Details

analyze2.7s (22.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
15.6%	84.3%	0.1%	8
15.6%	84.3%	0.1%	9
15.6%	84.3%	0.1%	10
30.4%	69.4%	0.1%	11
30.4%	69.4%	0.1%	12
30.4%	69.4%	0.1%	13
39.6%	60.3%	0.1%	14

Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.6s (38.5%)

Results

2.4s	2152×	body	1024	valid
1.0s	4550×	body	128	valid
748.0ms	1023×	body	512	valid
249.0ms	527×	body	256	valid
9.0ms	4×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1043×	`associate-*l/_binary64`
692×	`associate-/l/_binary64`
651×	`associate-/r/_binary64`
474×	`associate-/l*_binary64`
398×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	37	32
2	83	32
3	208	32
4	742	32
5	2273	32
6	2474	32
7	2875	32
8	3015	32
9	3126	32
10	3234	32
11	4835	32
12	4953	32
13	4880	32

prune5.0ms (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

8.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 96 to 76 computations (20.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
✓	0.2b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.2b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	7.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series217.0ms (1.8%)

Counts

4 → 120

Calls

4 calls:

139.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
55.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
12.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
11.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
23×	`pow1_binary64`
15×	`cbrt-unprod_binary64`
15×	`prod-exp_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
5.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
4.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
4.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

simplify171.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
375×	`associate-l_binary64`
303×	`fma-neg_binary64`
300×	`associate-r_binary64`
204×	`*-commutative_binary64`

Counts

208 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	5501
1	854	4903
2	3368	4868
3	4900	4868
4	4981	4868
5	4956	4868

prune217.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	183	7	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	7	191

Error

0.0b

Counts

191 → 7

Alt Table

Status	Error	Program
	47.2b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)
	24.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	9.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	45.9b	(neg.f64 U)
▶	8.2b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	36.5b	(.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))

Compiler

Compiled 6724 to 5041 computations (25% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	0.1b	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
	0.2b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	7.6b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

series244.0ms (2%)

Counts

2 → 72

Calls

2 calls:

137.0ms

(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

107.0ms

(*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms

(*.f64 (*.f64 -2 J) (*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

3.0ms

(*.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

421×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
287×	`associate-l_binary64`
281×	`associate-r_binary64`
213×	`*-commutative_binary64`

Counts

116 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	320	5675
1	870	5137
2	3407	5125
3	4984	5125
4	4974	5125

prune282.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	216	1	217
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	217	7	224

Error

0.0b

Counts

224 → 7

Alt Table

Status	Error	Program
	34.6b	(.f64 (.f64 -2 J) (log1p.f64 (expm1.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))))
▶	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	9.2b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	47.2b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)
	45.9b	(neg.f64 U)
✓	8.2b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	36.5b	(.f64 (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))

Compiler

Compiled 8352 to 6177 computations (26% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	7.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series591.0ms (4.9%)

Counts

3 → 60

Calls

3 calls:

243.0ms

(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

213.0ms

(cbrt.f64 (cos.f64 (/.f64 K 2)))

135.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`pow1_binary64`
30×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`pow-prod-down_binary64`
20×	`cbrt-unprod_binary64`

Counts

3 → 87

Calls

3 calls:

12.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

5.0ms

(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))

1.0ms

(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify209.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-def_binary64`
428×	`associate-l_binary64`
341×	`associate-r_binary64`
287×	`cancel-sign-sub-inv_binary64`
210×	`fma-neg_binary64`

Counts

147 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	4841
1	775	4214
2	3077	4078
3	4934	4078
4	4999	4078
5	4950	4078

prune346.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	250	7	257

Error

0.0b

Counts

257 → 7

Alt Table

Status	Error	Program
	34.6b	(.f64 (.f64 -2 J) (log1p.f64 (expm1.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))))
✓	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	9.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	47.2b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)
▶	8.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	45.9b	(neg.f64 U)
✓	8.2b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

Compiler

Compiled 11011 to 8678 computations (21.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.3b	(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	7.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series141.0ms (1.2%)

Counts

2 → 40

Calls

2 calls:

137.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

3.0ms

(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64`
38×	`prod-exp_binary64`
18×	`add-cbrt-cube_binary64`
17×	`cbrt-unprod_binary64`
9×	`pow-exp_binary64`

Counts

2 → 54

Calls

2 calls:

10.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (*.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

2.0ms

(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)

simplify143.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
389×	`associate-l_binary64`
280×	`associate-r_binary64`
264×	`cancel-sign-sub-inv_binary64`
232×	`unswap-sqr_binary64`

Counts

94 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	4402
1	739	3818
2	2837	3790
3	4877	3764
4	4917	3764
5	4976	3764

prune231.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	170	7	177

Error

Counts

177 → 7

Alt Table

Status	Error	Program
	8.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) 1/3)) (expm1.f64 (log1p.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	9.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))))
	34.6b	(.f64 (.f64 -2 J) (log1p.f64 (expm1.f64 (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))))
✓	8.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.2b	(fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U)
	45.9b	(neg.f64 U)
✓	8.2b	(.f64 (.f64 -2 J) (.f64 (cos.f64 (/.f64 K 2)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

Compiler

Compiled 7355 to 5792 computations (21.3% saved)

regimes1.1s (9.5%)

Accuracy

Total 8.2b remaining (99.3%)

Threshold costs 0b (0%)

Counts

123 → 3

Compiler

Compiled 24632 to 19932 computations (19.1% saved)

bsearch154.0ms (1.3%)

Steps

Iters	Range		Point
7	4.427845546763105e-253	1.1122055374965254e-250	4.5127680789433535e-253
9	-3.5151784645638495e-289	-2.3965879224399063e-294	-7.46424867012432e-294

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	98
1	41	98
2	40	98

end232.0ms (1.9%)

Compiler: Compiled 392 to 308 computations (21.4% saved)

Details

analyze2.7s (22.2%)

sample4.6s (38.5%)

simplify85.0ms (0.7%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series217.0ms (1.8%)

rewrite24.0ms (0.2%)

simplify171.0ms (1.4%)

prune217.0ms (1.8%)

localize13.0ms (0.1%)

series244.0ms (2%)

rewrite14.0ms (0.1%)

simplify156.0ms (1.3%)

prune282.0ms (2.4%)

localize18.0ms (0.2%)

series591.0ms (4.9%)

rewrite27.0ms (0.2%)

simplify209.0ms (1.7%)

prune346.0ms (2.9%)

localize21.0ms (0.2%)

series141.0ms (1.2%)

rewrite19.0ms (0.2%)

simplify143.0ms (1.2%)

prune231.0ms (1.9%)

regimes1.1s (9.5%)

bsearch154.0ms (1.3%)

simplify3.0ms (0%)

end232.0ms (1.9%)

Profiling