Details

analyze5.1s (20.5%)

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)

sample11.4s (45.8%)

Results

7.9s	3972×	body	1024	valid
1.7s	1463×	body	512	valid
1.2s	2299×	body	128	valid
377.0ms	508×	body	256	valid
66.0ms	14×	body	2048	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify57.0ms (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

prune12.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (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)) (-.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 (*.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)))))))))

▶

0.2b

(+.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 122 computations (44.5% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))))
✓	0.3b	(.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))))))
✓	0.5b	(-.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)))))))

series151.0ms (0.6%)

Counts

4 → 144

Calls

4 calls:

69.0ms	(-.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)))))))
49.0ms	(.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))))))
24.0ms	(.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
9.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

7.0ms	(.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 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
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))))

simplify172.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-neg_binary64`
426×	`distribute-rgt-neg-in_binary64`
374×	`distribute-lft-neg-in_binary64`
340×	`associate-r_binary64`
329×	`associate-l_binary64`

Counts

215 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	6638
1	762	6146
2	2587	5922
3	4828	5922
4	4979	5922

prune292.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	188	5	193

Error

0.0b

Counts

193 → 5

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.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 phi1)))) (fma.f64 (neg.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) (.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))))))
	9.7b	(+.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 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.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)) (log1p.f64 (expm1.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)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (log1p.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)))))))))))

Compiler

Compiled 8722 to 2024 computations (76.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
	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))))))
✓	0.5b	(expm1.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))))))))
	0.5b	(-.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)))))))

series121.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

120.0ms

(expm1.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))))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`log1p-expm1-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.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))))))))

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

485×	`cancel-sign-sub-inv_binary64`
435×	`associate-r_binary64`
403×	`fma-neg_binary64`
287×	`associate-l_binary64`
204×	`*-commutative_binary64`

Counts

47 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	2797
1	612	2643
2	2496	2394
3	4542	2393
4	4986	2393

prune351.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	182	5	187

Error

0.0b

Counts

187 → 5

Alt Table

Status	Error	Program
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 delta)) (cbrt.f64 (cos.f64 delta))) (cbrt.f64 (cos.f64 delta)) (neg.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 phi1)))) (fma.f64 (neg.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) (.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))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (cos.f64 theta) (*.f64 (cos.f64 phi1) (sin.f64 delta))))))))) 3)))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (log.f64 (exp.f64 (expm1.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)))))))))))))
▶	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.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)))))))))))
	2.5b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (fma.f64 (pow.f64 (cos.f64 phi1) 2) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (sin.f64 phi1))))))))

Compiler

Compiled 9655 to 2633 computations (72.7% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.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))))
	0.3b	(.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))))))
✓	0.5b	(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.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)))))))))

series68.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

68.0ms

(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (*.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)))))))))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
9×	`add-cube-cbrt_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

1 → 31

Calls

1 calls:

3.0ms

(-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (*.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)))))))))

simplify185.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-def_binary64`
437×	`cancel-sign-sub-inv_binary64`
399×	`sub-neg_binary64`
352×	`*-commutative_binary64`
297×	`distribute-rgt-neg-in_binary64`

Counts

67 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	3449
1	391	2894
2	1283	2486
3	3584	2486
4	4746	2486
5	4986	2486
6	4893	2486

prune783.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	203	6	209

Error

0.0b

Counts

209 → 6

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 (expm1.f64 (log1p.f64 (.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)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (+.f64 (.f64 (expm1.f64 (log1p.f64 (.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)))))))) (expm1.f64 (log1p.f64 (.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) (expm1.f64 (log1p.f64 (.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)) (log1p.f64 (log.f64 (exp.f64 (expm1.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)))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (exp.f64 (log1p.f64 (.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)))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (cos.f64 theta) (*.f64 (cos.f64 phi1) (sin.f64 delta))))))))) 3)))))
✓	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (expm1.f64 (log1p.f64 (.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)))))))))))
	2.5b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (fma.f64 (pow.f64 (cos.f64 phi1) 2) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (sin.f64 phi1))))))))

