Details

analyze2.6s (19.5%)

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)

sample214.0ms (1.6%)

Algorithm

1×

intervals

Results

48.0ms	56×	body	1024	valid
21.0ms	41×	body	512	valid
20.0ms	139×	body	128	valid
7.0ms	20×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 58 to 48 computations (17.2% saved)

simplify81.0ms (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

prune10.0ms (0.1%)

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)

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)))
✓	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)))))

series204.0ms (1.5%)

Counts

4 → 120

Calls

4 calls:

131.0ms	(.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (*.f64 J 2)))))
50.0ms	(/.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))

rewrite30.0ms (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))

simplify175.0ms (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

prune188.0ms (1.4%)

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
✓	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)))))
	35.5b	(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))
	35.4b	(.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)))))))
	48.1b	(neg.f64 U)
	24.7b	(.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)))))
	44.8b	U
▶	10.2b	(.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)))))

Compiler

Compiled 6592 to 4936 computations (25.1% saved)

localize15.0ms (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)))))

series1.7s (12.5%)

Counts

4 → 108

Calls

4 calls:

865.0ms	(.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))))
197.0ms	(.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)))))
78.0ms	(.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 (0.3%)

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)))))
7.0ms	(.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)))))
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))))

simplify135.0ms (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	5403
3	5423	5403

prune336.0ms (2.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	284	3	287
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	285	9	294

Error

0.0b

Counts

294 → 9

Alt Table

Status	Error	Program
	35.4b	(.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)))))))
	48.1b	(neg.f64 U)
	24.7b	(.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)))))
	44.8b	U
▶	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))
✓	10.2b	(.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)))))
	11.0b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) 6) (cbrt.f64 (.f64 J -2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
	10.3b	(.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)))))

Compiler

Compiled 14087 to 11062 computations (21.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (.f64 (*.f64 -2 J) (cos.f64 (/.f64 K 2))))))
✓	0.5b	(cbrt.f64 (*.f64 -2 J))
	0.6b	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
✓	8.5b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))

series1.1s (8%)

Counts

3 → 72

Calls

3 calls:

835.0ms

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

195.0ms

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

40.0ms

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

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

10.0ms

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

2.0ms

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

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary64`
420×	`associate-l_binary64`
361×	`associate-r_binary64`
254×	`unswap-sqr_binary64`
250×	`fma-neg_binary64`

Counts

131 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	6114
1	832	5288
2	3230	5230
3	4971	5230

prune281.0ms (2.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	211	10	221

Error

Counts

221 → 10

Alt Table

Status	Error	Program
	10.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))) (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))
	35.4b	(.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)))))))
	48.1b	(neg.f64 U)
	24.7b	(.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)))))
	44.8b	U
✓	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))
✓	10.2b	(.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)))))
	11.0b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) 6) (cbrt.f64 (.f64 J -2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
▶	10.3b	(.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)))))

Compiler

Compiled 11664 to 9177 computations (21.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (.f64 (.f64 -2 J) (cos.f64 (/.f64 K 2))))
✓	0.7b	(cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))
✓	1.0b	(cbrt.f64 -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))))) (.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)))))

series721.0ms (5.4%)

Counts

3 → 60

Calls

3 calls:

485.0ms

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

236.0ms

(*.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))))) (*.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)))))

0.0ms

(cbrt.f64 -2)

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64`
21×	`pow1_binary64`
13×	`cbrt-unprod_binary64`
13×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`

Counts

3 → 53

Calls

3 calls:

11.0ms

(*.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))))) (*.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)))))

5.0ms

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

1.0ms

(cbrt.f64 -2)

simplify167.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-l_binary64`
386×	`associate-r_binary64`
299×	`fma-neg_binary64`
243×	`unswap-sqr_binary64`
233×	`*-commutative_binary64`

Counts

113 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	5495
1	875	4617
2	3763	4494
3	4923	4494
4	4992	4494
5	4957	4494

prune228.0ms (1.7%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	191	10	201

Error

Counts

201 → 10

Alt Table

Status	Error	Program
	10.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))) (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))
	35.4b	(.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)))))))
	48.1b	(neg.f64 U)
	24.7b	(.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)))))
	44.8b	U
✓	10.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 -2 J)) (.f64 (cbrt.f64 (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)))))
✓	10.2b	(.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)))))
	11.0b	(.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 J -2) (cos.f64 (/.f64 K 2))))) 6) (cbrt.f64 (.f64 J -2))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) (hypot.f64 1 (/.f64 U (.f64 (cos.f64 (/.f64 K 2)) (.f64 J 2)))))
✓	10.3b	(.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)))))

Compiler

Compiled 10405 to 8200 computations (21.2% saved)

regimes693.0ms (5.2%)

Accuracy

Total 10.9b remaining (99.5%)

Threshold costs 0b (0%)

Counts

61 → 3

Compiler

Compiled 12818 to 10302 computations (19.6% saved)

bsearch147.0ms (1.1%)

Steps

Iters	Range		Point
9	4.525130494824117e-100	3.277320134903157e-95	4.561103969082136e-100
8	-1.9668262760400221e-274	-1.3077053359973588e-278	-1.6296351963608448e-276

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	33	47
2	32	47

end1.0ms (0%)

Compiler: Compiled 34 to 26 computations (23.5% saved)

sample4.1s (30.9%)

Algorithm

1×

intervals

Results

2.0s	2033×	body	1024	valid
735.0ms	4486×	body	128	valid
566.0ms	967×	body	512	valid
243.0ms	512×	body	256	valid
3.0ms	2×	body	2048	valid
1.0ms	1×	body	1024	invalid
1.0ms	5×	body	128	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 490 to 393 computations (19.8% saved)

Details

analyze2.6s (19.5%)

sample214.0ms (1.6%)

simplify81.0ms (0.6%)

prune10.0ms (0.1%)

localize12.0ms (0.1%)

series204.0ms (1.5%)

rewrite30.0ms (0.2%)

simplify175.0ms (1.3%)

prune188.0ms (1.4%)

localize15.0ms (0.1%)

series1.7s (12.5%)

rewrite37.0ms (0.3%)

simplify135.0ms (1%)

prune336.0ms (2.5%)

localize21.0ms (0.2%)

series1.1s (8%)

rewrite22.0ms (0.2%)

simplify125.0ms (0.9%)

prune281.0ms (2.1%)

localize22.0ms (0.2%)

series721.0ms (5.4%)

rewrite22.0ms (0.2%)

simplify167.0ms (1.2%)

prune228.0ms (1.7%)

regimes693.0ms (5.2%)

bsearch147.0ms (1.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.1s (30.9%)

Profiling