Details

analyze8.4s (17.3%)

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%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample19.5s (40.1%)

Results

15.1s	4034×	body	1024	valid
2.3s	1344×	body	512	valid
1.2s	2282×	body	128	valid
639.0ms	584×	body	256	valid
69.0ms	12×	body	2048	valid

Compiler

Compiled 77 to 47 computations (39% saved)

simplify1.6s (3.4%)

Algorithm

1×	egg-herbie

Rules

523×	`fma-def_binary64`
515×	`associate-r_binary64`
503×	`associate-+r+_binary64`
452×	`distribute-rgt-in_binary64`
429×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	41	53
2	71	53
3	96	53
4	120	53
5	186	53
6	330	53
7	491	53
8	793	53
9	1390	53
10	1530	53
11	1750	53
12	1913	53
13	2325	53
14	4434	53

prune9.0ms (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 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

Status

Error

Program

▶

0.2b

(+.f64 lambda1 (atan2.f64 (*.f64 (sin.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))

0.2b

(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

Compiler

Compiled 220 to 124 computations (43.6% saved)

localize49.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))
✓	0.3b	(.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))
✓	0.4b	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1))))
✓	0.6b	(fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))

series415.0ms (0.9%)

Counts

4 → 144

Calls

4 calls:

250.0ms	(fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))
86.0ms	(sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))
62.0ms	(.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))
16.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1))))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

4 → 52

Calls

4 calls:

18.0ms	(.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))
2.0ms	(fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))
2.0ms	(sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))
1.0ms	(asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1))))

simplify2.2s (4.5%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-r_binary64`
384×	`fma-neg_binary64`
330×	`distribute-lft-neg-in_binary64`
330×	`distribute-rgt-neg-in_binary64`
275×	`associate-l_binary64`

Counts

196 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	5350
1	818	5028
2	2889	4833

prune570.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	6	163

Error

0.0b

Counts

163 → 6

Alt Table

Status	Error	Program
	3.9b	(+.f64 lambda1 (atan2.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (.f64 (.f64 (.f64 (sin.f64 delta) (sin.f64 delta)) (sin.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 phi1))))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (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))))))))
	16.4b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (.f64 (sqrt.f64 (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))) (sqrt.f64 (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (*.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (cbrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (cos.f64 phi1)))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))
	11.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (.f64 (*.f64 delta (cos.f64 theta)) (sin.f64 phi1))))))

Compiler

Compiled 7120 to 1665 computations (76.6% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
✓	0.3b	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
✓	0.3b	(pow.f64 (sin.f64 phi1) 2)
✓	0.5b	(-.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))))))

series202.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

115.0ms	(-.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))))))
55.0ms	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
25.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
6.0ms	(pow.f64 (sin.f64 phi1) 2)

rewrite39.0ms (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:

11.0ms	(-.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))))))
10.0ms	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
7.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
2.0ms	(pow.f64 (sin.f64 phi1) 2)

simplify2.1s (4.4%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
482×	`associate-r_binary64`
384×	`associate-l_binary64`
256×	`*-commutative_binary64`
236×	`sub-neg_binary64`

Counts

133 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	4632
1	933	3768
2	3772	3486

prune921.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	195	6	201

Error

0.0b

Counts

201 → 6

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (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))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (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 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cbrt.f64 (sin.f64 phi1)) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (+.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))))) (+.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))))))) (+.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)))))))))
	16.3b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (.f64 (sqrt.f64 (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi1)) (.f64 (cos.f64 theta) (sin.f64 delta))))) (sqrt.f64 (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 theta) (sin.f64 delta))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (cbrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (cos.f64 phi1)))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))

Compiler

Compiled 9891 to 2911 computations (70.6% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))
	0.3b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (cos.f64 theta)))
	0.3b	(.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (cos.f64 theta))))
✓	0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

series8.0ms (0%)

Counts

1 → 12

Calls

1 calls:

7.0ms

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

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
3×	`associate-r_binary64`

Counts

1 → 29

Calls

1 calls:

9.0ms

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

simplify604.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
415×	`cancel-sign-sub-inv_binary64`
328×	`fma-neg_binary64`
216×	`associate-l_binary64`
211×	`*-commutative_binary64`

