Details

analyze5.0s (23.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
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 (49.7%)

Results

7.8s	4106×	body	1024	valid
1.5s	1348×	body	512	valid
783.0ms	2230×	body	128	valid
410.0ms	557×	body	256	valid
66.0ms	15×	body	2048	valid

Compiler

Compiled 78 to 48 computations (38.5% saved)

preprocess55.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

970×	`fma-def_binary64`
456×	`distribute-rgt-neg-out_binary64`
282×	`distribute-rgt-in_binary64`
225×	`cancel-sign-sub-inv_binary64`
210×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	583
1	290	583
2	508	583
3	715	583
4	891	583
5	1451	583
6	2671	583
7	3583	583
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 38 to 23 computations (39.5% saved)

simplify41.0ms (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))))
	0.2b	(+.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

▶

0.1b

(+.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))))

0.2b

(+.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 220 to 124 computations (43.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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))))
✓	0.6b	(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))

series116.0ms (0.5%)

Counts

4 → 144

Calls

36 calls:

9.0ms	(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))	theta	inf
8.0ms	(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))	delta	-inf
8.0ms	(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))	theta	-inf
7.0ms	(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))	phi1	-inf
7.0ms	(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))	phi1	inf

rewrite83.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

879×	`prod-diff_binary64`
194×	`add-sqr-sqrt_binary64`
191×	`*-un-lft-identity_binary64`
191×	`pow1_binary64`
177×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	88
1	390	86
2	4723	86
0	19	92

Stop Event

1×	saturated
1×	node limit

Counts

4 → 101

simplify96.0ms (0.5%)

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

prune419.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	9	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	169	10	179

Error

0.0b

Counts

179 → 10

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (expm1.f64 (log1p.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 (+.f64 (fma.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)))))) (fma.f64 (neg.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (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))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (log.f64 (+.f64 1 (expm1.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))))
	8.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (cbrt.f64 (fma.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))) (sin.f64 phi1) (cos.f64 delta))) 3)))
	25.7b	(+.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))))))))
	28.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))) 2) (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))))
	0.3b	(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (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))))
	8.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (log.f64 (exp.f64 (fma.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))) (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)))))))))
	13.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))

Compiler

Compiled 8867 to 2216 computations (75% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(expm1.f64 (log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))
✓	0.3b	(asin.f64 (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))))
✓	0.3b	(log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
✓	0.6b	(fma.f64 (sin.f64 (asin.f64 (expm1.f64 (log1p.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))

series1.1s (5.4%)

Counts

4 → 144

Calls

36 calls:

175.0ms	(log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))	theta	inf
174.0ms	(log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))	phi1	-inf
173.0ms	(log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))	delta	-inf
170.0ms	(log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))	phi1	inf
170.0ms	(log1p.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))	delta	inf

rewrite79.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

889×	`prod-diff_binary64`
172×	`add-sqr-sqrt_binary64`
170×	`pow1_binary64`
169×	`*-un-lft-identity_binary64`
160×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	98
1	351	96
2	4160	96
0	18	114

Stop Event

1×	saturated
1×	node limit

Counts

4 → 103

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

802×	`cancel-sign-sub-inv_binary64`
279×	`fma-neg_binary64`
271×	`associate-r_binary64`
269×	`unswap-sqr_binary64`
263×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4741
1	816	4629
2	3248	4594

Stop Event

1×	node limit

Counts

247 → 180

prune415.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	180	10	190

Error

0.0b

Counts

190 → 10

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (expm1.f64 (log1p.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 (+.f64 (fma.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)))))) (fma.f64 (neg.f64 (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (sqrt.f64 (acos.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))))) (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))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (log.f64 (+.f64 1 (expm1.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))))
	8.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (cbrt.f64 (fma.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))) (sin.f64 phi1) (cos.f64 delta))) 3)))
	9.7b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (-.f64 (fma.f64 1/2 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (.f64 theta theta)))) (cos.f64 delta)) (fma.f64 (cos.f64 delta) (pow.f64 (sin.f64 phi1) 2) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (cos.f64 phi1)))))))
	28.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))) 2) (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))))
	0.3b	(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (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))))
	8.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (log.f64 (exp.f64 (fma.f64 (fma.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)) (.f64 (cos.f64 delta) (sin.f64 phi1))) (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)))))))))
	13.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))

