Details

analyze4.9s (21.4%)

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)

sample10.8s (46.6%)

Results

8.0s	4106×	body	1024	valid
1.5s	1348×	body	512	valid
821.0ms	2230×	body	128	valid
401.0ms	557×	body	256	valid
73.0ms	15×	body	2048	valid

Compiler

Compiled 78 to 48 computations (38.5% saved)

preprocess65.0ms (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)

simplify49.0ms (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

prune6.0ms (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
	0.2b	(+.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)))))))))
▶	0.1b	(+.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))))

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)))))))))

▶

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))))

Compiler

Compiled 220 to 124 computations (43.6% saved)

localize26.0ms (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))

series117.0ms (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))	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
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))	delta	-inf

rewrite84.0ms (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

simplify76.0ms (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

prune479.0ms (2.1%)

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
	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)))))))
	4.7b	(+.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))))
	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)))
	28.1b	(+.f64 lambda1 (atan2.f64 (pow.f64 (sqrt.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (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 (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))))
	20.5b	(+.f64 lambda1 (atan2.f64 (pow.f64 (pow.f64 (.f64 (cos.f64 phi1) (.f64 (sin.f64 delta) (sin.f64 theta))) 3) 1/3) (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 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.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))))

Compiler

Compiled 8717 to 2105 computations (75.9% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) 2)
✓	0.4b	(.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (*.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)))
✓	0.6b	(fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
✓	3.0b	(/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))

series611.0ms (2.6%)

Counts

4 → 132

Calls

33 calls:

53.0ms	(fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	theta	0
47.0ms	(fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	delta	inf
41.0ms	(fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	theta	-inf
40.0ms	(fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	phi1	-inf
39.0ms	(fma.f64 (sin.f64 (asin.f64 (/.f64 (-.f64 (.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	delta	-inf

rewrite47.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

242×	`add-sqr-sqrt_binary64`
233×	`log1p-expm1-u_binary64`
233×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
224×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	145
1	486	145

Stop Event

1×	node limit

Counts

4 → 65

simplify115.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-r_binary64`
465×	`associate-l_binary64`
308×	`fma-def_binary64`
270×	`times-frac_binary64`
231×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	384	9187
1	1322	9059

Stop Event

1×	node limit

Counts

197 → 151

prune417.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	150	9	159

Error

0.0b

Counts

159 → 9

Alt Table

Status	Error	Program
	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)))))))
	4.7b	(+.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 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.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))) (log1p.f64 (expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.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 (/.f64 (-.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.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 (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))))
	17.4b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))) 2)))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))) 3)))
	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))))

Compiler

Compiled 13208 to 4519 computations (65.8% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2)
✓	0.5b	(expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta)))
✓	0.6b	(fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
✓	3.0b	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)))))

series1.2s (5%)

Counts

4 → 144

Calls

36 calls:

240.0ms	(expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta)))	theta	0
60.0ms	(fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	theta	0
54.0ms	(expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta)))	delta	-inf
53.0ms	(expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta)))	delta	inf
49.0ms	(fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))	phi1	-inf

rewrite55.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`
215×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	200
1	471	190

Stop Event

1×	node limit

Counts

4 → 74

simplify216.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

655×	`times-frac_binary64`
571×	`fma-def_binary64`
370×	`*-commutative_binary64`
250×	`associate-r_binary64`
156×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	737	20131
1	2578	20047

Stop Event

1×	node limit

Counts

218 → 169

prune657.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	169	9	178

Error

0.0b

Counts

178 → 9

Alt Table

Status	Error	Program
	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)))))))
	4.7b	(+.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 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.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))) (log1p.f64 (expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.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 (/.f64 (-.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.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 (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))))
	17.4b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))) 2)))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))) 3)))
	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))))

Compiler

Compiled 24176 to 8985 computations (62.8% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) 2)
	0.4b	(pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2)
	0.6b	(fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))
	3.0b	(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)))))

prune489.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	157	9	166

Error

0.0b

Counts

166 → 9

Alt Table

Status	Error	Program
	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)))))))
	4.7b	(+.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 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.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))) (log1p.f64 (expm1.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.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 (/.f64 (-.f64 (log.f64 (exp.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2))) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (-.f64 (.f64 (.f64 (cos.f64 theta) (cos.f64 phi1)) (sin.f64 delta)) (.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 (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))))
	17.4b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))) 2)))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (sin.f64 theta))) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta))) 2) (pow.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) 2)) (fma.f64 (cos.f64 theta) (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))) 3)))
	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))))

Compiler

Compiled 13052 to 4526 computations (65.3% saved)

regimes2.3s (10.1%)

Accuracy

Total 0.1b remaining (59.2%)

Threshold costs 0.1b (59.2%)

Counts

197 → 1

Compiler

Compiled 61969 to 36505 computations (41.1% 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

end302.0ms (1.3%)

Stop Event

1×

fuel

Compiler

Compiled 560 to 297 computations (47% saved)

Details

analyze4.9s (21.4%)

sample10.8s (46.6%)

preprocess65.0ms (0.3%)

simplify49.0ms (0.2%)

prune6.0ms (0%)

localize26.0ms (0.1%)

series117.0ms (0.5%)

rewrite84.0ms (0.4%)

simplify76.0ms (0.3%)

prune479.0ms (2.1%)

localize32.0ms (0.1%)

series611.0ms (2.6%)

rewrite47.0ms (0.2%)

simplify115.0ms (0.5%)

prune417.0ms (1.8%)

localize33.0ms (0.1%)

series1.2s (5%)

rewrite55.0ms (0.2%)

simplify216.0ms (0.9%)

prune657.0ms (2.8%)

localize33.0ms (0.1%)

prune489.0ms (2.1%)

regimes2.3s (10.1%)

simplify3.0ms (0%)

end302.0ms (1.3%)

Profiling