Details

analyze3.5s (17.3%)

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
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.9%	0.1%	11
0%	99.9%	0.1%	12
0%	99.9%	0.1%	13
0%	99.9%	0.1%	14

Compiler

Compiled 28 to 23 computations (17.9% saved)

sample4.7s (23.5%)

Results

2.3s	1992×	body	1024	valid
1.2s	4632×	body	128	valid
787.0ms	1094×	body	512	valid
262.0ms	535×	body	256	valid
11.0ms	4×	body	8192	exit
11.0ms	3×	body	2048	valid
0.0ms	2×	body	128	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 55 to 45 computations (18.2% saved)

simplify81.0ms (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

5.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.1b	(.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)

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 (cos.f64 (/.f64 K 2)) (.f64 J 2))
✓	0.1b	(.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))
✓	4.8b	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))

series206.0ms (1%)

Counts

4 → 120

Calls

4 calls:

137.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
46.0ms	(/.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:

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))

simplify178.0ms (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

prune221.0ms (1.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	6	191

Error

0.0b

Counts

191 → 6

Alt Table

Status	Error	Program
	47.3b	(neg.f64 U)
	33.6b	(.f64 (sqrt.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)))))) (sqrt.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)))))))
	48.9b	U
	20.9b	(.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)))))
	6.2b	(.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)))))
▶	5.6b	(.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))))))

Compiler

Compiled 6628 to 4967 computations (25.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))))))
✓	0.6b	(.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)))))))
✓	5.0b	(cbrt.f64 (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))

series3.5s (17.2%)

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	(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))))))
135.0ms	(.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))))))

rewrite52.0ms (0.3%)

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:

12.0ms	(.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))))))
12.0ms	(.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)))))))
4.0ms	(.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)))))

simplify306.0ms (1.5%)

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 (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	468	0	468
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	468	6	474

Error

0.0b

Counts

474 → 6

Alt Table

Status	Error	Program
	47.3b	(neg.f64 U)
	33.6b	(.f64 (sqrt.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)))))) (sqrt.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)))))))
	48.9b	U
	20.9b	(.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)))))
▶	6.2b	(.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)))))
✓	5.6b	(.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))))))

Compiler

Compiled 37807 to 29295 computations (22.5% 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))))
✓	4.8b	(.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)))))

series1.7s (8.6%)

Counts

4 → 108

Calls

4 calls:

903.0ms	(.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (cbrt.f64 (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2)))))
542.0ms	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
194.0ms	(.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)))))
83.0ms	(.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)))))

rewrite37.0ms (0.2%)

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:

12.0ms	(.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)))))
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)))))
5.0ms	(.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))))

simplify149.0ms (0.7%)

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	5403
3	5423	5403

prune387.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	282	5	287
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	283	10	293

Error

0.0b

Counts

293 → 10

Alt Table

Status	Error	Program
	6.6b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))))) (.f64 (cbrt.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)))))
	48.9b	U
	6.3b	(.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))))) (.f64 (cbrt.f64 -2) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	6.6b	(.f64 (.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))))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (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)))))
	47.3b	(neg.f64 U)
	33.6b	(.f64 (sqrt.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)))))) (sqrt.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)))))))
	6.3b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (.f64 -2 J))) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (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)))))
▶	6.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (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)))))
	20.9b	(.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)))))
✓	5.6b	(.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))))))

Compiler

Compiled 14359 to 11281 computations (21.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (*.f64 -2 J)) (cbrt.f64 (cos.f64 (/.f64 K 2)))))
	0.6b	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
✓	0.6b	(cbrt.f64 (*.f64 -2 J))
✓	4.8b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (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)))))

series1.1s (5.6%)

Counts

3 → 72

Calls

3 calls:

896.0ms

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

197.0ms

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

41.0ms

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

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
22×	`pow1_binary64`
17×	`pow-prod-down_binary64`
13×	`cbrt-unprod_binary64`
13×	`prod-exp_binary64`

Counts

3 → 62

Calls

3 calls:

12.0ms

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

6.0ms

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

2.0ms

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

simplify156.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary64`
394×	`associate-l_binary64`
337×	`associate-r_binary64`
268×	`fma-neg_binary64`
252×	`unswap-sqr_binary64`

Counts

134 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	6083
1	827	5326
2	3192	5266
3	4967	5258
4	4974	5258

prune286.0ms (1.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	215	4	219
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	218	11	229

Error

0.0b

Counts

229 → 11

Alt Table

Status	Error	Program
	48.9b	U
	6.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 -2) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	6.3b	(.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))))) (.f64 (cbrt.f64 -2) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	21.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (cos.f64 (/.f64 K 2))))) (.f64 (cbrt.f64 -2) (.f64 (cbrt.f64 J) (pow.f64 (cos.f64 (.f64 1/2 K)) 1/3)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	6.6b	(.f64 (.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))))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (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)))))
	47.3b	(neg.f64 U)
✓	6.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2)))) (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (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)))))
	20.9b	(.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)))))
	6.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (.f64 (cbrt.f64 (.f64 -2 J)) (cbrt.f64 (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)))))
✓	5.6b	(.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))))))
	29.6b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))) (.f64 (.f64 J -2) (pow.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) 3)))) (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)))))

Compiler

Compiled 11661 to 9174 computations (21.3% saved)

regimes2.0s (10.1%)

Accuracy

Total 7.8b remaining (99.6%)

Threshold costs 0b (0%)

Counts

226 → 1

Compiler

Compiled 49310 to 39420 computations (20.1% 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

end362.0ms (1.8%)

Compiler: Compiled 491 to 395 computations (19.6% saved)

Details

analyze3.5s (17.3%)

sample4.7s (23.5%)

simplify81.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series206.0ms (1%)

rewrite24.0ms (0.1%)

simplify178.0ms (0.9%)

prune221.0ms (1.1%)

localize16.0ms (0.1%)

series3.5s (17.2%)

rewrite52.0ms (0.3%)

simplify306.0ms (1.5%)

prune1.0s (5.1%)

localize16.0ms (0.1%)

series1.7s (8.6%)

rewrite37.0ms (0.2%)

simplify149.0ms (0.7%)

prune387.0ms (1.9%)

localize20.0ms (0.1%)

series1.1s (5.6%)

rewrite26.0ms (0.1%)

simplify156.0ms (0.8%)

prune286.0ms (1.4%)

regimes2.0s (10.1%)

simplify3.0ms (0%)

end362.0ms (1.8%)

Profiling