Details

analyze2.5s (12.7%)

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)

sample208.0ms (1%)

Algorithm

1×

intervals

Results

56.0ms	59×	body	1024	valid
22.0ms	156×	body	128	valid
19.0ms	30×	body	512	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify80.0ms (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

6.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.4b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

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)))
✓	5.9b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series208.0ms (1%)

Counts

4 → 120

Calls

4 calls:

136.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
47.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
13.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
10.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

rewrite24.0ms (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:

6.0ms	(.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))

simplify183.0ms (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

prune258.0ms (1.3%)

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
	43.1b	(.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)))))
	48.1b	(neg.f64 U)
	31.6b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	49.6b	U
	18.0b	(.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)))))
	6.8b	(.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)))))
	29.2b	(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))
▶	6.8b	(.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))))))
	33.2b	(.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)))))

Compiler

Compiled 6772 to 5079 computations (25% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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))))))
✓	0.2b	(.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))))))
✓	1.8b	(.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)))))))
✓	6.1b	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

series3.4s (17.3%)

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))))))
1.1s	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
141.0ms	(.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))))))

rewrite48.0ms (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:

14.0ms	(.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))))))
9.0ms	(.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)))))))
5.0ms	(.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)))))

simplify346.0ms (1.7%)

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

prune1.0s (5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	468	9	477

Error

0.0b

Counts

477 → 9

Alt Table

Status	Error	Program
	43.1b	(.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)))))
	48.1b	(neg.f64 U)
	31.6b	(.f64 (-.f64 (.f64 1/4 (.f64 (pow.f64 K 2) J)) (.f64 2 J)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	49.6b	U
	18.0b	(.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)))))
▶	6.8b	(.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)))))
	29.2b	(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))
✓	6.8b	(.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))))))
	33.2b	(.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)))))

Compiler

Compiled 37951 to 29407 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))))
✓	0.3b	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
✓	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	5.9b	(.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)))))

series595.0ms (3%)

Counts

4 → 84

Calls

4 calls:

242.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
183.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
145.0ms	(.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)))))
25.0ms	(.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))))

rewrite41.0ms (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)))))
10.0ms	(.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)))

simplify164.0ms (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

prune419.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	260	11	271

Error

Counts

271 → 11

Alt Table

Status	Error	Program
▶	6.5b	(.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)))))
	33.2b	(.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)))))
	43.1b	(.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)))))
	48.1b	(neg.f64 U)
	6.8b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (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)))))
	49.6b	U
	18.0b	(.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)))))
	29.2b	(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))
✓	6.8b	(.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))))))
	7.1b	(.f64 (.f64 (.f64 (.f64 -2 J) (log.f64 (exp.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)))))
	18.1b	(.f64 (.f64 (.f64 (.f64 -2 J) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (pow.f64 (cos.f64 (.f64 1/2 K)) 1/3))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

Compiler

Compiled 11555 to 9112 computations (21.1% saved)

localize22.0ms (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)))
✓	5.9b	(.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)))))

series152.0ms (0.8%)

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)))))

11.0ms

(*.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)

rewrite33.0ms (0.2%)

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 (*.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)))))

9.0ms

(*.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))))

2.0ms

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

simplify228.0ms (1.1%)

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

prune590.0ms (3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	181	4	185
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	186	10	196

Error

Counts

196 → 10

Alt Table

Status	Error	Program
	18.0b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) 1/3)) (pow.f64 (cos.f64 (/.f64 K 2)) 1/3)) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	49.6b	U
	6.5b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 6)) 1/3)) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	6.6b	(.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)))))
	6.6b	(.f64 (.f64 (.f64 (.f64 -2 J) (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) 1/3)) (log.f64 (exp.f64 (cbrt.f64 (cos.f64 (/.f64 K 2)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	18.0b	(.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)))))
	29.2b	(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))
✓	6.8b	(.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))))))
	33.2b	(.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)))))
	48.1b	(neg.f64 U)

Compiler

Compiled 7961 to 6286 computations (21% saved)

regimes3.2s (15.9%)

Accuracy

Total 8.3b remaining (99.7%)

Threshold costs 0b (0%)

Counts

177 → 2

Compiler

Compiled 34088 to 27258 computations (20% saved)

bsearch139.0ms (0.7%)

Steps

Iters	Range		Point
8	2.9074795012020107e+251	8.522749833557217e+253	5.114698291459075e+251

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	29	39
2	28	39

end1.0ms (0%)

Compiler: Compiled 29 to 22 computations (24.1% saved)

sample6.0s (30%)

Algorithm

1×

intervals

Results

2.9s	2011×	body	1024	valid
1.0s	4513×	body	128	valid
847.0ms	995×	body	512	valid
260.0ms	477×	body	256	valid
11.0ms	4×	body	2048	valid

Compiler

Compiled 353 to 285 computations (19.3% saved)

Details

analyze2.5s (12.7%)

sample208.0ms (1%)

simplify80.0ms (0.4%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series208.0ms (1%)

rewrite24.0ms (0.1%)

simplify183.0ms (0.9%)

prune258.0ms (1.3%)

localize15.0ms (0.1%)

series3.4s (17.3%)

rewrite48.0ms (0.2%)

simplify346.0ms (1.7%)

prune1.0s (5%)

localize15.0ms (0.1%)

series595.0ms (3%)

rewrite41.0ms (0.2%)

simplify164.0ms (0.8%)

prune419.0ms (2.1%)

localize22.0ms (0.1%)

series152.0ms (0.8%)

rewrite33.0ms (0.2%)

simplify228.0ms (1.1%)

prune590.0ms (3%)

regimes3.2s (15.9%)

bsearch139.0ms (0.7%)

simplify5.0ms (0%)

end1.0ms (0%)

sample6.0s (30%)

Profiling