Details

analyze2.6s (21.2%)

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)

sample4.4s (37%)

Results

2.3s	2086×	body	1024	valid
1.0s	4653×	body	128	valid
718.0ms	1038×	body	512	valid
226.0ms	476×	body	256	valid
6.0ms	3×	body	2048	valid
1.0ms	1×	body	512	invalid
1.0ms	3×	body	128	invalid

Compiler

Compiled 83 to 68 computations (18.1% saved)

simplify84.0ms (0.7%)

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)

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)))
✓	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)))))

series190.0ms (1.6%)

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)))))
42.0ms	(/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))
11.0ms	(.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:

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))

simplify161.0ms (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

prune220.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	182	9	191

Error

0.0b

Counts

191 → 9

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)))))
	24.1b	(.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)))))
	48.4b	U
▶	10.6b	(.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)))))
	28.7b	(.f64 -2 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (sqrt.f64 (fma.f64 1/4 (/.f64 U (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U)) 1))))
	44.2b	(neg.f64 U)
	11.1b	(.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)))))))
	37.2b	(.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)))))
	44.3b	(.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 6792 to 5096 computations (25% saved)

localize14.0ms (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)))
✓	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)))))

series557.0ms (4.6%)

Counts

4 → 84

Calls

4 calls:

228.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
172.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))
144.0ms	(.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))))

rewrite41.0ms (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:

11.0ms	(.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))))
6.0ms	(*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))
1.0ms	(cbrt.f64 (cos.f64 (/.f64 K 2)))

simplify151.0ms (1.3%)

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

prune423.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	261	10	271

Error

0.0b

Counts

271 → 10

Alt Table

Status	Error	Program
	10.7b	(.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)))))
✓	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)))))
	24.1b	(.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)))))
	48.4b	U
	37.2b	(.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)))))
▶	10.3b	(.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)))))
	44.2b	(neg.f64 U)
	10.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	11.1b	(.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)))))))
	28.7b	(.f64 -2 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (sqrt.f64 (fma.f64 1/4 (/.f64 U (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U)) 1))))

Compiler

Compiled 11538 to 9097 computations (21.2% saved)

localize22.0ms (0.2%)

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))))
✓	0.3b	(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	9.5b	(.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)))))

series151.0ms (1.3%)

Counts

3 → 64

Calls

3 calls:

135.0ms

(*.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)))))

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))))

3.0ms

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

rewrite77.0ms (0.6%)

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:

53.0ms

(*.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))))

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)))))

2.0ms

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

simplify204.0ms (1.7%)

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

prune329.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	185	10	195

Error

0.0b

Counts

195 → 10

Alt Table

Status	Error	Program
	10.7b	(.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)))))
✓	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)))))
	48.4b	U
▶	10.3b	(.f64 (.f64 (.f64 -2 J) (.f64 (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)))))
	37.2b	(.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)))))
✓	10.3b	(.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)))))
	44.2b	(neg.f64 U)
	10.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	11.1b	(.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)))))))
	28.7b	(.f64 -2 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (sqrt.f64 (fma.f64 1/4 (/.f64 U (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U)) 1))))

Compiler

Compiled 8252 to 6518 computations (21% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (pow.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2) 1/3) (cbrt.f64 (cos.f64 (/.f64 K 2))))
	0.3b	(pow.f64 (cos.f64 (*.f64 1/2 K)) 2)
	0.3b	(cbrt.f64 (cos.f64 (/.f64 K 2)))
✓	9.5b	(.f64 (.f64 (.f64 -2 J) (.f64 (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)))))

series141.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

138.0ms

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

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

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-exp-log_binary64`
46×	`prod-exp_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`add-cbrt-cube_binary64`
22×	`cbrt-unprod_binary64`

Counts

2 → 85

Calls

2 calls:

12.0ms

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

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
472×	`associate-l_binary64`
359×	`associate-r_binary64`
277×	`cancel-sign-sub-inv_binary64`
231×	`unswap-sqr_binary64`

Counts

133 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	5834
1	809	5117
2	3156	5081
3	4945	5081

prune360.0ms (3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	214	10	224

Error

0.0b

Counts

224 → 10

Alt Table

Status	Error	Program
	10.7b	(.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)))))
✓	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)))))
	48.4b	U
✓	10.3b	(.f64 (.f64 (.f64 -2 J) (.f64 (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)))))
	37.2b	(.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)))))
✓	10.3b	(.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)))))
	10.5b	(.f64 (.f64 (.f64 -2 J) (log.f64 (exp.f64 (.f64 (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2)) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	44.2b	(neg.f64 U)
	10.4b	(.f64 (.f64 (.f64 (.f64 -2 J) (cbrt.f64 (pow.f64 (cos.f64 (.f64 1/2 K)) 2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
	28.7b	(.f64 -2 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (sqrt.f64 (fma.f64 1/4 (/.f64 U (/.f64 (.f64 (.f64 J J) (pow.f64 (cos.f64 (*.f64 1/2 K)) 2)) U)) 1))))

Compiler

Compiled 9362 to 7473 computations (20.2% saved)

regimes1.2s (9.6%)

Accuracy

Total 9.2b remaining (99.7%)

Threshold costs 0b (0%)

Counts

84 → 5

Compiler

Compiled 18302 to 14982 computations (18.1% saved)

bsearch254.0ms (2.1%)

Steps

Iters	Range		Point
6	1.2699217916627073e-207	1.1380379481904234e-206	1.289364658539573e-207
9	-1.7821180058434887e-305	5.15823284907191e-307	-1.3007612218473472e-306
4	-4.054790297758471e-219	-2.101232179269345e-219	-3.970878637552764e-219
7	-4.58832338734728e-179	-2.184539626827755e-180	-2.282917432201898e-180

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (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	30	124
1	40	124
2	42	124
3	43	124
4	42	124

end259.0ms (2.2%)

Compiler: Compiled 455 to 359 computations (21.1% saved)

Details

analyze2.6s (21.2%)

sample4.4s (37%)

simplify84.0ms (0.7%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series190.0ms (1.6%)

rewrite23.0ms (0.2%)

simplify161.0ms (1.3%)

prune220.0ms (1.8%)

localize14.0ms (0.1%)

series557.0ms (4.6%)

rewrite41.0ms (0.3%)

simplify151.0ms (1.3%)

prune423.0ms (3.5%)

localize22.0ms (0.2%)

series151.0ms (1.3%)

rewrite77.0ms (0.6%)

simplify204.0ms (1.7%)

prune329.0ms (2.7%)

localize20.0ms (0.2%)

series141.0ms (1.2%)

rewrite31.0ms (0.3%)

simplify141.0ms (1.2%)

prune360.0ms (3%)

regimes1.2s (9.6%)

bsearch254.0ms (2.1%)

simplify5.0ms (0%)

end259.0ms (2.2%)

Profiling