Details

analyze1.1s (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)

sample8.4s (53%)

Results

5.7s	3574×	body	1024	valid
1.4s	1460×	body	512	valid
878.0ms	2588×	body	128	valid
412.0ms	618×	body	256	valid
47.0ms	16×	body	2048	valid

Compiler

Compiled 106 to 82 computations (22.6% saved)

preprocess31.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

736×	`distribute-rgt-in_binary64`
734×	`distribute-lft-in_binary64`
515×	`fma-def_binary64`
127×	`distribute-lft-neg-out_binary64`
127×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	160
1	120	148
2	353	148
3	1524	146
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 52 to 40 computations (23.1% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

444×	`distribute-rgt-neg-out_binary64`
418×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`
350×	`unsub-neg_binary64`
270×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	80	74
2	211	74
3	809	73
4	3815	73

Stop Event

1×	node limit

Counts

1 → 2

prune9.0ms (0.1%)

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 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 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 (sqrt.f64 2) (*.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 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 298 to 221 computations (25.8% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1))
✓	0.7b	(/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3)
✓	1.0b	(-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3))
✓	1.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series15.0ms (0.1%)

Counts

4 → 32

Calls

12 calls:

2.0ms	(/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3)	x	-inf
2.0ms	(/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3)	x	inf
2.0ms	(/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3)	x	0
1.0ms	(*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1))	x	0
1.0ms	(*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1))	x	inf

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

191×	`add-sqr-sqrt_binary64`
185×	`add-cbrt-cube_binary64`
185×	`log1p-expm1-u_binary64`
185×	`expm1-log1p-u_binary64`
181×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	378	39

Stop Event

1×	node limit

Counts

4 → 126

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

743×	`sub-neg_binary64`
515×	`fma-def_binary64`
343×	`associate--r+_binary64`
326×	`cancel-sign-sub-inv_binary64`
322×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	644
1	261	606
2	954	579
3	4565	579

Stop Event

1×	node limit

Counts

158 → 161

prune388.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	153	8	161
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	154	9	163

Error

0.2b

Counts

163 → 9

Alt Table

Status	Error	Program
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (pow.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) 3))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 5) (cos.f64 x)) 3) (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 (.f64 (.f64 (sqrt.f64 5) (cos.f64 x)) (.f64 (sqrt.f64 5) (cos.f64 x))) (-.f64 (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (.f64 (*.f64 (sqrt.f64 5) (cos.f64 x)) (neg.f64 (cos.f64 x)))))) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (/.f64 1 (+.f64 (cos.f64 x) (cos.f64 y)))))) 2) (+.f64 (/.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 x)) (+.f64 (sqrt.f64 5) -1)) 3/2)) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2)) (.f64 (cbrt.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1))) 3/2)) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
▶	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 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)))))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 3)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.9b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1))) 3) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))

Compiler

Compiled 9597 to 6360 computations (33.7% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y))))
✓	0.3b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	1.0b	(-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3))
	1.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series355.0ms (2.2%)

Counts

2 → 48

Calls

12 calls:

87.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))	x	inf
64.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))	y	inf
64.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))	y	-inf
58.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))	x	-inf
25.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))	y	0

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

378×	`log1p-expm1-u_binary64`
378×	`expm1-log1p-u_binary64`
365×	`add-log-exp_binary64`
364×	`add-exp-log_binary64`
337×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	105
1	794	105

Stop Event

1×	node limit

Counts

2 → 29

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

420×	`fma-def_binary64`
371×	`associate-r_binary64`
294×	`associate-+r+_binary64`
258×	`fma-neg_binary64`
246×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	341	7143
1	1203	7029
2	4960	7029

Stop Event

1×	node limit

Counts

77 → 66

prune679.0ms (4.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	139	9	148
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Error

0.0b

Counts

157 → 13

Alt Table

Status	Error	Program
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (pow.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) 3))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3)))))
▶	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 5) (cos.f64 x)) 3) (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 (.f64 (.f64 (sqrt.f64 5) (cos.f64 x)) (.f64 (sqrt.f64 5) (cos.f64 x))) (-.f64 (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (.f64 (*.f64 (sqrt.f64 5) (cos.f64 x)) (neg.f64 (cos.f64 x)))))) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (.f64 (-.f64 (pow.f64 (cos.f64 x) 2) (pow.f64 (cos.f64 y) 2)) (/.f64 1 (+.f64 (cos.f64 x) (cos.f64 y)))))) 2) (+.f64 (/.f64 (.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3)))) 2)
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y)))))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (/.f64 1 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (.f64 (sqrt.f64 5) 3/2)) 3))))
	0.6b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3))))))
	0.4b	(pow.f64 (/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (.f64 (sqrt.f64 5) 3/2)) 3)) (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2)) -1)
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (.f64 (sqrt.f64 5) 3/2)) 3)))) 2) (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3)))))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))))) 1) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))

Compiler

Compiled 13639 to 9783 computations (28.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))
	0.3b	(.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y))))
✓	0.3b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))
	1.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series308.0ms (1.9%)

Counts

2 → 48

Calls

12 calls:

78.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))	y	inf
58.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))	y	-inf
54.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))	x	-inf
54.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))	x	inf
27.0ms	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))	y	0

