta) 1/24) (pow.f64 theta 4)) (sin.f64 delta))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (+.f64 (fma.f64 (PI.f64) 1/2 (neg.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))))) (fma.f64 (neg.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (.f64 (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (cbrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) 1 (.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))) 1)))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	3.7b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 3)) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))

Compiler

Compiled 9001 to 2177 computations (75.8% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))
	0.3b	(asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
✓	0.5b	(fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
✓	2.4b	(log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))

series61.0ms (0.3%)

Counts

2 → 72

Calls

2 calls:

55.0ms

(fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))

6.0ms

(log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))))

rewrite65.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

854×	`prod-diff_binary64`
174×	`add-sqr-sqrt_binary64`
166×	`log1p-expm1-u_binary64`
166×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	58
1	348	52
2	4241	52

Stop Event

1×	node limit

Counts

2 → 59

Calls

2 calls:

62.0ms

(fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))

62.0ms

(log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))))

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-l_binary64`
481×	`associate-r_binary64`
463×	`fma-def_binary64`
367×	`cancel-sign-sub-inv_binary64`
364×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	2146
1	282	2132
2	946	2012
3	4414	2012

Stop Event

1×	node limit

Counts

131 → 85

prune398.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	164	8	172

Error

0.0b

Counts

172 → 8

Alt Table

Status	Error	Program
	8.0b	(+.f64 lambda1 (atan2.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 phi1)) (sin.f64 theta)) (sin.f64 delta))) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	19.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (fma.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 1/2 (.f64 (cos.f64 phi1) (.f64 theta theta)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta))) (.f64 (.f64 (sin.f64 delta) (sin.f64 phi1)) (+.f64 (cos.f64 phi1) (.f64 1/24 (.f64 (cos.f64 phi1) (pow.f64 theta 4))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta)))) 3) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 1) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) 1 (.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))) 1)))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	3.7b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 3)) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))

Compiler

Compiled 9197 to 2040 computations (77.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))
✓	0.2b	(*.f64 (sin.f64 delta) (sin.f64 theta))
	0.3b	(asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
	0.5b	(fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))

series8.0ms (0%)

Counts

1 → 8

Calls

1 calls:

8.0ms

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

rewrite35.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log1p-expm1-u_binary64`
614×	`expm1-log1p-u_binary64`
270×	`prod-diff_binary64`
120×	`expm1-udef_binary64`
120×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	123	8
2	1614	8

Stop Event

1×	node limit

Counts

1 → 20

Calls

1 calls:

35.0ms

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

simplify27.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

487×	`fma-neg_binary64`
429×	`distribute-rgt-neg-in_binary64`
370×	`distribute-lft-neg-in_binary64`
288×	`*-commutative_binary64`
238×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	204
1	130	196
2	407	172
3	1582	148
4	3383	148

Stop Event

1×	node limit

Counts

28 → 35

prune342.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	168	2	170
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	172	6	178

Error

0.0b

Counts

178 → 6

Alt Table

Status	Error	Program
	11.8b	(+.f64 lambda1 (atan2.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 1) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
	3.7b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 3)) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.2b	(+.f64 lambda1 (atan2.f64 (pow.f64 (.f64 (cos.f64 phi1) (pow.f64 (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) 3)) 1) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) 1 (.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))) 1)))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))

Compiler

Compiled 8445 to 2280 computations (73% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
✓	0.5b	(fma.f64 (sin.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
✓	2.4b	(log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))
✓	2.7b	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))

series82.0ms (0.4%)

Counts

4 → 144

Calls

4 calls:

55.0ms	(fma.f64 (sin.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
12.0ms	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))
10.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))
5.0ms	(acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))

rewrite60.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

228×	`add-sqr-sqrt_binary64`
213×	`log1p-expm1-u_binary64`
213×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
208×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	125
1	446	102

Stop Event

1×	node limit

Counts

4 → 133

Calls

4 calls:

55.0ms	(acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
55.0ms	(fma.f64 (sin.f64 (log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
55.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))))
55.0ms	(-.f64 (/.f64 (PI.f64) 2) (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))

simplify120.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
397×	`associate-l_binary64`
387×	`cancel-sign-sub-inv_binary64`
381×	`sub-neg_binary64`
356×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	4616
1	143	4612
2	389	4548
3	1285	4512
4	4654	4512

Stop Event

1×	node limit

Counts

277 → 110

prune224.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	111	5	116

Error

0.0b

Counts

116 → 5

Alt Table

Status	Error	Program
	11.8b	(+.f64 lambda1 (atan2.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 1) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
	3.7b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 3)) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.2b	(+.f64 lambda1 (atan2.f64 (pow.f64 (.f64 (cos.f64 phi1) (pow.f64 (cbrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) 3)) 1) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (asin.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (log.f64 (exp.f64 (fma.f64 (sqrt.f64 (.f64 (PI.f64) 1/2)) (sqrt.f64 (.f64 (PI.f64) 1/2)) (neg.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))

Compiler

Compiled 5894 to 1506 computations (74.4% saved)

regimes1.5s (7.9%)

Accuracy

Total 0.1b remaining (51.9%)

Threshold costs 0.1b (51.9%)

Counts

165 → 1

Compiler

Compiled 46891 to 28245 computations (39.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	33	57
2	35	57
3	36	57

Stop Event

1×

saturated

end163.0ms (0.8%)

Compiler: Compiled 279 to 177 computations (36.6% saved)

Details

analyze4.9s (25.1%)

sample10.6s (54.5%)

simplify42.0ms (0.2%)

prune5.0ms (0%)

localize24.0ms (0.1%)

series114.0ms (0.6%)

rewrite83.0ms (0.4%)

simplify66.0ms (0.3%)

prune380.0ms (1.9%)

localize26.0ms (0.1%)

series61.0ms (0.3%)

rewrite65.0ms (0.3%)

simplify58.0ms (0.3%)

prune398.0ms (2%)

localize27.0ms (0.1%)

series8.0ms (0%)

rewrite35.0ms (0.2%)

simplify27.0ms (0.1%)

prune342.0ms (1.8%)

localize29.0ms (0.1%)

series82.0ms (0.4%)

rewrite60.0ms (0.3%)

simplify120.0ms (0.6%)

prune224.0ms (1.1%)

regimes1.5s (7.9%)

simplify3.0ms (0%)

end163.0ms (0.8%)

Profiling