Details

analyze2.7s (20.7%)

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 (34.7%)

Results

2.3s	2065×	body	1024	valid
1.1s	4670×	body	128	valid
790.0ms	1022×	body	512	valid
259.0ms	496×	body	256	valid
5.0ms	3×	body	2048	valid
0.0ms	1×	body	256	invalid
0.0ms	2×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify83.0ms (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

4.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.9b	(.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)

localize15.0ms (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)))
✓	4.6b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series214.0ms (1.6%)

Counts

4 → 120

Calls

4 calls:

142.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
48.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
12.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
11.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))

rewrite25.0ms (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:

7.0ms	(.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 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))

simplify189.0ms (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

prune219.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	184	7	191

Error

0.0b

Counts

191 → 7

Alt Table

Status	Error	Program
	17.2b	(.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)))))
	34.2b	(fma.f64 J (.f64 (cos.f64 (.f64 1/2 K)) -2) (.f64 (/.f64 (.f64 U U) (.f64 J (cos.f64 (.f64 1/2 K)))) -1/4))
	6.0b	(.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)))))))
✓	4.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	48.8b	U
▶	5.4b	(.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)))))
	45.4b	(neg.f64 U)

Compiler

Compiled 6622 to 4960 computations (25.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 -2 J) (*.f64 (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)))
✓	4.6b	(.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)))))

series1.3s (9.8%)

Counts

4 → 84

Calls

4 calls:

714.0ms	(.f64 (.f64 -2 J) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
253.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
185.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
143.0ms	(.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)))))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`pow1_binary64`
43×	`add-exp-log_binary64`
29×	`pow-prod-down_binary64`
28×	`cbrt-unprod_binary64`
28×	`add-cbrt-cube_binary64`

Counts

4 → 111

Calls

4 calls:

14.0ms	(.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)))))
9.0ms	(.f64 (.f64 -2 J) (*.f64 (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)))

simplify170.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
443×	`associate-l_binary64`
362×	`associate-r_binary64`
237×	`fma-neg_binary64`
200×	`*-commutative_binary64`

Counts

195 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	5964
1	834	5179
2	3251	4953
3	4897	4953
4	4949	4953

prune414.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	251	9	260

Error

Counts

260 → 9

Alt Table

Status	Error	Program
✓	4.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	5.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (log.f64 (exp.f64 (.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)))))
	17.2b	(.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)))))
	34.2b	(fma.f64 J (.f64 (cos.f64 (.f64 1/2 K)) -2) (.f64 (/.f64 (.f64 U U) (.f64 J (cos.f64 (.f64 1/2 K)))) -1/4))
▶	5.1b	(.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)))))
	6.0b	(.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)))))))
	48.8b	U
	5.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) 6)))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	45.4b	(neg.f64 U)

Compiler

Compiled 11133 to 8777 computations (21.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (*.f64 1/2 K)) 2) 1/3))
✓	0.3b	(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	4.6b	(.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)))))

series857.0ms (6.5%)

Counts

3 → 64

Calls

3 calls:

707.0ms

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

146.0ms

(*.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)))))

4.0ms

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

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-exp-log_binary64`
53×	`prod-exp_binary64`
27×	`add-cbrt-cube_binary64`
23×	`cbrt-unprod_binary64`
17×	`pow-exp_binary64`

Counts

3 → 91

Calls

3 calls:

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)))))

8.0ms

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

2.0ms

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

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-def_binary64`
463×	`associate-l_binary64`
346×	`associate-r_binary64`
267×	`unswap-sqr_binary64`
232×	`fma-neg_binary64`

Counts

155 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	342	5603
1	862	4854
2	3249	4810
3	4964	4810

prune331.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	192	9	201

Error

Counts

201 → 9

Alt Table

Status	Error	Program
✓	4.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
▶	5.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (log.f64 (exp.f64 (.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)))))
	17.2b	(.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)))))
	34.2b	(fma.f64 J (.f64 (cos.f64 (.f64 1/2 K)) -2) (.f64 (/.f64 (.f64 U U) (.f64 J (cos.f64 (.f64 1/2 K)))) -1/4))
✓	5.1b	(.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)))))
	6.0b	(.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)))))))
	48.8b	U
	5.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) 6)))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	45.4b	(neg.f64 U)

Compiler

Compiled 8455 to 6693 computations (20.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.2b	(log.f64 (exp.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)))
✓	4.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (log.f64 (exp.f64 (.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)))))

series407.0ms (3.1%)

Counts

2 → 48

Calls

2 calls:

261.0ms

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

146.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (log.f64 (exp.f64 (*.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)))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`pow1_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`cbrt-unprod_binary64`
10×	`prod-exp_binary64`

Counts

2 → 42

Calls

2 calls:

8.0ms

(*.f64 (*.f64 (*.f64 (*.f64 -2 J) (log.f64 (exp.f64 (*.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)))))

1.0ms

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

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
344×	`associate-l_binary64`
316×	`fma-neg_binary64`
258×	`associate-r_binary64`
253×	`cancel-sign-sub-inv_binary64`

Counts

90 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	4511
1	694	3266
2	2701	3168
3	4618	3152
4	4962	3152

prune428.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	243	9	252

Error

Counts

252 → 9

Alt Table

Status	Error	Program
✓	4.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	5.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (log.f64 (exp.f64 (.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)))))
	17.2b	(.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)))))
	34.2b	(fma.f64 J (.f64 (cos.f64 (.f64 1/2 K)) -2) (.f64 (/.f64 (.f64 U U) (.f64 J (cos.f64 (.f64 1/2 K)))) -1/4))
✓	5.1b	(.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)))))
	6.0b	(.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)))))))
	48.8b	U
	5.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))) 6)))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	45.4b	(neg.f64 U)

Compiler

Compiled 10793 to 8623 computations (20.1% saved)

regimes654.0ms (4.9%)

Accuracy

Total 8.2b remaining (99.6%)

Threshold costs 0b (0%)

Counts

68 → 1

Compiler

Compiled 14780 to 12084 computations (18.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	23	32
2	22	32

end234.0ms (1.8%)

Compiler: Compiled 315 to 252 computations (20% saved)

Details

analyze2.7s (20.7%)

sample4.6s (34.7%)

simplify83.0ms (0.6%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series214.0ms (1.6%)

rewrite25.0ms (0.2%)

simplify189.0ms (1.4%)

prune219.0ms (1.7%)

localize18.0ms (0.1%)

series1.3s (9.8%)

rewrite39.0ms (0.3%)

simplify170.0ms (1.3%)

prune414.0ms (3.1%)

localize20.0ms (0.2%)

series857.0ms (6.5%)

rewrite31.0ms (0.2%)

simplify127.0ms (1%)

prune331.0ms (2.5%)

localize19.0ms (0.1%)

series407.0ms (3.1%)

rewrite14.0ms (0.1%)

simplify117.0ms (0.9%)

prune428.0ms (3.2%)

regimes654.0ms (4.9%)

simplify3.0ms (0%)

end234.0ms (1.8%)

Profiling