Details

analyze1.4s (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)

sample293.0ms (1.8%)

Algorithm

1×

intervals

Results

168.0ms	120×	body	1024	valid
32.0ms	37×	body	512	valid
19.0ms	81×	body	128	valid
9.0ms	18×	body	256	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify52.0ms (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
▶	0.4b	(/.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)))
	0.5b	(/.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)))))

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)))

0.5b

(/.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)))))

Compiler

Compiled 295 to 218 computations (26.1% saved)

localize33.0ms (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))
✓	2.4b	(-.f64 (cos.f64 x) (cos.f64 y))

series20.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

13.0ms	(*.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)

rewrite56.0ms (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:

12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
8.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
4.0ms	(-.f64 3 (sqrt.f64 5))
4.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify254.0ms (1.6%)

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

prune1.0s (6.2%)

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
	0.7b	(/.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 (pow.f64 (sqrt.f64 5) 3) (pow.f64 1 3)) (.f64 2/3 (+.f64 6 (sqrt.f64 5)))) (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)))
	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 (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 (.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 (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)))
	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))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.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))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.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)))

Compiler

Compiled 21942 to 14197 computations (35.3% saved)

localize35.0ms (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)
	2.4b	(-.f64 (cos.f64 x) (cos.f64 y))
✓	4.4b	(/.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)))

series186.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

186.0ms

(/.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)))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 29

Calls

1 calls:

20.0ms

(/.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)))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

491×	`associate-/l*_binary64`
360×	`fma-def_binary64`
320×	`times-frac_binary64`
270×	`div-sub_binary64`
242×	`distribute-rgt-in_binary64`

Counts

53 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	2097
1	381	1838
2	1219	1724
3	4585	1723
4	5537	1723

prune840.0ms (5.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	234	10	244

Error

0.1b

Counts

244 → 10

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.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 (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 (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 (sqrt.f64 5) 1) 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 (pow.f64 (sqrt.f64 5) 3) (pow.f64 1 3)) (.f64 2/3 (+.f64 6 (sqrt.f64 5)))) (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)))
	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)))
	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 (.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 (+.f64 -1 (sqrt.f64 5)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 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))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.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))) (fma.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (cbrt.f64 (cos.f64 x)) (neg.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)))

Compiler

Compiled 17210 to 10916 computations (36.6% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	2.4b	(-.f64 (cos.f64 x) (cos.f64 y))
✓	3.8b	(log.f64 (exp.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)))))
	4.4b	(/.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)))

series98.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

98.0ms

(log.f64 (exp.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)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`log-pow_binary64`
10×	`exp-prod_binary64`
6×	`*-un-lft-identity_binary64`
4×	`times-frac_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

1 → 24

Calls

1 calls:

6.0ms

(log.f64 (exp.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)))))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

622×	`times-frac_binary64`
591×	`cancel-sign-sub-inv_binary64`
502×	`fma-neg_binary64`
207×	`fma-def_binary64`
175×	`associate-r_binary64`

Counts

48 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	117	1738
1	263	1596
2	668	1498
3	2221	1194
4	5320	1194

prune844.0ms (5.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	245	3	248
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	247	11	258

Error

0.1b

Counts

258 → 11

Alt Table

Status	Error	Program
	0.5b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.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 1 (/.f64 2/3 (+.f64 -1 (sqrt.f64 5)))) (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)))
	0.7b	(/.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 (pow.f64 (sqrt.f64 5) 3) (pow.f64 1 3)) (.f64 2/3 (+.f64 6 (sqrt.f64 5)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.6b	(/.f64 (fma.f64 (.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.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))))) (cbrt.f64 (exp.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))))))) (log.f64 (cbrt.f64 (exp.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 (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 (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 (+.f64 -1 (sqrt.f64 5)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.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) (-.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 (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)))
	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)))))
	0.6b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) 1)) (sqrt.f64 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) 1)) (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))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.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)))

Compiler

Compiled 18433 to 11737 computations (36.3% saved)

localize33.0ms (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 3 (sqrt.f64 5))
✓	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))
	2.4b	(-.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)))

rewrite70.0ms (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:

38.0ms	(*.f64 (/.f64 1 (sqrt.f64 2/3)) (/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3)))
8.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) (sqrt.f64 2/3))

simplify184.0ms (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

prune983.0ms (6.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	308	0	308
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	308	11	319

Error

0.1b

Counts

319 → 11

Alt Table

Status	Error	Program
	0.5b	(/.f64 (fma.f64 (.f64 (log.f64 (exp.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 1 (/.f64 2/3 (+.f64 -1 (sqrt.f64 5)))) (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)))
	0.7b	(/.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 (pow.f64 (sqrt.f64 5) 3) (pow.f64 1 3)) (.f64 2/3 (+.f64 6 (sqrt.f64 5)))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.6b	(/.f64 (fma.f64 (.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.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))))) (cbrt.f64 (exp.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))))))) (log.f64 (cbrt.f64 (exp.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 (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 (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 (+.f64 -1 (sqrt.f64 5)) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.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) (-.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 (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)))
	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)))))
	0.6b	(/.f64 (fma.f64 (.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) 1)) (sqrt.f64 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) 1)) (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))) (log.f64 (/.f64 (exp.f64 (cos.f64 x)) (exp.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)))

Compiler

Compiled 19511 to 13804 computations (29.3% saved)

regimes1.5s (9.5%)

Accuracy

Total 0.3b remaining (74.1%)

Threshold costs 0.3b (74.1%)

Counts

250 → 1

Compiler

Compiled 44348 to 33610 computations (24.2% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-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	37	87
1	52	87
2	66	87
3	76	87
4	83	87
5	85	87
6	83	87

end1.0ms (0%)

Compiler: Compiled 56 to 44 computations (21.4% saved)

sample7.9s (49.1%)

Algorithm

1×

intervals

Results

5.0s	3485×	body	1024	valid
1.1s	1276×	body	512	valid
672.0ms	2617×	body	128	valid
327.0ms	607×	body	256	valid
41.0ms	15×	body	2048	valid

Compiler

Compiled 822 to 616 computations (25.1% saved)

Details

analyze1.4s (9%)

sample293.0ms (1.8%)

simplify52.0ms (0.3%)

prune7.0ms (0%)

localize33.0ms (0.2%)

series20.0ms (0.1%)

rewrite56.0ms (0.3%)

simplify254.0ms (1.6%)

prune1.0s (6.2%)

localize35.0ms (0.2%)

series186.0ms (1.2%)

rewrite22.0ms (0.1%)

simplify82.0ms (0.5%)

prune840.0ms (5.2%)

localize39.0ms (0.2%)

series98.0ms (0.6%)

rewrite9.0ms (0.1%)

simplify69.0ms (0.4%)

prune844.0ms (5.2%)

localize33.0ms (0.2%)

series0.0ms (0%)

rewrite70.0ms (0.4%)

simplify184.0ms (1.1%)

prune983.0ms (6.1%)

regimes1.5s (9.5%)

simplify5.0ms (0%)

end1.0ms (0%)

sample7.9s (49.1%)

Profiling