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

390×	`log1p-expm1-u_binary64`
390×	`expm1-log1p-u_binary64`
377×	`add-log-exp_binary64`
376×	`add-exp-log_binary64`
350×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	92
1	830	92

Stop Event

1×	node limit

Counts

2 → 29

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

460×	`cancel-sign-sub-inv_binary64`
307×	`fma-def_binary64`
255×	`associate-r_binary64`
251×	`sub-neg_binary64`
212×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	277	6121
1	965	6105
2	3968	6105

Stop Event

1×	node limit

Counts

77 → 66

prune511.0ms (3.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	151	12	163

Error

0.0b

Counts

163 → 12

Alt Table

Status	Error	Program
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (pow.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) 3))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 5) (cos.f64 x)) 3) (pow.f64 (neg.f64 (cos.f64 x)) 3)) (+.f64 (.f64 (.f64 (sqrt.f64 5) (cos.f64 x)) (.f64 (sqrt.f64 5) (cos.f64 x))) (-.f64 (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (cos.f64 x))) (.f64 (*.f64 (sqrt.f64 5) (cos.f64 x)) (neg.f64 (cos.f64 x)))))) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
▶	0.4b	(pow.f64 (/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2)) -1)
	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 (sqrt.f64 2) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))))) 1) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (/.f64 1 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3))))
	0.6b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3))))))
	0.4b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))))
	0.4b	(pow.f64 (/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (.f64 (sqrt.f64 5) 3/2)) 3)) (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2)) -1)
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3)))) 2)
	1.2b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))) 2) (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y)))))) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))

Compiler

Compiled 13238 to 9564 computations (27.8% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))
✓	0.2b	(/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2))
✓	0.3b	(.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y))))
	1.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series1.1s (6.8%)

Counts

3 → 72

Calls

18 calls:

182.0ms	(/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2))	x	inf
180.0ms	(/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2))	y	inf
173.0ms	(/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2))	x	-inf
173.0ms	(/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2))	y	-inf
160.0ms	(/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2))	x	0

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

360×	`log1p-expm1-u_binary64`
360×	`expm1-log1p-u_binary64`
358×	`add-cbrt-cube_binary64`
350×	`add-log-exp_binary64`
349×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	126
1	751	126

Stop Event

1×	node limit

Counts

3 → 41

simplify209.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

808×	`associate-/r*_binary64`
320×	`*-commutative_binary64`
240×	`+-commutative_binary64`
227×	`fma-def_binary64`
202×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	799	17865
1	3177	16728

Stop Event

1×	node limit

Counts

113 → 94

prune687.0ms (4.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	149	11	160

Error

Counts

160 → 11

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2)))) 1) -1)
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))))) 1) 2) (+.f64 (.f64 (cos.f64 x) (/.f64 1 (.f64 1/6 (+.f64 (sqrt.f64 5) 1)))) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (/.f64 1 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3))))
	0.4b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (pow.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) 3))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.4b	(pow.f64 (/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)) (fma.f64 (sqrt.f64 2) (log.f64 (+.f64 1 (expm1.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y))))))) 2)) -1)
	0.6b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3))))))
	0.4b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))))
	0.4b	(pow.f64 (/.f64 (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (.f64 (sqrt.f64 5) 3/2)) 3)) (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2)) -1)
	0.5b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (cos.f64 x) (cos.f64 y))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (-.f64 9/2 (*.f64 (sqrt.f64 5) 3/2)) 3)))) 2)
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))) 2) (cbrt.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)) (.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 y) 1/16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (cos.f64 x) (fma.f64 1/6 (sqrt.f64 5) 1/6)) (fma.f64 (cos.f64 y) (/.f64 9 (+.f64 9/2 (sqrt.f64 45/4))) 3)))))

Compiler

Compiled 25125 to 18344 computations (27% saved)

regimes1.1s (6.8%)

Accuracy

Total 0.4b remaining (85.8%)

Threshold costs 0.4b (85.8%)

Counts

193 → 1

Compiler

Compiled 30899 to 23743 computations (23.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	75
1	59	75
2	83	75
3	93	75
4	98	75

Stop Event

1×

saturated

end397.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 706 to 533 computations (24.5% saved)

Details

analyze1.1s (7%)

sample8.4s (53%)

preprocess31.0ms (0.2%)

simplify23.0ms (0.1%)

prune9.0ms (0.1%)

localize29.0ms (0.2%)

series15.0ms (0.1%)

rewrite40.0ms (0.3%)

simplify41.0ms (0.3%)

prune388.0ms (2.5%)

localize30.0ms (0.2%)

series355.0ms (2.2%)

rewrite38.0ms (0.2%)

simplify129.0ms (0.8%)

prune679.0ms (4.3%)

localize30.0ms (0.2%)

series308.0ms (1.9%)

rewrite40.0ms (0.3%)

simplify123.0ms (0.8%)

prune511.0ms (3.2%)

localize31.0ms (0.2%)

series1.1s (6.8%)

rewrite43.0ms (0.3%)

simplify209.0ms (1.3%)

prune687.0ms (4.3%)

regimes1.1s (6.8%)

simplify4.0ms (0%)

end397.0ms (2.5%)

Profiling