Details

analyze1.3s (7.3%)

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)

sample8.9s (50%)

Results

6.0s	3670×	body	1024	valid
1.5s	1446×	body	512	valid
844.0ms	2534×	body	128	valid
420.0ms	585×	body	256	valid
62.0ms	21×	body	2048	valid

Compiler

Compiled 158 to 122 computations (22.8% saved)

simplify45.0ms (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

0.4b

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)

localize28.0ms (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))
✓	1.6b	(-.f64 (cos.f64 x) (cos.f64 y))

series21.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
6.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))
0.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)

rewrite65.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

241×	`add-sqr-sqrt_binary64`
237×	`log1p-expm1-u_binary64`
237×	`expm1-log1p-u_binary64`
232×	`add-log-exp_binary64`
231×	`add-exp-log_binary64`

Counts

4 → 85

Calls

4 calls:

64.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
64.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
64.0ms	(-.f64 3 (sqrt.f64 5))
64.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	39
1	500	39
2	4834	39
3	4819	39

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

819×	`sub-neg_binary64`
783×	`fma-neg_binary64`
287×	`fma-def_binary64`
277×	`associate-+l-_binary64`
267×	`distribute-rgt-neg-in_binary64`

Counts

117 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	605
1	233	566
2	699	510
3	2122	507
4	4683	507
5	5552	507

prune256.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Error

0.2b

Counts

117 → 8

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 (log.f64 (pow.f64 (exp.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 (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 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)) 2) (cbrt.f64 (/.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 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 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 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (+.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)))
	0.6b	(/.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) (pow.f64 (/.f64 2/3 (-.f64 (sqrt.f64 5) 1)) -1) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	35.7b	(/.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 (fma.f64 1/2 (.f64 y y) (cos.f64 x)) 1) 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 6649 to 4400 computations (33.8% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
	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)
	1.6b	(-.f64 (cos.f64 x) (cos.f64 y))

series28.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

28.0ms

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

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

281×	`expm1-udef_binary64`
281×	`log1p-udef_binary64`
186×	`fma-neg_binary64`
154×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`

Counts

1 → 22

Calls

1 calls:

62.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	314	29
2	4040	29
3	4977	29

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
439×	`distribute-rgt-neg-in_binary64`
414×	`distribute-lft-neg-in_binary64`
312×	`fma-def_binary64`
303×	`neg-mul-1_binary64`

Counts

46 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	751
1	186	714
2	569	636
3	2151	610
4	4770	610
5	4992	610

prune373.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	128	6	134
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	130	12	142

Error

0.1b

Counts

142 → 12

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 (log.f64 (pow.f64 (exp.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 (log.f64 (pow.f64 (pow.f64 (exp.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)))
▶	0.4b	(/.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 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (+.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)))
	0.4b	(/.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 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (+.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)))
	35.7b	(/.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 (fma.f64 1/2 (.f64 y y) (cos.f64 x)) 1) 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 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 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 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 (fma.f64 1 (cos.f64 x) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)))) 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)))
	0.4b	(/.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 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)) 2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.6b	(/.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) (pow.f64 (/.f64 2/3 (-.f64 (sqrt.f64 5) 1)) -1) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	4.7b	(/.f64 (fma.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))) 1) (-.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 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)) 2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 8409 to 5695 computations (32.3% saved)

localize32.0ms (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)))
✓	0.7b	(+.f64 (cos.f64 x) (cos.f64 y))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
✓	1.9b	(-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2))

series22.0ms (0.1%)

Counts

2 → 32

Calls

2 calls:

15.0ms	(-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2))
6.0ms	(+.f64 (cos.f64 x) (cos.f64 y))

rewrite97.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`fma-def_binary64`
244×	`fma-neg_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
178×	`log-pow_binary64`

Counts

2 → 151

Calls

2 calls:

94.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
94.0ms	(-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	229	22
2	2837	22
3	4988	22
4	4958	22

