Details

analyze1.2s (6.3%)

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
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 53 to 41 computations (22.6% saved)

sample295.0ms (1.6%)

Algorithm

1×

intervals

Results

161.0ms	119×	body	1024	valid
35.0ms	41×	body	512	valid
18.0ms	73×	body	128	valid
14.0ms	23×	body	256	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

770×	`neg-mul-1_binary64`
444×	`distribute-rgt-neg-out_binary64`
438×	`distribute-lft-neg-out_binary64`
418×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	80	74
2	201	74
3	626	73
4	2261	71
5	4460	71
6	5422	71

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
▶	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Status

Error

Program

0.5b

(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))

▶

0.4b

(/.f64 (fma.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 295 to 218 computations (26.1% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
✓	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
✓	1.0b	(-.f64 3 (sqrt.f64 5))
✓	2.3b	(-.f64 (cos.f64 x) (cos.f64 y))

series26.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

19.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
7.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))
0.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)

rewrite66.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`add-sqr-sqrt_binary64`
154×	`*-un-lft-identity_binary64`
128×	`add-cube-cbrt_binary64`
106×	`times-frac_binary64`
105×	`prod-diff_binary64`

Counts

4 → 273

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
7.0ms	(-.f64 3 (sqrt.f64 5))
7.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify251.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

387×	`cancel-sign-sub-inv_binary64`
375×	`fma-neg_binary64`
336×	`associate-l_binary64`
316×	`associate-r_binary64`
280×	`*-commutative_binary64`

Counts

305 → 333

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	594	8679
1	1199	6233
2	3223	5425
3	4633	5425
4	4981	5425
5	4696	5425

prune1.3s (7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	325	8	333
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	326	9	335

Error

0.1b

Counts

335 → 9

Alt Table

Status	Error	Program
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	0.9b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (.f64 (cbrt.f64 (+.f64 -1 (sqrt.f64 5))) (cbrt.f64 (+.f64 -1 (sqrt.f64 5)))) (/.f64 (cbrt.f64 (+.f64 -1 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
▶	0.4b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 (fma.f64 1 3 (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 5)) (sqrt.f64 (sqrt.f64 5))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5)) (*.f64 (sqrt.f64 (sqrt.f64 5)) (sqrt.f64 (sqrt.f64 5)))))) 3)))
	1.1b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 (-.f64 (sqrt.f64 5) 1))) (sqrt.f64 2/3)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.9b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))

Compiler

Compiled 21978 to 14233 computations (35.2% saved)

localize80.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
	1.0b	(-.f64 3 (sqrt.f64 5))
✓	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
	2.3b	(-.f64 (cos.f64 x) (cos.f64 y))

series0.0ms (0%)

Counts

2 → 0

Calls

2 calls:

0.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
0.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))

rewrite69.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`add-sqr-sqrt_binary64`
172×	`times-frac_binary64`
146×	`*-un-lft-identity_binary64`
141×	`sqrt-prod_binary64`
75×	`add-cube-cbrt_binary64`

Counts

2 → 233

Calls

2 calls:

32.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
10.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))

simplify208.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

633×	`times-frac_binary64`
528×	`cancel-sign-sub-inv_binary64`
496×	`associate-/l*_binary64`
318×	`sub-neg_binary64`
318×	`fma-def_binary64`

Counts

233 → 212

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	5163
1	375	4567
2	1216	4565
3	3122	4503
4	4095	4447
5	5281	4447

prune876.0ms (4.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	309	8	317

Error

0.1b

Counts

317 → 8

Alt Table

Status	Error	Program
	0.9b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 3 (.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5))))) 3)))
▶	0.3b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	1.1b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 (-.f64 (sqrt.f64 5) 1))) (sqrt.f64 2/3)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (+.f64 (fma.f64 1 3 (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 5)) (sqrt.f64 (sqrt.f64 5))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 5))) (sqrt.f64 (sqrt.f64 5)) (*.f64 (sqrt.f64 (sqrt.f64 5)) (sqrt.f64 (sqrt.f64 5)))))) 3)))
	0.9b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 19734 to 13993 computations (29.1% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
	1.0b	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
	2.3b	(-.f64 (cos.f64 x) (cos.f64 y))

prune1.2s (6.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	420	4	424
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	424	8	432

Error

0.1b

Counts

432 → 8

Alt Table

Status	Error	Program
	0.7b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (cbrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	1.1b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 (-.f64 (sqrt.f64 5) 1))) (sqrt.f64 2/3)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
▶	0.3b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.9b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.3b	(/.f64 (fma.f64 (.f64 (/.f64 (.f64 (sqrt.f64 2) (-.f64 (.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 y) 16)) 6))) (+.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 1 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))

