Details

analyze3.0s (21.7%)

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 (33.2%)

Results

2.4s	2066×	body	1024	valid
1.0s	4580×	body	128	valid
781.0ms	1084×	body	512	valid
245.0ms	525×	body	256	valid
2.0ms	1×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify84.0ms (0.6%)

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

11.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.1b	(.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)))
✓	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	10.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series205.0ms (1.5%)

Counts

4 → 120

Calls

4 calls:

127.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
49.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
19.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
10.0ms	(.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)))))
4.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
4.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
4.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

simplify174.0ms (1.3%)

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

prune225.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Error

0.0b

Counts

191 → 9

Alt Table

Status	Error	Program
	26.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (cbrt.f64 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 3))))
▶	11.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))
	47.4b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U))
	12.1b	(.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)))))))
	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)))))
	11.6b	(.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)))))
	36.7b	(.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)))))
	48.6b	(.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)))))
	44.5b	U

Compiler

Compiled 6868 to 5157 computations (24.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	0.2b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))
✓	0.2b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2))))))
✓	10.4b	(sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

series424.0ms (3.1%)

Counts

3 → 84

Calls

3 calls:

181.0ms

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

132.0ms

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

110.0ms

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

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

10.0ms

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

7.0ms

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

1.0ms

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

simplify153.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-l_binary64`
379×	`associate-r_binary64`
379×	`fma-neg_binary64`
281×	`*-commutative_binary64`
240×	`fma-def_binary64`

Counts

154 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	376	7658
1	1056	6900
2	4321	6874
3	4981	6874

prune415.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	249	9	258

Error

0.0b

Counts

258 → 9

Alt Table

Status	Error	Program
	26.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (cbrt.f64 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 3))))
✓	11.3b	(.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))) (sqrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))))))
	47.4b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U))
	12.1b	(.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)))))))
	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)))))
▶	11.6b	(.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)))))
	36.7b	(.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)))))
	48.6b	(.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)))))
	44.5b	U

Compiler

Compiled 14194 to 10833 computations (23.7% saved)

localize18.0ms (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))))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	10.4b	(.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)))))

series570.0ms (4.1%)

Counts

4 → 84

Calls

4 calls:

248.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
177.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
132.0ms	(.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 (0.3%)

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 (1.1%)

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

prune383.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	0	7	7
Picked	1	0	1
Done	1	0	1
Total	262	9	271

Error

Counts

271 → 9

Alt Table

Status	Error	Program
	48.6b	(.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)))))
	11.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (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)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	26.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (cbrt.f64 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 3))))
	47.4b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U) U))
▶	11.3b	(.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)))))
	12.1b	(.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)))))))
	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)))))
	36.7b	(.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)))))
	44.5b	U

Compiler

Compiled 11556 to 9110 computations (21.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))))
✓	0.2b	(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	10.4b	(.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)))))

series154.0ms (1.1%)

Counts

3 → 64

Calls

3 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)))))

13.0ms

(*.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))))

3.0ms

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

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-exp-log_binary64`
64×	`prod-exp_binary64`
28×	`cbrt-unprod_binary64`
28×	`add-cbrt-cube_binary64`
17×	`pow-exp_binary64`

Counts

3 → 88

Calls

3 calls:

12.0ms

(*.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))))

11.0ms

(*.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)

simplify203.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
452×	`associate-l_binary64`
308×	`associate-r_binary64`
281×	`fma-neg_binary64`
236×	`unswap-sqr_binary64`

Counts

152 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	324	5836
1	807	5096
2	3124	5058
3	4880	5008
4	4955	5008
5	4990	5008
6	4943	5008

prune261.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	186	8	194

Error

Counts

194 → 8

Alt Table

Status	Error	Program
	11.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (log.f64 (exp.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)))))
	11.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (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)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	26.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (cbrt.f64 (pow.f64 (/.f64 U (.f64 (*.f64 2 J) (cos.f64 (/.f64 K 2)))) 3))))
	11.7b	(.f64 (.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)))) (.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))))))
	47.4b	(neg.f64 (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)))))
	36.7b	(.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)))))
	44.5b	U

Compiler

Compiled 7934 to 6264 computations (21% saved)

regimes2.1s (15.3%)

Accuracy

Total 10.0b remaining (99.7%)

Threshold costs 0b (0%)

Counts

174 → 4

Compiler

Compiled 34550 to 28008 computations (18.9% saved)

bsearch261.0ms (1.9%)

Steps

Iters	Range	Point
10	8.105157445422227e-206	3.279495073039574e-192	9.096025868775934e-206
9	-1.720217475873151e-278	-2.968884789068076e-287	-7.086648613513012e-283
9	-4.1995540793340414e-148	-3.4763475684672655e-157	-3.733683180945843e-157

Iters

Range

Point

8.105157445422227e-206

3.279495073039574e-192

9.096025868775934e-206

-1.720217475873151e-278

-2.968884789068076e-287

-7.086648613513012e-283

-4.1995540793340414e-148

-3.4763475684672655e-157

-3.733683180945843e-157

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-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	42	107
1	52	107
2	54	107
3	55	107
4	54	107

end228.0ms (1.7%)

Compiler: Compiled 414 to 325 computations (21.5% saved)

Details

analyze3.0s (21.7%)

sample4.6s (33.2%)

simplify84.0ms (0.6%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series205.0ms (1.5%)

rewrite24.0ms (0.2%)

simplify174.0ms (1.3%)

prune225.0ms (1.6%)

localize16.0ms (0.1%)

series424.0ms (3.1%)

rewrite26.0ms (0.2%)

simplify153.0ms (1.1%)

prune415.0ms (3%)

localize18.0ms (0.1%)

series570.0ms (4.1%)

rewrite42.0ms (0.3%)

simplify153.0ms (1.1%)

prune383.0ms (2.8%)

localize20.0ms (0.1%)

series154.0ms (1.1%)

rewrite35.0ms (0.3%)

simplify203.0ms (1.5%)

prune261.0ms (1.9%)

regimes2.1s (15.3%)

bsearch261.0ms (1.9%)

simplify5.0ms (0%)

end228.0ms (1.7%)

Profiling