Details

analyze2.5s (20.4%)

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)

sample4.5s (36.3%)

Results

2.3s	2135×	body	1024	valid
1.1s	4569×	body	128	valid
740.0ms	1048×	body	512	valid
229.0ms	501×	body	256	valid
5.0ms	3×	body	2048	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify80.0ms (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

9.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.1b	(.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)

localize11.0ms (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)))
✓	8.5b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series193.0ms (1.6%)

Counts

4 → 120

Calls

4 calls:

103.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
68.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
12.0ms	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
10.0ms	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))

rewrite23.0ms (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:

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)))))
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))

simplify169.0ms (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

prune216.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	183	7	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	8	191

Error

0.0b

Counts

191 → 8

Alt Table

Status	Error	Program
	22.1b	(.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)))))
	37.4b	(.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)))))
	43.0b	(.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)))))
	34.9b	(.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)))))
▶	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.7b	U
	47.4b	(neg.f64 U)

Compiler

Compiled 6660 to 4992 computations (25% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))
✓	0.6b	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
✓	8.5b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series1.4s (11.2%)

Counts

4 → 108

Calls

4 calls:

721.0ms	(.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))
420.0ms	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
163.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
81.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`pow1_binary64`
20×	`add-exp-log_binary64`
16×	`pow1/3_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`pow-prod-down_binary64`

Counts

4 → 102

Calls

4 calls:

10.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
9.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))
4.0ms	(.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))
2.0ms	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))

simplify135.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

500×	`cancel-sign-sub-inv_binary64`
396×	`associate-l_binary64`
346×	`associate-r_binary64`
342×	`fma-neg_binary64`
309×	`unswap-sqr_binary64`

Counts

210 → 219

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	6401
1	916	5713
2	3410	5443
3	5423	5443

prune340.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	286	9	295

Error

0.0b

Counts

295 → 9

Alt Table

Status	Error	Program
	34.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
▶	22.1b	(.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)))))
	37.4b	(.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)))))
	43.0b	(.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)))))
	34.9b	(.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)))))
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.7b	U
	47.4b	(neg.f64 U)

Compiler

Compiled 14030 to 11012 computations (21.5% 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 (.f64 (*.f64 -2 J) (sqrt.f64 (cos.f64 (/.f64 K 2)))) (sqrt.f64 (cos.f64 (/.f64 K 2))))
	0.1b	(.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	7.5b	(.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)))))

series108.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

98.0ms

(*.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)))))

10.0ms

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

10.0ms

(*.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)))))

7.0ms

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

simplify137.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-def_binary64`
408×	`associate-l_binary64`
321×	`fma-neg_binary64`
278×	`associate-r_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

112 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	4014
1	695	3530
2	2794	3500
3	4850	3492
4	4983	3492
5	4964	3492

prune260.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	200	9	209

Error

0.0b

Counts

209 → 9

Alt Table

Status	Error	Program
▶	34.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	22.1b	(.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)))))
	37.4b	(.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)))))
	43.0b	(.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)))))
	34.9b	(.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)))))
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.7b	U
	47.4b	(neg.f64 U)

Compiler

Compiled 8079 to 6187 computations (23.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))
	0.6b	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
✓	8.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	31.1b	(cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))

series971.0ms (7.8%)

Counts

3 → 84

Calls

3 calls:

624.0ms

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

272.0ms

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

75.0ms

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

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 57

Calls

3 calls:

8.0ms

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

7.0ms

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

5.0ms

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

simplify138.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-r_binary64`
461×	`associate-l_binary64`
350×	`fma-neg_binary64`
318×	`*-commutative_binary64`
238×	`times-frac_binary64`

Counts

141 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	379	7202
1	1094	6388
2	4150	6370
3	5002	6370

prune234.0ms (1.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	197	9	206

Error

0.0b

Counts

206 → 9

Alt Table

Status	Error	Program
✓	34.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
✓	22.1b	(.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)))))
	37.4b	(.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)))))
	43.0b	(.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)))))
	34.9b	(.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)))))
✓	9.1b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	47.7b	U
	47.4b	(neg.f64 U)

Compiler

Compiled 10677 to 8463 computations (20.7% saved)

regimes613.0ms (4.9%)

Accuracy

Total 9.3b remaining (99.7%)

Threshold costs 0b (0%)

Counts

63 → 2

Compiler

Compiled 12296 to 9822 computations (20.1% saved)

bsearch49.0ms (0.4%)

Steps

Iters	Range		Point
5	1.8496974450358866e+172	7.358482293982686e+172	7.165885222303086e+172

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-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	21	41
1	31	41
2	33	41
3	34	41
4	33	41

end187.0ms (1.5%)

Compiler: Compiled 318 to 251 computations (21.1% saved)

Details

analyze2.5s (20.4%)

sample4.5s (36.3%)

simplify80.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series193.0ms (1.6%)

rewrite23.0ms (0.2%)

simplify169.0ms (1.4%)

prune216.0ms (1.7%)

localize16.0ms (0.1%)

series1.4s (11.2%)

rewrite34.0ms (0.3%)

simplify135.0ms (1.1%)

prune340.0ms (2.7%)

localize13.0ms (0.1%)

series108.0ms (0.9%)

rewrite22.0ms (0.2%)

simplify137.0ms (1.1%)

prune260.0ms (2.1%)

localize16.0ms (0.1%)

series971.0ms (7.8%)

rewrite23.0ms (0.2%)

simplify138.0ms (1.1%)

prune234.0ms (1.9%)

regimes613.0ms (4.9%)

bsearch49.0ms (0.4%)

simplify3.0ms (0%)

end187.0ms (1.5%)

Profiling