Details

analyze5.2s (21.1%)

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)

sample11.9s (49%)

Results

8.4s	4071×	body	1024	valid
1.9s	1366×	body	512	valid
918.0ms	2241×	body	128	valid
445.0ms	573×	body	256	valid
23.0ms	5×	body	2048	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify51.0ms (0.2%)

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

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
	0.1b	(+.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 (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 (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 (*.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)))))))))

▶

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 122 computations (44.5% 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))
✓	0.3b	(.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))))
✓	0.6b	(-.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)))))))

series134.0ms (0.5%)

Counts

4 → 132

Calls

4 calls:

67.0ms	(-.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)))))))
50.0ms	(.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))))))
9.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
8.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(.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))))))
4.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
3.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify192.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

447×	`fma-neg_binary64`
377×	`distribute-rgt-neg-in_binary64`
326×	`distribute-lft-neg-in_binary64`
259×	`associate-r_binary64`
241×	`neg-mul-1_binary64`

Counts

204 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	6113
1	697	5704
2	2228	5493
3	4799	5493
4	4992	5493
5	4927	5493

prune365.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	174	11	185
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	176	11	187

Error

0.0b

Counts

187 → 11

Alt Table

Status	Error	Program
	2.7b	(+.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	31.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) 3))))
	11.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (cos.f64 phi1))))
	2.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (.f64 (.f64 (sin.f64 delta) (sin.f64 delta)) (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))))
	30.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sqrt.f64 (sin.f64 delta))) (sqrt.f64 (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (pow.f64 (sin.f64 phi1) 2) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)) (fma.f64 (cos.f64 delta) (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1)))))

Compiler

Compiled 9026 to 2037 computations (77.4% 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))
✓	0.3b	(.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1))
	0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
✓	0.6b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1)))

series123.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

72.0ms

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

51.0ms

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

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms

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

4.0ms

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

simplify189.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

755×	`cancel-sign-sub-inv_binary64`
558×	`sub-neg_binary64`
359×	`*-commutative_binary64`
342×	`fma-neg_binary64`
279×	`distribute-rgt-neg-in_binary64`

Counts

113 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	4363
1	506	4043
2	1576	3863
3	4032	3863
4	4970	3863
5	4998	3863
6	4923	3863

prune480.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	185	11	196

Error

0.0b

Counts

196 → 11

Alt Table

Status	Error	Program
	2.7b	(+.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	31.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1)))))))
	11.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (cos.f64 phi1))))
	2.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (.f64 (.f64 (sin.f64 delta) (sin.f64 delta)) (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))))
	30.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sqrt.f64 (sin.f64 delta))) (sqrt.f64 (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (pow.f64 (sin.f64 phi1) 2) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)) (fma.f64 (cos.f64 delta) (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1)))))

Compiler

Compiled 8992 to 2005 computations (77.7% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
✓	0.3b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
✓	0.3b	(pow.f64 (sin.f64 phi1) 2)
✓	0.6b	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))

series120.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

66.0ms	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))
35.0ms	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
15.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
4.0ms	(pow.f64 (sin.f64 phi1) 2)

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

7.0ms	(-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))
6.0ms	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
5.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
3.0ms	(pow.f64 (sin.f64 phi1) 2)

simplify105.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
445×	`associate-r_binary64`
404×	`distribute-rgt-neg-in_binary64`
367×	`distribute-lft-neg-in_binary64`
362×	`associate-l_binary64`

Counts

133 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	4632
1	865	3768
2	3035	3479
3	5127	3479

prune572.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	181	11	192

Error

0.0b

Counts

192 → 11

Alt Table

Status	Error	Program
	2.7b	(+.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	31.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (pow.f64 (sin.f64 phi1) 2) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (log1p.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))))
	2.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (.f64 (.f64 (sin.f64 delta) (sin.f64 delta)) (sin.f64 delta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))) (cbrt.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))))) (cbrt.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))))
	30.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sqrt.f64 (sin.f64 delta))) (sqrt.f64 (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (+.f64 (.f64 (pow.f64 (sin.f64 phi1) 2) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)) (fma.f64 (cos.f64 delta) (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1)))))

Compiler

Compiled 9879 to 3011 computations (69.5% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.5s (10.1%)

Counts

3 → 84

Calls

3 calls:

2.4s

(log1p.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))))

65.0ms

(expm1.f64 (log1p.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))

3.0ms

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

3.0ms

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

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta))))))

0.0ms

(log1p.f64 (fma.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.f64 delta)))))

simplify109.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-def_binary64`
467×	`unswap-sqr_binary64`
364×	`associate-r_binary64`
268×	`associate-l_binary64`
222×	`fma-neg_binary64`

Counts

135 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	4626
1	752	4395
2	3137	4329
3	5225	4329

prune477.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	4	4	8
Picked	1	0	1
Done	1	1	2
Total	169	9	178

Error

0.0b

Counts

178 → 9

Alt Table

Status	Error	Program
	2.7b	(+.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 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	31.6b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (sin.f64 theta)) (.f64 (sqrt.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)))))))))
	2.7b	(+.f64 lambda1 (atan2.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (.f64 (.f64 (sin.f64 delta) (sin.f64 delta)) (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1)))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 delta) (pow.f64 (cos.f64 phi1) 2)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 theta) (cos.f64 phi1)))))) 3)))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (log1p.f64 (fma.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta) (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta))) 3)) (neg.f64 (sin.f64 delta))))))))
	30.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sqrt.f64 (sin.f64 delta))) (sqrt.f64 (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 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (log1p.f64 (fma.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 phi1) 2)) (cbrt.f64 (pow.f64 (cos.f64 phi1) 2))) (cbrt.f64 (pow.f64 (cos.f64 phi1) 2))) (cos.f64 delta) (.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))) (neg.f64 (sin.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 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 phi1)))))

Compiler

Compiled 8153 to 2560 computations (68.6% saved)

regimes1.5s (6.1%)

Accuracy

Total 0.0b remaining (60.2%)

Threshold costs 0.0b (60.2%)

Counts

154 → 1

Compiler

Compiled 45064 to 25648 computations (43.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	51
1	33	51
2	43	51
3	55	51
4	69	51
5	78	51
6	84	51
7	86	51
8	86	51

end252.0ms (1%)

Compiler: Compiled 456 to 279 computations (38.8% 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

analyze5.2s (21.1%)

sample11.9s (49%)

simplify51.0ms (0.2%)

prune6.0ms (0%)

localize26.0ms (0.1%)

series134.0ms (0.5%)

rewrite17.0ms (0.1%)

simplify192.0ms (0.8%)

prune365.0ms (1.5%)

localize26.0ms (0.1%)

series123.0ms (0.5%)

rewrite11.0ms (0%)

simplify189.0ms (0.8%)

prune480.0ms (2%)

localize23.0ms (0.1%)

series120.0ms (0.5%)

rewrite28.0ms (0.1%)

simplify105.0ms (0.4%)

prune572.0ms (2.3%)

localize28.0ms (0.1%)

series2.5s (10.1%)

rewrite6.0ms (0%)

simplify109.0ms (0.4%)

prune477.0ms (2%)

regimes1.5s (6.1%)

simplify5.0ms (0%)

end252.0ms (1%)

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