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

773×	`sub-neg_binary64`
422×	`fma-neg_binary64`
399×	`associate-+l+_binary64`
351×	`associate-+l-_binary64`
314×	`associate--l+_binary64`

Counts

183 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	428
1	187	412
2	546	401
3	1716	401
4	3693	401
5	4692	401
6	4961	401
7	4999	401
8	4987	401

prune979.0ms (5.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	232	13	245

Error

0.1b

Counts

245 → 13

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 (log.f64 (pow.f64 (exp.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 (log.f64 (pow.f64 (pow.f64 (exp.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)))
✓	0.4b	(/.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 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (+.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)))
	0.4b	(/.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 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (+.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)))
	8.1b	(/.f64 (fma.f64 (.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))))) 1) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (/.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (+.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 (cos.f64 x) (cos.f64 y)) 2) (fma.f64 (cos.f64 x) (.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)) 2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	35.7b	(/.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 (fma.f64 1/2 (.f64 y y) (cos.f64 x)) 1) 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 (log.f64 (.f64 (exp.f64 (neg.f64 (pow.f64 (cos.f64 y) 2))) (exp.f64 (pow.f64 (cos.f64 x) 2)))) (+.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 (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 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 4 (+.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 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)) 2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.6b	(/.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) (pow.f64 (/.f64 2/3 (-.f64 (sqrt.f64 5) 1)) -1) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	4.7b	(/.f64 (fma.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))) 1) (-.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)))

Compiler

Compiled 16522 to 10779 computations (34.8% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (fma.f64 (log.f64 (pow.f64 (pow.f64 (exp.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)))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	1.6b	(-.f64 (cos.f64 x) (cos.f64 y))
✓	3.0b	(log.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

series3.3s (18.7%)

Counts

2 → 48

Calls

2 calls:

1.8s

(/.f64 (fma.f64 (log.f64 (pow.f64 (pow.f64 (exp.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)))

1.5s

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

rewrite43.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

379×	`log1p-expm1-u_binary64`
379×	`expm1-log1p-u_binary64`
372×	`add-log-exp_binary64`
370×	`add-exp-log_binary64`
341×	`pow1_binary64`

Counts

2 → 39

Calls

2 calls:

41.0ms

(/.f64 (fma.f64 (log.f64 (pow.f64 (pow.f64 (exp.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)))

41.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	108
1	799	100
2	4836	100

simplify138.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

468×	`cancel-sign-sub-inv_binary64`
301×	`fma-def_binary64`
294×	`associate-r_binary64`
260×	`fma-neg_binary64`
247×	`associate-+r+_binary64`

Counts

87 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	282	6823
1	976	6710
2	3900	6708
3	5105	6708

prune422.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	8	3	11
Picked	0	1	1
Done	1	0	1
Total	140	10	150

