Details

analyze1.6s (8.7%)

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)

sample8.8s (46%)

Results

6.0s	3635×	body	1024	valid
1.4s	1430×	body	512	valid
833.0ms	2547×	body	128	valid
445.0ms	624×	body	256	valid
65.0ms	20×	body	2048	valid

Compiler

Compiled 158 to 122 computations (22.8% 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

prune9.0ms (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
	0.6b	(/.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)))))
▶	0.5b	(/.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 3 (sqrt.f64 5))) 3)))

Status

Error

Program

0.6b

(/.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)))))

▶

0.5b

(/.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 3 (sqrt.f64 5))) 3)))

Compiler

Compiled 295 to 218 computations (26.1% saved)

localize28.0ms (0.1%)

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))
✓	1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

series23.0ms (0.1%)

Counts

4 → 32

Calls

4 calls:

16.0ms	(*.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)

rewrite71.0ms (0.4%)

Algorithm

2×	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 → 81

Calls

4 calls:

68.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
68.0ms	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
68.0ms	(-.f64 3 (sqrt.f64 5))
68.0ms	(-.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
0	0	0
1	0	0

simplify64.0ms (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

113 → 111

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

prune331.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Error

0.2b

Counts

113 → 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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 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 (+.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)))))
	0.7b	(/.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 (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)))
	27.4b	(/.f64 (fma.f64 (.f64 (.f64 -1/16 (.f64 (sin.f64 y) (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)))
	0.5b	(/.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 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (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)))
	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) (/.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)))
	0.7b	(/.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) (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)))
	10.7b	(/.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 (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 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))

Compiler

Compiled 6651 to 4428 computations (33.4% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

series25.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

25.0ms

(pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)

rewrite54.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

582×	`prod-diff_binary64`
411×	`log-prod_binary64`
265×	`fma-def_binary64`
167×	`expm1-udef_binary64`
167×	`log1p-udef_binary64`

Counts

1 → 37

Calls

1 calls:

53.0ms

(pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	181	11
2	2279	11
3	5212	11
0	0	0
1	0	0

simplify39.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

744×	`associate--r+_binary64`
636×	`associate--l+_binary64`
342×	`associate-l_binary64`
326×	`associate-r_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

45 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	573
1	383	533
2	1454	516
3	5627	516

prune564.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	125	6	131
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	129	12	141

Error

0.2b

Counts

141 → 12

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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))
	0.8b	(/.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))) (cbrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))))) 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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 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)))
	10.7b	(/.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 (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 (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)))
	27.4b	(/.f64 (fma.f64 (.f64 (.f64 -1/16 (.f64 (sin.f64 y) (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)))
▶	0.5b	(/.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))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 3)) 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)))
	9.9b	(/.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))) (cbrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))) 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)))
	1.0b	(/.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))) (cbrt.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))) (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))))) 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 3 (sqrt.f64 5))) 3)))
	0.6b	(/.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)))))
	0.7b	(/.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) (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)))

Compiler

Compiled 9152 to 6119 computations (33.1% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 3)
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
✓	1.8b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y)))

series1.4s (7.3%)

Counts

2 → 48

Calls

2 calls:

713.0ms	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y)))
686.0ms	(pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 3)

rewrite93.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

854×	`log1p-expm1-u_binary64`
854×	`expm1-log1p-u_binary64`
224×	`prod-diff_binary64`
133×	`egg-rr`
114×	`add-sqr-sqrt_binary64`

Counts

2 → 133

Calls

2 calls:

89.0ms	(pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 3)
89.0ms	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	243	19
2	2262	19
3	5464	19
0	0	0
1	0	0

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

705×	`associate--l+_binary64`
379×	`associate-l_binary64`
368×	`associate-r_binary64`
296×	`cancel-sign-sub-inv_binary64`
220×	`fma-def_binary64`