Compiler

Compiled 30165 to 20885 computations (30.8% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
	2.3b	(-.f64 (cos.f64 x) (cos.f64 y))
✓	3.5b	(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))))

series16.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

16.0ms

(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))))

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`log-prod_binary64`
106×	`exp-sum_binary64`
84×	`*-un-lft-identity_binary64`
84×	`add-sqr-sqrt_binary64`
84×	`add-cube-cbrt_binary64`

Counts

1 → 122

Calls

1 calls:

13.0ms

(log.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))))

simplify141.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-def_binary64`
442×	`exp-prod_binary64`
410×	`associate-/l*_binary64`
348×	`log-pow_binary64`
334×	`fma-neg_binary64`

Counts

146 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	582	5236
1	903	3812
2	1684	2529
3	4415	2529
4	4661	2529

prune1.3s (6.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	411	4	415
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	413	10	423

Error

0.1b

Counts

423 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (.f64 (-.f64 (sqrt.f64 5) 1) (/.f64 1 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (cbrt.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))))) (log.f64 (cbrt.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.8b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (pow.f64 (sqrt.f64 (sqrt.f64 2/3)) 3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	1.1b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (cbrt.f64 (-.f64 (sqrt.f64 5) 1))) (sqrt.f64 2/3)) (/.f64 (cbrt.f64 (-.f64 (sqrt.f64 5) 1)) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.7b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) (.f64 (cbrt.f64 (sqrt.f64 2/3)) (cbrt.f64 (sqrt.f64 2/3)))) (cbrt.f64 (sqrt.f64 2/3)))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.4b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 (sqrt.f64 2) (sin.f64 x)) (.f64 (sqrt.f64 2) (neg.f64 (/.f64 (sin.f64 y) (pow.f64 (cbrt.f64 16) 3))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.3b	(/.f64 (fma.f64 (.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 (sqrt.f64 2) (fma.f64 -1/16 (sin.f64 y) (sin.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (sqrt.f64 2) (fma.f64 -1/16 (sin.f64 y) (sin.f64 x))))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.3b	(/.f64 (fma.f64 (.f64 (/.f64 (.f64 (sqrt.f64 2) (-.f64 (.f64 (sin.f64 x) (sin.f64 x)) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 y) 16)) 6))) (+.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (*.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.3b	(/.f64 (fma.f64 (.f64 (+.f64 (log.f64 (exp.f64 (.f64 (sin.f64 x) (sqrt.f64 2)))) (log.f64 (exp.f64 (.f64 (.f64 (neg.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 (sin.f64 y))) (.f64 (cbrt.f64 16) (cbrt.f64 16)))) (/.f64 (cbrt.f64 (sin.f64 y)) (cbrt.f64 16))) (sqrt.f64 2))))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))

Compiler

Compiled 30219 to 21212 computations (29.8% saved)

regimes3.1s (16.8%)

Accuracy

Total 0.3b remaining (71.7%)

Threshold costs 0.3b (71.7%)

Counts

447 → 1

Compiler

Compiled 83435 to 64564 computations (22.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	93
1	56	93
2	70	93
3	80	93
4	87	93
5	89	93
6	87	93

end1.0ms (0%)

Compiler: Compiled 60 to 48 computations (20% saved)

sample8.4s (44.8%)

Algorithm

1×

intervals

Results

5.2s	3630×	body	1024	valid
1.2s	1344×	body	512	valid
641.0ms	2421×	body	128	valid
373.0ms	586×	body	256	valid
55.0ms	19×	body	2048	valid

Compiler

Compiled 780 to 600 computations (23.1% saved)

Details

analyze1.2s (6.3%)

sample295.0ms (1.6%)

simplify50.0ms (0.3%)

prune7.0ms (0%)

localize31.0ms (0.2%)

series26.0ms (0.1%)

rewrite66.0ms (0.4%)

simplify251.0ms (1.3%)

prune1.3s (7%)

localize80.0ms (0.4%)

series0.0ms (0%)

rewrite69.0ms (0.4%)

simplify208.0ms (1.1%)

prune876.0ms (4.7%)

localize40.0ms (0.2%)

prune1.2s (6.3%)

localize37.0ms (0.2%)

series16.0ms (0.1%)

rewrite43.0ms (0.2%)

simplify141.0ms (0.8%)

prune1.3s (6.9%)

regimes3.1s (16.8%)

simplify5.0ms (0%)

end1.0ms (0%)

sample8.4s (44.8%)

Profiling