Counts

41 → 46

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	361
1	118	313
2	358	305
3	1196	294
4	2772	264

prune916.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	194	6	200

Error

0.0b

Counts

200 → 6

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (cbrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (cos.f64 phi1)))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (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 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (cbrt.f64 (sin.f64 phi1)))))))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (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))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (+.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))))) (+.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))))))) (+.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)))))))))
	16.3b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (.f64 (sqrt.f64 (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi1)) (.f64 (cos.f64 theta) (sin.f64 delta))))) (sqrt.f64 (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 theta) (sin.f64 delta))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (cbrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (cos.f64 phi1)))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))

Compiler

Compiled 8365 to 1959 computations (76.6% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (.f64 (cos.f64 theta) (cbrt.f64 (sin.f64 phi1)))))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1)))
✓	0.6b	(cbrt.f64 (sin.f64 phi1))

series826.0ms (1.7%)

Counts

3 → 48

Calls

3 calls:

426.0ms

(*.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1)))

368.0ms

(cbrt.f64 (sin.f64 phi1))

31.0ms

(*.f64 (*.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (cbrt.f64 (sin.f64 phi1)))))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
17×	`pow-prod-down_binary64`

Counts

3 → 85

Calls

3 calls:

22.0ms

(*.f64 (*.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (*.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (cbrt.f64 (sin.f64 phi1)))))

11.0ms

(*.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1)))

2.0ms

(cbrt.f64 (sin.f64 phi1))

simplify1.9s (4%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-neg_binary64`
386×	`fma-def_binary64`
317×	`associate-r_binary64`
285×	`associate-l_binary64`
278×	`cancel-sign-sub-inv_binary64`

Counts

133 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	2521
1	526	1714
2	1985	1632
3	4702	1632

prune1.1s (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	234	6	240

Error

Counts

240 → 6

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (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 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cbrt.f64 (pow.f64 (sin.f64 phi1) 2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 theta) (cbrt.f64 (sin.f64 phi1)))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (cbrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (cos.f64 phi1)))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (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 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (-.f64 (.f64 (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi1)) 1/2)) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (.f64 (cbrt.f64 (sin.f64 phi1)) (cbrt.f64 (sin.f64 phi1))) (.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (cbrt.f64 (sin.f64 phi1)))))))))
	16.3b	(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))) (.f64 (sqrt.f64 (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi1)) (.f64 (cos.f64 theta) (sin.f64 delta))))) (sqrt.f64 (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi1)) (*.f64 (cos.f64 theta) (sin.f64 delta))))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (.f64 (cbrt.f64 (sin.f64 theta)) (.f64 (sin.f64 delta) (cos.f64 phi1)))) (fma.f64 (sin.f64 phi1) (neg.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)) (.f64 (cos.f64 delta) (sin.f64 phi1)))))) (cos.f64 delta))))

Compiler

Compiled 10956 to 2318 computations (78.8% saved)

regimes6.1s (12.7%)

Accuracy

Total 0.0b remaining (49.4%)

Threshold costs 0.0b (49.4%)

Counts

213 → 1

Compiler

Compiled 61220 to 35364 computations (42.2% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`cancel-sign-sub-inv_binary64`
10×	`sub-neg_binary64`
9×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	64
1	40	64
2	53	64
3	65	64
4	79	64
5	94	64
6	104	64
7	110	64
8	112	64

soundness422.0ms (0.9%)

Compiler: Compiled 11167 to 7095 computations (36.5% saved)

end328.0ms (0.7%)

Compiler: Compiled 367 to 204 computations (44.4% saved)

Details

analyze8.4s (17.3%)

sample19.5s (40.1%)

simplify1.6s (3.4%)

prune9.0ms (0%)

localize49.0ms (0.1%)

series415.0ms (0.9%)

rewrite29.0ms (0.1%)

simplify2.2s (4.5%)

prune570.0ms (1.2%)

localize39.0ms (0.1%)

series202.0ms (0.4%)

rewrite39.0ms (0.1%)

simplify2.1s (4.4%)

prune921.0ms (1.9%)

localize42.0ms (0.1%)

series8.0ms (0%)

rewrite11.0ms (0%)

simplify604.0ms (1.2%)

prune916.0ms (1.9%)

localize55.0ms (0.1%)

series826.0ms (1.7%)

rewrite46.0ms (0.1%)

simplify1.9s (4%)

prune1.1s (2.2%)

regimes6.1s (12.7%)

simplify11.0ms (0%)

soundness422.0ms (0.9%)

end328.0ms (0.7%)

Profiling