Compiler

Compiled 10707 to 2445 computations (77.2% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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	(pow.f64 (cos.f64 delta) 3)
✓	0.3b	(.f64 (expm1.f64 (log1p.f64 (.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)))))))) (expm1.f64 (log1p.f64 (.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)))))))))
✓	0.5b	(pow.f64 (expm1.f64 (log1p.f64 (.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)

series295.0ms (1.2%)

Counts

3 → 76

Calls

3 calls:

181.0ms

(pow.f64 (expm1.f64 (log1p.f64 (*.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)

107.0ms

(*.f64 (expm1.f64 (log1p.f64 (*.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)))))))) (expm1.f64 (log1p.f64 (*.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)))))))))

6.0ms

(pow.f64 (cos.f64 delta) 3)

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 77

Calls

3 calls:

3.0ms

(pow.f64 (expm1.f64 (log1p.f64 (*.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)

3.0ms

(*.f64 (expm1.f64 (log1p.f64 (*.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)))))))) (expm1.f64 (log1p.f64 (*.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)))))))))

2.0ms

(pow.f64 (cos.f64 delta) 3)

simplify207.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

394×	`cancel-sign-sub-inv_binary64`
373×	`*-commutative_binary64`
349×	`fma-neg_binary64`
330×	`fma-def_binary64`
191×	`sub-neg_binary64`

Counts

153 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	372	6797
1	1132	6059
2	2884	5963
3	4432	5960
4	4863	5960
5	4971	5960

prune1.0s (4.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	388	1	389
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	389	6	395

Error

0.0b

Counts

395 → 6

Alt Table

Status	Error	Program
	17.4b	(+.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 (pow.f64 (expm1.f64 (log1p.f64 (.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)))))))) (sqrt.f64 3)) (sqrt.f64 3))) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (+.f64 (.f64 (expm1.f64 (log1p.f64 (.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)))))))) (expm1.f64 (log1p.f64 (.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) (expm1.f64 (log1p.f64 (.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 (cos.f64 delta) (expm1.f64 (log1p.f64 (.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 (cos.f64 delta) (exp.f64 (log1p.f64 (.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)))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (cos.f64 theta) (*.f64 (cos.f64 phi1) (sin.f64 delta))))))))) 3)))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (log.f64 (exp.f64 (expm1.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)))))))))))))
	2.5b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (fma.f64 (pow.f64 (cos.f64 phi1) 2) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (neg.f64 (sin.f64 phi1))))))))

Compiler

Compiled 49712 to 7316 computations (85.3% saved)

regimes4.2s (16.8%)

Accuracy

Total 0.1b remaining (55.9%)

Threshold costs 0.1b (55.9%)

Counts

290 → 1

Compiler

Compiled 143974 to 62055 computations (56.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	25	55
1	40	55
2	49	55
3	55	55
4	59	55
5	60	55
6	59	55

end200.0ms (0.8%)

Compiler: Compiled 399 to 213 computations (46.6% 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

analyze5.1s (20.5%)

sample11.4s (45.8%)

simplify57.0ms (0.2%)

prune12.0ms (0%)

localize27.0ms (0.1%)

series151.0ms (0.6%)

rewrite19.0ms (0.1%)

simplify172.0ms (0.7%)

prune292.0ms (1.2%)

localize28.0ms (0.1%)

series121.0ms (0.5%)

rewrite1.0ms (0%)

simplify96.0ms (0.4%)

prune351.0ms (1.4%)

localize28.0ms (0.1%)

series68.0ms (0.3%)

rewrite7.0ms (0%)

simplify185.0ms (0.7%)

prune783.0ms (3.2%)

localize41.0ms (0.2%)

series295.0ms (1.2%)

rewrite13.0ms (0.1%)

simplify207.0ms (0.8%)

prune1.0s (4.1%)

regimes4.2s (16.8%)

simplify4.0ms (0%)

end200.0ms (0.8%)

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