Details

analyze3.1s (15.6%)

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)

sample4.7s (23.7%)

Results

2.5s	2166×	body	1024	valid
1.1s	4568×	body	128	valid
745.0ms	1013×	body	512	valid
256.0ms	508×	body	256	valid
2.0ms	1×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify79.0ms (0.4%)

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

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

10.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.1b	(.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)

localize13.0ms (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)))
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	9.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series199.0ms (1%)

Counts

4 → 120

Calls

4 calls:

131.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
46.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
11.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
11.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

rewrite25.0ms (0.1%)

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 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
4.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
4.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

simplify174.0ms (0.9%)

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

prune227.0ms (1.1%)

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
	35.5b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.6b	U
▶	10.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
	46.8b	(neg.f64 U)
	20.4b	(.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)))))
	10.5b	(.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	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 6672 to 5003 computations (25% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
✓	0.3b	(.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
✓	2.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))))
✓	9.7b	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

series3.4s (17.1%)

Counts

4 → 144

Calls

4 calls:

1.2s	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))))
1.1s	(.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
1.0s	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
130.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))

rewrite47.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64`
56×	`add-exp-log_binary64`
39×	`pow-prod-down_binary64`
38×	`cbrt-unprod_binary64`
38×	`prod-exp_binary64`

Counts

4 → 123

Calls

4 calls:

12.0ms	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
8.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))))
6.0ms	(.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
1.0ms	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

simplify305.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-def_binary64`
302×	`times-frac_binary64`
282×	`associate-/l*_binary64`
257×	`*-commutative_binary64`
249×	`associate-/r*_binary64`

Counts

267 → 338

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	727	17181
1	2113	15833
2	4852	15767
3	5222	15767

prune973.0ms (4.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	467	1	468
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	468	7	475

Error

0.0b

Counts

475 → 7

Alt Table

Status	Error	Program
	35.5b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.6b	U
	11.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))) 1/3))
	46.8b	(neg.f64 U)
	20.4b	(.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)))))
▶	10.5b	(.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	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 37906 to 29375 computations (22.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))))
✓	0.2b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	9.5b	(.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)))))

series587.0ms (3%)

Counts

4 → 84

Calls

4 calls:

262.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
181.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
131.0ms	(.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)))))
12.0ms	(.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))))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`pow1_binary64`
49×	`add-exp-log_binary64`
34×	`pow-prod-down_binary64`
33×	`cbrt-unprod_binary64`
33×	`prod-exp_binary64`

Counts

4 → 119

Calls

4 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)))))
11.0ms	(.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))))
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)))

simplify153.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
491×	`associate-l_binary64`
370×	`associate-r_binary64`
270×	`fma-neg_binary64`
205×	`*-commutative_binary64`

Counts

203 → 214

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	5881
1	836	5091
2	3332	4908
3	4961	4908
4	4995	4908

prune444.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	260	9	269

Error

0.0b

Counts

269 → 9

Alt Table

Status	Error	Program
	35.5b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.6b	U
▶	10.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (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)))))
	11.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))) 1/3))
	20.6b	(.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	46.8b	(neg.f64 U)
	10.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	20.4b	(.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)))))
	47.2b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 11566 to 9124 computations (21.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	9.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (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)))))

series575.0ms (2.9%)

Counts

3 → 60

Calls

3 calls:

246.0ms

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

182.0ms

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

147.0ms

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

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-exp-log_binary64`
41×	`pow1_binary64`
30×	`cbrt-unprod_binary64`
30×	`prod-exp_binary64`
30×	`pow-prod-down_binary64`

Counts

3 → 65

Calls

3 calls:

16.0ms

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

3.0ms

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

1.0ms

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

simplify179.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
585×	`associate-l_binary64`
475×	`associate-r_binary64`
236×	`*-commutative_binary64`
210×	`fma-neg_binary64`

Counts

125 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	7138
1	837	5672
2	3314	3891
3	4653	3891
4	4941	3891
5	4951	3891

prune486.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	251	9	260

Error

0.0b

Counts

260 → 9

Alt Table

Status	Error	Program
	35.5b	(.f64 (.f64 (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	47.6b	U
✓	10.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (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)))))
	11.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))) (cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))) (pow.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))) 1/3))
	20.6b	(.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (sqrt.f64 (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	46.8b	(neg.f64 U)
	10.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	20.4b	(.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)))))
	47.2b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 -2 J) (.f64 -2 J)) (.f64 -2 J)) (.f64 (.f64 (cos.f64 (/.f64 K 2)) (cos.f64 (/.f64 K 2))) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

Compiler

Compiled 13959 to 11201 computations (19.8% saved)

regimes3.6s (18.3%)

Accuracy

Total 8.4b remaining (99.6%)

Threshold costs 0b (0%)

Counts

310 → 3

Compiler

Compiled 69458 to 55974 computations (19.4% saved)

bsearch172.0ms (0.9%)

Steps

Iters	Range		Point
8	1.4407286554018424e-238	3.7955009457899113e-236	3.03198560535342e-237
9	-1.2988792094181284e-288	-4.0388671018558494e-296	-8.778931361479822e-290

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	100
1	45	100
2	47	100
3	48	100
4	47	100

end263.0ms (1.3%)

Compiler: Compiled 458 to 363 computations (20.7% saved)

Details

analyze3.1s (15.6%)

sample4.7s (23.7%)

simplify79.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series199.0ms (1%)

rewrite25.0ms (0.1%)

simplify174.0ms (0.9%)

prune227.0ms (1.1%)

localize16.0ms (0.1%)

series3.4s (17.1%)

rewrite47.0ms (0.2%)

simplify305.0ms (1.5%)

prune973.0ms (4.9%)

localize15.0ms (0.1%)

series587.0ms (3%)

rewrite42.0ms (0.2%)

simplify153.0ms (0.8%)

prune444.0ms (2.2%)

localize21.0ms (0.1%)

series575.0ms (2.9%)

rewrite33.0ms (0.2%)

simplify179.0ms (0.9%)

prune486.0ms (2.4%)

regimes3.6s (18.3%)

bsearch172.0ms (0.9%)

simplify4.0ms (0%)

end263.0ms (1.3%)

Profiling