Counts

181 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1021
1	458	969
2	1730	953
3	5162	953

prune547.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	199	12	211

Error

0.2b

Counts

211 → 12

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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))
	0.8b	(/.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))) (cbrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))))) 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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 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)))
	10.7b	(/.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 (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 (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)))
	27.4b	(/.f64 (fma.f64 (.f64 (.f64 -1/16 (.f64 (sin.f64 y) (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)))
✓	0.5b	(/.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))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 3)) 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)))
	9.9b	(/.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))) (cbrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))) 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)))
	1.0b	(/.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))) (cbrt.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))) (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))))) 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 3 (sqrt.f64 5))) 3)))
	0.6b	(/.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)))))
	0.7b	(/.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) (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)))

Compiler

Compiled 14348 to 9072 computations (36.8% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) 3)
	1.0b	(/.f64 (-.f64 (sqrt.f64 5) 1) 2/3)
	1.0b	(-.f64 3 (sqrt.f64 5))
	1.8b	(-.f64 (cos.f64 x) (cos.f64 y))

series1.2s (6.3%)

Counts

1 → 24

Calls

1 calls:

1.2s	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) 3)

rewrite82.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

538×	`prod-diff_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
131×	`log1p-expm1-u_binary64`
131×	`expm1-log1p-u_binary64`

Counts

1 → 41

Calls

1 calls:

80.0ms

(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	284	16
2	3206	16
3	4823	16
0	0	0
1	0	0

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-neg_binary64`
634×	`distribute-rgt-neg-in_binary64`
369×	`sub-neg_binary64`
261×	`distribute-lft-neg-in_binary64`
258×	`associate-r_binary64`

Counts

65 → 58

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	508
1	160	476
2	505	402
3	1796	392
4	3992	392
5	5058	392

prune1.2s (6.1%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	136	14	150

Error

0.2b

Counts

150 → 14

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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 2) (fma.f64 (cos.f64 x) (/.f64 (-.f64 (sqrt.f64 5) 1) 2/3) (fma.f64 (cos.f64 y) (*.f64 3/2 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5))))) 3)))
	0.8b	(/.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))) (cbrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))))) 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))) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)) 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)))
	10.7b	(/.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 (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 (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (cbrt.f64 2)) (cbrt.f64 (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)))
	0.7b	(/.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 (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)))
	27.4b	(/.f64 (fma.f64 (.f64 (.f64 -1/16 (.f64 (sin.f64 y) (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)))
✓	0.5b	(/.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))) (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (cos.f64 y))) 3)) 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)))
	9.9b	(/.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))) (cbrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))) 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)))
	1.0b	(/.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))) (cbrt.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))) (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (-.f64 (cos.f64 x) (cos.f64 y)) 3)))))) 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 3 (sqrt.f64 5))) 3)))
	0.6b	(/.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)))))
	0.7b	(/.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) (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)))
	0.5b	(/.f64 (fma.f64 (.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (-.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 8263 to 5537 computations (33% saved)

regimes1.5s (7.7%)

Accuracy

Total 0.3b remaining (66%)

Threshold costs 0.3b (66%)

Counts

127 → 1

Compiler

Compiled 19916 to 15013 computations (24.6% saved)

simplify9.0ms (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	35	81
1	51	81
2	68	81
3	80	81
4	88	81
5	90	81
6	88	81

end1.1s (5.9%)

Compiler: Compiled 866 to 658 computations (24% saved)

Details

analyze1.6s (8.7%)

sample8.8s (46%)

simplify50.0ms (0.3%)

prune9.0ms (0%)

localize28.0ms (0.1%)

series23.0ms (0.1%)

rewrite71.0ms (0.4%)

simplify64.0ms (0.3%)

prune331.0ms (1.7%)

localize35.0ms (0.2%)

series25.0ms (0.1%)

rewrite54.0ms (0.3%)

simplify39.0ms (0.2%)

prune564.0ms (3%)

localize42.0ms (0.2%)

series1.4s (7.3%)

rewrite93.0ms (0.5%)

simplify90.0ms (0.5%)

prune547.0ms (2.9%)

localize37.0ms (0.2%)

series1.2s (6.3%)

rewrite82.0ms (0.4%)

simplify85.0ms (0.4%)

prune1.2s (6.1%)

regimes1.5s (7.7%)

simplify9.0ms (0%)

end1.1s (5.9%)

Profiling