Details

analyze1.1s (5.9%)

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)

sample8.7s (46.7%)

Results

5.8s	3571×	body	1024	valid
1.6s	1379×	body	512	valid
868.0ms	2682×	body	128	valid
376.0ms	607×	body	256	valid
50.0ms	17×	body	2048	valid

Compiler

Compiled 158 to 122 computations (22.8% saved)

simplify46.0ms (0.2%)

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
▶	0.4b	(/.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)))
	0.4b	(/.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)))))

Status

Error

Program

▶

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)))

0.4b

(/.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)))))

Compiler

Compiled 295 to 218 computations (26.1% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.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))
✓	1.1b	(-.f64 (cos.f64 x) (cos.f64 y))

series22.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

15.0ms	(*.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)

rewrite58.0ms (0.3%)

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:

11.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
9.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms	(-.f64 3 (sqrt.f64 5))
3.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify235.0ms (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

prune843.0ms (4.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	327	6	333
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	328	7	335

Error

0.1b

Counts

335 → 7

Alt Table

Status	Error	Program
	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 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (sqrt.f64 5))) 2/3)) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(/.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 (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 (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 (.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (cbrt.f64 (sin.f64 x)) (neg.f64 (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16)))))) (sqrt.f64 2)) (.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (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 (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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 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 21828 to 14069 computations (35.5% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
✓	1.1b	(fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))
✓	26.6b	(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

series2.3s (12.6%)

Counts

2 → 36

Calls

2 calls:

1.6s

(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

766.0ms

(fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms

(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (*.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
686×	`associate-l_binary64`
572×	`associate-r_binary64`
414×	`cancel-sign-sub-inv_binary64`
283×	`fma-neg_binary64`

Counts

56 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	523
1	152	458
2	433	411
3	1345	411
4	4407	411
5	4740	411
6	4866	411

prune520.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	173	7	180

Error

0.1b

Counts

180 → 7

Alt Table

Status	Error	Program
	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 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (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 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (+.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 (.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (cbrt.f64 (sin.f64 x)) (neg.f64 (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16)))))) (sqrt.f64 2)) (.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (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 (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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 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 17069 to 6913 computations (59.5% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(cbrt.f64 16)
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	1.1b	(-.f64 (cos.f64 x) (cos.f64 y))
✓	59.4b	(fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (*.f64 (cbrt.f64 16) (cbrt.f64 16)))))

series186.0ms (1%)

Counts

2 → 12

Calls

2 calls:

186.0ms	(fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (*.f64 (cbrt.f64 16) (cbrt.f64 16)))))
0.0ms	(cbrt.f64 16)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 23

Calls

2 calls:

1.0ms	(cbrt.f64 16)
0.0ms	(fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (*.f64 (cbrt.f64 16) (cbrt.f64 16)))))

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
650×	`div-sub_binary64`
399×	`times-frac_binary64`
288×	`distribute-rgt-in_binary64`
244×	`associate-/l*_binary64`

Counts

35 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	570
1	56	457
2	123	205
3	421	119
4	966	119
5	2321	119
6	4479	119
7	5075	119

prune1.2s (6.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	281	7	288

Error

0.1b

Counts

288 → 7

Alt Table

Status	Error	Program
	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 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (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 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (+.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 (.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (cbrt.f64 (sin.f64 x)) (neg.f64 (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16)))))) (sqrt.f64 2)) (.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (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 (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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 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 28909 to 20136 computations (30.3% saved)

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	1.1b	(fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))
	26.6b	(fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))

prune724.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	239	7	246

Error

0.1b

Counts

246 → 7

Alt Table

Status	Error	Program
	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 (sqrt.f64 5))) (/.f64 (+.f64 -1 (sqrt.f64 (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 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))))) (cbrt.f64 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (+.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 (.f64 (fma.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (cbrt.f64 (sin.f64 x)) (neg.f64 (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16)))))) (sqrt.f64 2)) (.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 y) (cbrt.f64 16))) (/.f64 1 (.f64 (cbrt.f64 16) (cbrt.f64 16))) (.f64 (/.f64 (sin.f64 y) (cbrt.f64 16)) (/.f64 1 (.f64 (cbrt.f64 16) (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 (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 (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))) (.f64 (cbrt.f64 (cos.f64 y)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (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 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (expm1.f64 (log1p.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 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 34330 to 9039 computations (73.7% saved)

regimes2.0s (10.9%)

Accuracy

Total 0.3b remaining (65.4%)

Threshold costs 0.3b (65.4%)

Counts

297 → 1

Compiler

Compiled 70517 to 42481 computations (39.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
11×	`sub-neg_binary64`
9×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	83
1	50	83
2	66	83
3	78	83
4	86	83
5	88	83
6	86	83

end293.0ms (1.6%)

Compiler: Compiled 641 to 409 computations (36.2% saved)

Details

analyze1.1s (5.9%)

sample8.7s (46.7%)

simplify46.0ms (0.2%)

prune7.0ms (0%)

localize28.0ms (0.2%)

series22.0ms (0.1%)

rewrite58.0ms (0.3%)

simplify235.0ms (1.3%)

prune843.0ms (4.5%)

localize41.0ms (0.2%)

series2.3s (12.6%)

rewrite2.0ms (0%)

simplify75.0ms (0.4%)

prune520.0ms (2.8%)

localize41.0ms (0.2%)

series186.0ms (1%)

rewrite2.0ms (0%)

simplify73.0ms (0.4%)

prune1.2s (6.4%)

localize50.0ms (0.3%)

prune724.0ms (3.9%)

regimes2.0s (10.9%)

simplify4.0ms (0%)

end293.0ms (1.6%)

Profiling