Compiler

Compiled 9893 to 2769 computations (72% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))))))

series129.0ms (0.6%)

Counts

4 → 132

Calls

33 calls:

11.0ms	(-.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)))))))	theta	inf
10.0ms	(-.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)))))))	delta	inf
9.0ms	(.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))))))	delta	inf
9.0ms	(-.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)))))))	theta	-inf
8.0ms	(-.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)))))))	phi1	inf

rewrite50.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

221×	`add-sqr-sqrt_binary64`
219×	`*-un-lft-identity_binary64`
219×	`pow1_binary64`
204×	`add-exp-log_binary64`
204×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	88
1	423	88
0	19	102

Stop Event

1×	saturated
1×	node limit

Counts

4 → 97

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

849×	`cancel-sign-sub-inv_binary64`
737×	`associate-l_binary64`
345×	`fma-neg_binary64`
278×	`distribute-rgt-neg-in_binary64`
253×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	143	3588
1	482	3470
2	1685	3370

Stop Event

1×	node limit

Counts

229 → 166

prune371.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	169	7	176

Error

0.0b

Counts

176 → 7

Alt Table

Status	Error	Program
	28.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))) 2) (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))))
	0.3b	(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (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 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 delta)) 2) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))))))
✓	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)))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (expm1.f64 (log1p.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))))
	13.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
▶	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) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))))

Compiler

Compiled 7580 to 1828 computations (75.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
✓	0.3b	(.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))
✓	0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))
✓	0.7b	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))

series154.0ms (0.7%)

Counts

3 → 108

Calls

27 calls:

10.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))	theta	inf
9.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))	theta	-inf
8.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))	delta	inf
8.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))	phi1	inf
8.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))	theta	-inf

rewrite77.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

297×	`expm1-udef_binary64`
297×	`log1p-udef_binary64`
167×	`add-sqr-sqrt_binary64`
166×	`pow1_binary64`
165×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	88
1	317	88
2	4194	88
0	16	92

Stop Event

1×	saturated
1×	node limit

Counts

3 → 101

simplify67.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
689×	`cancel-sign-sub-inv_binary64`
607×	`associate-r_binary64`
577×	`associate-l_binary64`
284×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	3746
1	365	3542
2	1292	3409

Stop Event

1×	node limit

Counts

209 → 111

prune254.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	28.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (sqrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta)))) 2) (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))))
	0.3b	(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (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 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 delta)) 2) (cbrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))))))
✓	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)))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (expm1.f64 (log1p.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))))
	13.0b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
✓	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) (fma.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))))))

Compiler

Compiled 6515 to 1588 computations (75.6% saved)

regimes1.7s (7.8%)

Accuracy

Total 0.1b remaining (58.8%)

Threshold costs 0.1b (58.8%)

Counts

173 → 1

Compiler

Compiled 45449 to 26971 computations (40.7% 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	22	53
1	31	53
2	33	53
3	34	53

Stop Event

1×

saturated

end217.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 339 to 205 computations (39.5% saved)

Details

analyze5.0s (23.6%)

sample10.6s (49.7%)

preprocess55.0ms (0.3%)

simplify41.0ms (0.2%)

prune5.0ms (0%)

localize25.0ms (0.1%)

series116.0ms (0.5%)

rewrite83.0ms (0.4%)

simplify96.0ms (0.5%)

prune419.0ms (2%)

localize28.0ms (0.1%)

series1.1s (5.4%)

rewrite79.0ms (0.4%)

simplify87.0ms (0.4%)

prune415.0ms (2%)

localize25.0ms (0.1%)

series129.0ms (0.6%)

rewrite50.0ms (0.2%)

simplify67.0ms (0.3%)

prune371.0ms (1.7%)

localize24.0ms (0.1%)

series154.0ms (0.7%)

rewrite77.0ms (0.4%)

simplify67.0ms (0.3%)

prune254.0ms (1.2%)

regimes1.7s (7.8%)

simplify3.0ms (0%)

end217.0ms (1%)

Profiling