Error

0.0b

Counts

150 → 10

Alt Table

Status	Error	Program
	0.5b	(/.f64 (-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (cos.f64 y) (sqrt.f64 2)))) (+.f64 2 (+.f64 (.f64 1/16 (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)))) (.f64 257/256 (.f64 (sin.f64 y) (.f64 (sqrt.f64 2) (.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (sqrt.f64 2) (cos.f64 x)))) (+.f64 (.f64 257/256 (.f64 (sin.f64 y) (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (sin.f64 x))))) (.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))))) (-.f64 (+.f64 3 (+.f64 (.f64 6 (/.f64 (cos.f64 y) (+.f64 3 (sqrt.f64 5)))) (.f64 3/2 (.f64 (cos.f64 x) (sqrt.f64 5))))) (.f64 3/2 (cos.f64 x))))
	0.6b	(/.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) (pow.f64 (/.f64 2/3 (-.f64 (sqrt.f64 5) 1)) -1) (fma.f64 (cos.f64 y) (*.f64 3/2 (-.f64 3 (sqrt.f64 5))) 3)))
	0.4b	(.f64 (fma.f64 (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (cos.f64 x) (cos.f64 y)) 2) (/.f64 1 (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3)) 3))))
	33.5b	(-.f64 (fma.f64 1/16 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)) (-.f64 (+.f64 3 (fma.f64 3/2 (.f64 (sqrt.f64 5) (cos.f64 x)) (/.f64 6 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (cos.f64 x)))) (fma.f64 257/256 (/.f64 (.f64 y (.f64 (sqrt.f64 2) (.f64 (sin.f64 x) (cos.f64 x)))) (-.f64 (+.f64 3 (fma.f64 3/2 (.f64 (sqrt.f64 5) (cos.f64 x)) (/.f64 6 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (cos.f64 x)))) (/.f64 2 (-.f64 (+.f64 3 (fma.f64 3/2 (.f64 (sqrt.f64 5) (cos.f64 x)) (/.f64 6 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (cos.f64 x)))))) (fma.f64 257/256 (/.f64 (.f64 y (.f64 (sqrt.f64 2) (sin.f64 x))) (-.f64 (+.f64 3 (fma.f64 3/2 (.f64 (sqrt.f64 5) (cos.f64 x)) (/.f64 6 (+.f64 3 (sqrt.f64 5))))) (.f64 3/2 (cos.f64 x)))) (.f64 1/16 (/.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (-.f64 (+.f64 3 (fma.f64 3/2 (.f64 (sqrt.f64 5) (cos.f64 x)) (/.f64 6 (+.f64 3 (sqrt.f64 5))))) (*.f64 3/2 (cos.f64 x)))))))
✓	0.4b	(/.f64 (fma.f64 (log.f64 (pow.f64 (pow.f64 (exp.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)))
	0.4b	(/.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 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)) 2) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3))) (fma.f64 (cos.f64 y) (.f64 3/2 (/.f64 4 (+.f64 3 (sqrt.f64 5)))) 3)))
	0.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 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 6 (+.f64 (sqrt.f64 5) 3)) 3)))))
	0.4b	(pow.f64 (/.f64 (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (/.f64 6 (+.f64 (sqrt.f64 5) 3)) 3)) (fma.f64 (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (cos.f64 x) (cos.f64 y)) 2)) -1)
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 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 6 (+.f64 (sqrt.f64 5) 3)) 3)))) 2)
	35.7b	(/.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 (fma.f64 1/2 (.f64 y y) (cos.f64 x)) 1) 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 11986 to 8660 computations (27.7% saved)

regimes914.0ms (5.1%)

Accuracy

Total 0.3b remaining (81.8%)

Threshold costs 0.3b (81.8%)

Counts

168 → 1

Compiler

Compiled 27950 to 21265 computations (23.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	79
1	50	79
2	64	79
3	74	79
4	81	79
5	83	79
6	81	79

end441.0ms (2.5%)

Compiler: Compiled 771 to 589 computations (23.6% saved)

Details

analyze1.3s (7.3%)

sample8.9s (50%)

simplify45.0ms (0.3%)

prune7.0ms (0%)

localize28.0ms (0.2%)

series21.0ms (0.1%)

rewrite65.0ms (0.4%)

simplify60.0ms (0.3%)

prune256.0ms (1.4%)

localize29.0ms (0.2%)

series28.0ms (0.2%)

rewrite63.0ms (0.4%)

simplify60.0ms (0.3%)

prune373.0ms (2.1%)

localize32.0ms (0.2%)

series22.0ms (0.1%)

rewrite97.0ms (0.5%)

simplify104.0ms (0.6%)

prune979.0ms (5.5%)

localize38.0ms (0.2%)

series3.3s (18.7%)

rewrite43.0ms (0.2%)

simplify138.0ms (0.8%)

prune422.0ms (2.4%)

regimes914.0ms (5.1%)

simplify5.0ms (0%)

end441.0ms (2.5%)

Profiling