Details

analyze5.3s (14.6%)

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)

sample11.9s (32.7%)

Results

8.7s	4049×	body	1024	valid
1.6s	1345×	body	512	valid
860.0ms	2267×	body	128	valid
415.0ms	577×	body	256	valid
76.0ms	18×	body	2048	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify51.0ms (0.1%)

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

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	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 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (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 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 144 to 76 computations (47.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
✓	0.2b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
✓	0.3b	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓	0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))

series129.0ms (0.4%)

Counts

4 → 132

Calls

4 calls:

62.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
50.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
10.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
6.0ms	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

rewrite54.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

101× egg-rr

Counts

4 → 101

Calls

2 calls:

51.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	88
1	372	88
2	4964	88
0	0	0
1	0	0

simplify173.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

849×	`cancel-sign-sub-inv_binary64`
743×	`associate-l_binary64`
354×	`sub-neg_binary64`
345×	`fma-neg_binary64`
278×	`distribute-rgt-neg-in_binary64`

Counts

233 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	144	3588
1	473	3470
2	1555	3362
3	4252	3362
4	4960	3362
5	4981	3362
6	4981	3362

prune313.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	8	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	8	169

Error

0.0b

Counts

169 → 8

Alt Table

Status	Error	Program
	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta))))))))
	10.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
	22.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (+.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (-.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
	3.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	7.8b	(+.f64 lambda1 (atan2.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 delta)) (sin.f64 theta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	14.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

Compiler

Compiled 7867 to 1924 computations (75.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
✓	0.2b	(.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓	0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
✓	52.4b	(fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))

series404.0ms (1.1%)

Counts

3 → 108

Calls

3 calls:

236.0ms

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

116.0ms

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

52.0ms

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

rewrite120.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

79× egg-rr

Counts

3 → 79

Calls

2 calls:

117.0ms

((fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	111
1	341	106
2	4069	106
3	4966	106
4	5282	106
0	0	0
1	0	0

simplify109.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
689×	`cancel-sign-sub-inv_binary64`
615×	`associate-r_binary64`
584×	`associate-l_binary64`
333×	`sub-neg_binary64`

Counts

187 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	2464
1	356	2354
2	1194	2263
3	4452	2263
4	4952	2263
5	5045	2263

prune569.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	209	8	217

Error

0.0b

Counts

217 → 8

Alt Table

Status	Error	Program
▶	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta))))))))
	10.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
	22.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (+.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (-.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3))))
	3.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
	7.8b	(+.f64 lambda1 (atan2.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 delta)) (sin.f64 theta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	14.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

Compiler

Compiled 15909 to 2261 computations (85.8% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta))))))
✓	0.3b	(pow.f64 (cos.f64 delta) 3)
✓	0.3b	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3))
✓	0.4b	(pow.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)

series10.5s (28.9%)

Counts

4 → 112

Calls

4 calls:

10.0s	(.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta))))))
285.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3))
146.0ms	(pow.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)
6.0ms	(pow.f64 (cos.f64 delta) 3)

rewrite97.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

104× egg-rr

Counts

4 → 104

Calls

2 calls:

91.0ms

((pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3) (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (pow.f64 (cos.f64 delta) 3) (*.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (*.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta)))))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	176
1	552	174
2	4961	174
3	5178	174
0	0	0
1	0	0

simplify793.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

400×	`associate-+r+_binary64`
380×	`associate-r_binary64`
362×	`fma-def_binary64`
253×	`associate-/l*_binary64`
237×	`associate-/r*_binary64`

Counts

216 → 195

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1544	89385
1	5346	89385

prune2.0s (5.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	195	8	203

Error

0.0b

Counts

203 → 8

Alt Table

Status	Error	Program
✓	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta))))))))
	10.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
	22.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (+.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (-.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
▶	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3))))
	3.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
	7.8b	(+.f64 lambda1 (atan2.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 delta)) (sin.f64 theta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	14.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

Compiler

Compiled 121433 to 56032 computations (53.9% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓	0.4b	(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3))
	0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
✓	0.5b	(pow.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3)

series296.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

236.0ms

(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3)

60.0ms

(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3))

rewrite79.0ms (0.2%)

Algorithm

2×	batch-egg-rewrite

Rules

76× egg-rr

Counts

2 → 76

Calls

2 calls:

76.0ms

((pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3)))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65
1	342	65
2	4244	65
3	5104	65
0	0	0
1	0	0

simplify115.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

634×	`associate-l_binary64`
579×	`fma-def_binary64`
443×	`associate-+r+_binary64`
393×	`*-commutative_binary64`
314×	`+-commutative_binary64`

Counts

148 → 125

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	375	4920
1	1331	4841
2	4697	4841
3	4993	4841

prune633.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	229	8	237

Error

0.0b

Counts

237 → 8

Alt Table

Status	Error	Program
✓	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (/.f64 1 (+.f64 (pow.f64 (cos.f64 delta) 2) (.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta))))))))
	10.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (sin.f64 phi1) (*.f64 delta (cos.f64 theta)))))))
	22.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (+.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (-.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
✓	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) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) 3))))
	3.8b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
	7.8b	(+.f64 lambda1 (atan2.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (sin.f64 delta)) (sin.f64 theta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
	14.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

Compiler

Compiled 13759 to 4316 computations (68.6% saved)

regimes2.3s (6.4%)

Accuracy

Total 0.1b remaining (56.3%)

Threshold costs 0.1b (56.3%)

Counts

221 → 1

Compiler

Compiled 74359 to 38094 computations (48.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	105
1	39	105
2	48	105
3	53	105
4	55	105
5	55	105

end213.0ms (0.6%)

Compiler: Compiled 567 to 238 computations (58% saved)

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

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

Details

analyze5.3s (14.6%)

sample11.9s (32.7%)

simplify51.0ms (0.1%)

prune4.0ms (0%)

localize26.0ms (0.1%)

series129.0ms (0.4%)

rewrite54.0ms (0.1%)

simplify173.0ms (0.5%)

prune313.0ms (0.9%)

localize27.0ms (0.1%)

series404.0ms (1.1%)

rewrite120.0ms (0.3%)

simplify109.0ms (0.3%)

prune569.0ms (1.6%)

localize31.0ms (0.1%)

series10.5s (28.9%)

rewrite97.0ms (0.3%)

simplify793.0ms (2.2%)

prune2.0s (5.6%)

localize24.0ms (0.1%)

series296.0ms (0.8%)

rewrite79.0ms (0.2%)

simplify115.0ms (0.3%)

prune633.0ms (1.7%)

regimes2.3s (6.4%)

simplify4.0ms (0%)

end213.0ms (0.6%)

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