Details

analyze5.3s (21.8%)

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)

sample11.6s (47.5%)

Results

8.6s	4148×	body	1024	valid
1.6s	1337×	body	512	valid
847.0ms	2219×	body	128	valid
431.0ms	540×	body	256	valid
52.0ms	12×	body	2048	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify49.0ms (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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

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

Status

Error

Program

▶

0.2b

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

Compiler

Compiled 144 to 76 computations (47.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
✓	0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
✓	0.3b	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓	0.5b	(-.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)))))))

series136.0ms (0.6%)

Counts

4 → 144

Calls

4 calls:

56.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
47.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
25.0ms	(.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
7.0ms	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

rewrite16.0ms (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 → 72

Calls

4 calls:

5.0ms	(.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
4.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
3.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
0.0ms	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

simplify170.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-neg_binary64`
438×	`distribute-rgt-neg-in_binary64`
384×	`distribute-lft-neg-in_binary64`
373×	`associate-r_binary64`
358×	`associate-l_binary64`

Counts

216 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	6669
1	815	6209
2	2749	6018
3	4976	6018
4	4939	6018

prune418.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	186	8	194
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	8	195

Error

0.0b

Counts

195 → 8

Alt Table

Status	Error	Program
	17.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.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)))))))) (sqrt.f64 (-.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 (fma.f64 1 (cos.f64 delta) (neg.f64 (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1)))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))) (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)))) (cbrt.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 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)))))))
	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 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1)))) (cbrt.f64 (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)))))))))
	10.3b	(+.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)) (expm1.f64 (log1p.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))

Compiler

Compiled 9068 to 1956 computations (78.4% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))
	0.3b	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓	0.5b	(fma.f64 1 (cos.f64 delta) (neg.f64 (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))
✓	54.4b	(fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1)))

series324.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

214.0ms

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

59.0ms

(fma.f64 1 (cos.f64 delta) (neg.f64 (*.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))

50.0ms

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

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 41

Calls

3 calls:

4.0ms

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

0.0ms

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

0.0ms

(fma.f64 1 (cos.f64 delta) (neg.f64 (*.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))

simplify137.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

727×	`cancel-sign-sub-inv_binary64`
550×	`distribute-rgt-neg-in_binary64`
530×	`sub-neg_binary64`
355×	`*-commutative_binary64`
331×	`fma-neg_binary64`

Counts

149 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	4398
1	462	3814
2	1518	3440
3	3679	3440
4	4794	3440
5	4915	3440

prune688.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	239	8	247

Error

0.0b

Counts

247 → 8

Alt Table

Status	Error	Program
	17.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.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)))))))) (sqrt.f64 (-.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 (fma.f64 1 (cos.f64 delta) (neg.f64 (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1)))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))) (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)))) (cbrt.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 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (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))))))))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1)))) (cbrt.f64 (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)))))))))
	10.3b	(+.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)) (expm1.f64 (log1p.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))

Compiler

Compiled 19968 to 2744 computations (86.3% saved)

localize28.0ms (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))))
✓	0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.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 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)
✓	6.6b	(cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3))

series112.0ms (0.5%)

Counts

4 → 144

Calls

4 calls:

57.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)))))
44.0ms	(pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)
6.0ms	(cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3))
6.0ms	(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

3.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)))))
2.0ms	(cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3))
1.0ms	(pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3)
0.0ms	(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

simplify233.0ms (1%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
411×	`cancel-sign-sub-inv_binary64`
387×	`sub-neg_binary64`
364×	`*-commutative_binary64`
226×	`unswap-sqr_binary64`

Counts

222 → 133

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	186	7182
1	446	6669
2	1374	6437
3	3820	6437
4	4763	6434
5	4984	6434
6	4918	6434

prune367.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	133	8	141

Error

0.0b

Counts

141 → 8

Alt Table

Status	Error	Program
	20.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (fma.f64 1/2 (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (.f64 theta theta)))) (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 1/24 (.f64 (cos.f64 phi1) (pow.f64 theta 4))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (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))))))))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	15.9b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1)))) (cbrt.f64 (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)))))))))
	10.3b	(+.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)) (expm1.f64 (log1p.f64 (-.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 (fma.f64 1 (cos.f64 delta) (neg.f64 (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1)))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))) (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 6875 to 1860 computations (72.9% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (-.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))))))))
	0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
	0.3b	(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
	0.5b	(-.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)))))))

series1.8s (7.4%)

Counts

1 → 36

Calls

1 calls:

1.8s	(log1p.f64 (-.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))))))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-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

(log1p.f64 (-.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))))))))

simplify92.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

387×	`fma-def_binary64`
349×	`unswap-sqr_binary64`
257×	`associate-r_binary64`
220×	`cancel-sign-sub-inv_binary64`
177×	`associate-l_binary64`

Counts

47 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	190	2936
1	589	2769
2	2529	2642
3	4967	2642
4	5065	2642

prune470.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	180	8	188

Error

0.0b

Counts

188 → 8

Alt Table

Status	Error	Program
	20.8b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (fma.f64 1/2 (.f64 (sin.f64 delta) (.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (.f64 theta theta)))) (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1)))) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 1/24 (.f64 (cos.f64 phi1) (pow.f64 theta 4))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (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))))))))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	15.9b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (sqrt.f64 (cos.f64 delta)) (sqrt.f64 (cos.f64 delta)) (neg.f64 (.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 3))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (.f64 (cbrt.f64 (cos.f64 phi1)) (cbrt.f64 (cos.f64 phi1)))) (cbrt.f64 (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)))))))))
	10.3b	(+.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)) (expm1.f64 (log1p.f64 (-.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 (fma.f64 1 (cos.f64 delta) (neg.f64 (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1)))) (fma.f64 (neg.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))) (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (sin.f64 phi1))))))
	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))) (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)))) (cbrt.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)))) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

Compiler

Compiled 9662 to 2655 computations (72.5% saved)

regimes2.1s (8.5%)

Accuracy

Total 0.1b remaining (65.4%)

Threshold costs 0.1b (65.4%)

Counts

209 → 1

Compiler

Compiled 64433 to 36134 computations (43.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	117
1	44	117
2	52	117
3	56	117
4	57	117
5	57	117

end235.0ms (1%)

Compiler: Compiled 577 to 260 computations (54.9% 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 (21.8%)

sample11.6s (47.5%)

simplify49.0ms (0.2%)

prune4.0ms (0%)

localize26.0ms (0.1%)

series136.0ms (0.6%)

rewrite16.0ms (0.1%)

simplify170.0ms (0.7%)

prune418.0ms (1.7%)

localize31.0ms (0.1%)

series324.0ms (1.3%)

rewrite7.0ms (0%)

simplify137.0ms (0.6%)

prune688.0ms (2.8%)

localize28.0ms (0.1%)

series112.0ms (0.5%)

rewrite11.0ms (0%)

simplify233.0ms (1%)

prune367.0ms (1.5%)

localize31.0ms (0.1%)

series1.8s (7.4%)

rewrite1.0ms (0%)

simplify92.0ms (0.4%)

prune470.0ms (1.9%)

regimes2.1s (8.5%)

simplify4.0ms (0%)

end235.0ms (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