Details

analyze5.3s (24.4%)

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)

sample11.2s (51.8%)

Results

8.1s	4020×	body	1024	valid
1.6s	1418×	body	512	valid
846.0ms	2264×	body	128	valid
397.0ms	542×	body	256	valid
58.0ms	12×	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

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 (.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)

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))))
✓	0.4b	(-.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

4 calls:

64.0ms	(-.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)))))))
47.0ms	(.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))))

rewrite15.0ms (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:

4.0ms	(.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))))))
3.0ms	(*.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))))

simplify216.0ms (1%)

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

prune281.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	178	7	185
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	180	7	187

Error

0.0b

Counts

187 → 7

Alt Table

Status	Error	Program
	2.6b	(+.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) (log.f64 (exp.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)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (.f64 (.f64 (-.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))))))) (-.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)))))))) (-.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 (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)))))))))))
	12.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.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 (expm1.f64 (log1p.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 8568 to 1829 computations (78.7% saved)

localize28.0ms (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))))
	0.4b	(-.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)))))))

prune374.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	185	7	192

Error

0.0b

Counts

192 → 7

Alt Table

Status	Error	Program
	2.6b	(+.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) (log.f64 (exp.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)))))))))))
	0.1b	(+.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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
	12.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.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 (expm1.f64 (log1p.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))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (expm1.f64 (log1p.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 8812 to 1898 computations (78.5% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))))
✓	0.3b	(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))
✓	0.4b	(-.f64 (cos.f64 delta) (log.f64 (exp.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)))))))))
✓	2.9b	(log.f64 (exp.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))))))))

series218.0ms (1%)

Counts

4 → 144

Calls

4 calls:

101.0ms	(.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))))))
59.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.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)))))))))
51.0ms	(log.f64 (exp.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))))))))
6.0ms	(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

rewrite349.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`log-pow_binary64`

Counts

4 → 93

Calls

4 calls:

5.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.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)))))))))
3.0ms	(.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))))))
2.0ms	(log.f64 (exp.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))))))))
0.0ms	(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

simplify244.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-neg_binary64`
322×	`distribute-rgt-neg-in_binary64`
272×	`distribute-lft-neg-in_binary64`
230×	`neg-mul-1_binary64`
221×	`associate--l+_binary64`

Counts

237 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	8257
1	564	7598
2	1992	7448
3	4565	7439
4	4947	7439
5	4895	7439

prune405.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	174	7	181

Error

0.0b

Counts

181 → 7

Alt Table

Status	Error	Program
	2.6b	(+.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) (log.f64 (exp.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)))))))))))
	0.1b	(+.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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
	12.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.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 (expm1.f64 (log1p.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))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (expm1.f64 (log1p.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 9328 to 1713 computations (81.6% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))
✓	0.4b	(-.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)))))))
✓	0.5b	(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))
✓	0.6b	(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)

series361.0ms (1.7%)

Counts

3 → 108

Calls

3 calls:

242.0ms

(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)

59.0ms

(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))

59.0ms

(-.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)))))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 72

Calls

3 calls:

3.0ms

(-.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)))))))

3.0ms

(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)

3.0ms

(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))

simplify184.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-l_binary64`
599×	`fma-def_binary64`
445×	`associate-+r+_binary64`
270×	`associate-+l+_binary64`
192×	`*-commutative_binary64`

Counts

180 → 128

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	463	10410
1	1513	9779
2	5174	9779

prune381.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	147	8	155

Error

0.0b

Counts

155 → 8

Alt Table

Status	Error	Program
	2.6b	(+.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) (log.f64 (exp.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)))))))))))
	0.1b	(+.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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
	12.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.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 (expm1.f64 (log1p.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))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (expm1.f64 (log1p.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)))))))))
	16.9b	(+.f64 lambda1 (atan2.f64 (.f64 (expm1.f64 (log1p.f64 (.f64 (sin.f64 theta) (sin.f64 delta)))) (cos.f64 phi1)) (.f64 (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))))))) 3/2)) (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))))))) 3/2)))))

Compiler

Compiled 10805 to 3437 computations (68.2% saved)

regimes1.5s (7.2%)

Accuracy

Total 0.1b remaining (62.9%)

Threshold costs 0.1b (62.9%)

Counts

157 → 1

Compiler

Compiled 47472 to 26320 computations (44.6% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
13×	`+-commutative_binary64`
11×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	36	55
2	46	55
3	56	55
4	77	55
5	94	55
6	106	55
7	113	55
8	115	55
9	115	55

end222.0ms (1%)

Compiler: Compiled 430 to 249 computations (42.1% 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 (24.4%)

sample11.2s (51.8%)

simplify51.0ms (0.2%)

prune5.0ms (0%)

localize25.0ms (0.1%)

series129.0ms (0.6%)

rewrite15.0ms (0.1%)

simplify216.0ms (1%)

prune281.0ms (1.3%)

localize28.0ms (0.1%)

prune374.0ms (1.7%)

localize28.0ms (0.1%)

series218.0ms (1%)

rewrite349.0ms (1.6%)

simplify244.0ms (1.1%)

prune405.0ms (1.9%)

localize30.0ms (0.1%)

series361.0ms (1.7%)

rewrite15.0ms (0.1%)

simplify184.0ms (0.9%)

prune381.0ms (1.8%)

regimes1.5s (7.2%)

simplify6.0ms (0%)

end222.0ms (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