Details

analyze5.8s (26.5%)

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 (52%)

Results

8.3s	4040×	body	1024	valid
1.6s	1389×	body	512	valid
837.0ms	2244×	body	128	valid
407.0ms	569×	body	256	valid
68.0ms	14×	body	2048	valid

Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify54.0ms (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

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

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

Compiler

Compiled 146 to 78 computations (46.6% saved)

localize30.0ms (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))))
✓	0.5b	(-.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)))))))

series134.0ms (0.6%)

Counts

4 → 132

Calls

4 calls:

66.0ms	(-.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)))))))
51.0ms	(.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))))))
10.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
7.0ms	(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 theta) (sin.f64 delta))
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 (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))))

simplify198.0ms (0.9%)

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

prune308.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	180	5	185
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	180	6	186

Error

0.0b

Counts

186 → 6

Alt Table

Status	Error	Program
▶	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)))))))))
	26.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 theta theta)) 1/2) (.f64 (.f64 (cos.f64 phi1) (pow.f64 theta 6)) 1/720))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)) 1/24)))))))
	2.9b	(+.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)))))))))
✓	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)))))))))
	11.0b	(+.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))))))
	33.3b	(+.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)))))))))

Compiler

Compiled 8398 to 1774 computations (78.9% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sin.f64 theta) (*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.f64 (sin.f64 delta)))
	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)))))))
✓	0.5b	(*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))
✓	0.7b	(cbrt.f64 (sin.f64 delta))

series430.0ms (2%)

Counts

3 → 48

Calls

3 calls:

233.0ms

(*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))

186.0ms

(cbrt.f64 (sin.f64 delta))

10.0ms

(*.f64 (*.f64 (sin.f64 theta) (*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.f64 (sin.f64 delta)))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (sin.f64 theta) (*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.f64 (sin.f64 delta)))

6.0ms

(*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))

1.0ms

(cbrt.f64 (sin.f64 delta))

simplify116.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

846×	`unswap-sqr_binary64`
553×	`fma-neg_binary64`
464×	`*-commutative_binary64`
364×	`log-prod_binary64`
291×	`fma-def_binary64`

Counts

129 → 144

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	164	1723
1	423	1469
2	1372	1386
3	2750	1350
4	4535	1332
5	4938	1332
6	5049	1332

prune410.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	0	4	4
Picked	0	1	1
Done	1	0	1
Total	252	6	258

Error

0.0b

Counts

258 → 6

Alt Table

Status	Error	Program
✓	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)))))))))
	26.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 theta theta)) 1/2) (.f64 (.f64 (cos.f64 phi1) (pow.f64 theta 6)) 1/720))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)) 1/24)))))))
	2.9b	(+.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)))))))))
▶	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta))))) (cbrt.f64 (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)))))))))
	11.0b	(+.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))))))
	33.3b	(+.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)))))))))

Compiler

Compiled 12826 to 2509 computations (80.4% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))
✓	0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 delta)))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta))))
	0.7b	(cbrt.f64 (sin.f64 delta))

series380.0ms (1.7%)

Counts

2 → 24

Calls

2 calls:

215.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta))))
165.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 delta)))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

3.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta))))
1.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 delta)))

simplify106.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

517×	`sub-neg_binary64`
483×	`fma-def_binary64`
467×	`distribute-rgt-neg-in_binary64`
381×	`distribute-lft-neg-in_binary64`
339×	`neg-mul-1_binary64`

Counts

51 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	82	640
1	183	640
2	400	616
3	963	610
4	2721	592
5	4143	592
6	4602	592
7	4983	592
8	4860	592

prune493.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	309	6	315

Error

0.0b

Counts

315 → 6

Alt Table

Status	Error	Program
✓	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)))))))))
	26.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 theta theta)) 1/2) (.f64 (.f64 (cos.f64 phi1) (pow.f64 theta 6)) 1/720))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)) 1/24)))))))
▶	2.9b	(+.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)))))))))
✓	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta))))) (cbrt.f64 (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)))))))))
	11.0b	(+.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))))))
	33.3b	(+.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)))))))))

Compiler

Compiled 18380 to 3372 computations (81.7% saved)

localize30.0ms (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	(pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3)
	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)))))))
✓	25.6b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3))

series47.0ms (0.2%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3)
10.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`cbrt-prod_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`
5×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3))

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
424×	`fma-def_binary64`
395×	`*-commutative_binary64`
293×	`cancel-sign-sub-inv_binary64`

Counts

93 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1409
1	330	1341
2	1175	1249
3	3061	1225
4	4934	1225

prune318.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	175	6	181

Error

0.0b

Counts

181 → 6

Alt Table

Status	Error	Program
✓	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)))))))))
	26.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (.f64 theta theta)) 1/2) (.f64 (.f64 (cos.f64 phi1) (pow.f64 theta 6)) 1/720))) (-.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)) 1/24)))))))
✓	2.9b	(+.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)))))))))
✓	0.3b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 theta) (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta)))) (cbrt.f64 (.f64 (cbrt.f64 (sin.f64 delta)) (cbrt.f64 (sin.f64 delta))))) (cbrt.f64 (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)))))))))
	11.0b	(+.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))))))
	33.3b	(+.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)))))))))

Compiler

Compiled 8161 to 2176 computations (73.3% saved)

regimes1.3s (5.8%)

Accuracy

Total 0.1b remaining (50.5%)

Threshold costs 0.1b (50.5%)

Counts

126 → 1

Compiler

Compiled 38323 to 22694 computations (40.8% 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	23	55
1	36	55
2	46	55
3	52	55
4	56	55
5	57	55
6	57	55

end181.0ms (0.8%)

Compiler: Compiled 359 to 207 computations (42.3% 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

analyze5.8s (26.5%)

sample11.4s (52%)

simplify54.0ms (0.2%)

prune5.0ms (0%)

localize30.0ms (0.1%)

series134.0ms (0.6%)

rewrite17.0ms (0.1%)

simplify198.0ms (0.9%)

prune308.0ms (1.4%)

localize31.0ms (0.1%)

series430.0ms (2%)

rewrite21.0ms (0.1%)

simplify116.0ms (0.5%)

prune410.0ms (1.9%)

localize32.0ms (0.1%)

series380.0ms (1.7%)

rewrite7.0ms (0%)

simplify106.0ms (0.5%)

prune493.0ms (2.3%)

localize30.0ms (0.1%)

series47.0ms (0.2%)

rewrite7.0ms (0%)

simplify69.0ms (0.3%)

prune318.0ms (1.5%)

regimes1.3s (5.8%)

simplify4.0ms (0%)

end181.0ms (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